Package 'MASS' reference manual

Title:	Support Functions and Datasets for Venables and Ripley's MASS
Description:	Functions and datasets to support Venables and Ripley, "Modern Applied Statistics with S" (4th edition, 2002).
Authors:	Brian Ripley [aut, cre, cph], Bill Venables [aut, cph], Douglas M. Bates [ctb], Kurt Hornik [trl] (partial port ca 1998), Albrecht Gebhardt [trl] (partial port ca 1998), David Firth [ctb] (support functions for polr)
Maintainer:	Brian Ripley <[email protected]>
License:	GPL-2 \| GPL-3
Version:	7.3-61
Built:	2024-06-13 08:44:38 UTC
Source:	CRAN

Determinations of Nickel Content

Description

A numeric vector of 31 determinations of nickel content (ppm) in a Canadian syenite rock.

Usage

abbey
abbey

Source

S. Abbey (1988) Geostandards Newsletter 12, 241.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Accidental Deaths in the US 1973-1978

Description

A regular time series giving the monthly totals of accidental deaths in the USA.

Usage

accdeaths
accdeaths

Details

The values for first six months of 1979 (p. 326) were 7798 7406 8363 8460 9217 9316.

Source

P. J. Brockwell and R. A. Davis (1991) Time Series: Theory and Methods. Springer, New York.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Try All One-Term Additions to a Model

Description

Try fitting all models that differ from the current model by adding a single term from those supplied, maintaining marginality.

This function is generic; there exist methods for classes lm and glm and the default method will work for many other classes.

Usage

addterm(object, ...)

## Default S3 method:
addterm(object, scope, scale = 0, test = c("none", "Chisq"),
        k = 2, sorted = FALSE, trace = FALSE, ...)
## S3 method for class 'lm'
addterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
        k = 2, sorted = FALSE, ...)
## S3 method for class 'glm'
addterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
        k = 2, sorted = FALSE, trace = FALSE, ...)
addterm(object, ...)

## Default S3 method:
addterm(object, scope, scale = 0, test = c("none", "Chisq"),
        k = 2, sorted = FALSE, trace = FALSE, ...)
## S3 method for class 'lm'
addterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
        k = 2, sorted = FALSE, ...)
## S3 method for class 'glm'
addterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
        k = 2, sorted = FALSE, trace = FALSE, ...)

Arguments

`object`	An object fitted by some model-fitting function.
`scope`	a formula specifying a maximal model which should include the current one. All additional terms in the maximal model with all marginal terms in the original model are tried.
`scale`	used in the definition of the AIC statistic for selecting the models, currently only for `lm`, `aov` and `glm` models. Specifying `scale` asserts that the residual standard error or dispersion is known.
`test`	should the results include a test statistic relative to the original model? The F test is only appropriate for `lm` and `aov` models, and perhaps for some over-dispersed `glm` models. The Chisq test can be an exact test (`lm` models with known scale) or a likelihood-ratio test depending on the method.
`k`	the multiple of the number of degrees of freedom used for the penalty. Only `k=2` gives the genuine AIC: `k = log(n)` is sometimes referred to as BIC or SBC.
`sorted`	should the results be sorted on the value of AIC?
`trace`	if `TRUE` additional information may be given on the fits as they are tried.
`...`	arguments passed to or from other methods.

Details

The definition of AIC is only up to an additive constant: when appropriate (lm models with specified scale) the constant is taken to be that used in Mallows' Cp statistic and the results are labelled accordingly.

Value

A table of class "anova" containing at least columns for the change in degrees of freedom and AIC (or Cp) for the models. Some methods will give further information, for example sums of squares, deviances, log-likelihoods and test statistics.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.lo <- aov(log(Days+2.5) ~ 1, quine)
addterm(quine.lo, quine.hi, test="F")

house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family=poisson,
                   data=housing)
addterm(house.glm0, ~. + Sat:(Infl+Type+Cont), test="Chisq")
house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
addterm(house.glm1, ~. + Sat:(Infl+Type+Cont)^2, test = "Chisq")
quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.lo <- aov(log(Days+2.5) ~ 1, quine)
addterm(quine.lo, quine.hi, test="F")

house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family=poisson,
                   data=housing)
addterm(house.glm0, ~. + Sat:(Infl+Type+Cont), test="Chisq")
house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
addterm(house.glm1, ~. + Sat:(Infl+Type+Cont)^2, test = "Chisq")

Australian AIDS Survival Data

Description

Data on patients diagnosed with AIDS in Australia before 1 July 1991.

Usage

Aids2
Aids2

Format

This data frame contains 2843 rows and the following columns:

state: Grouped state of origin: "NSW "includes ACT and "other" is WA, SA, NT and TAS.
sex: Sex of patient.
diag: (Julian) date of diagnosis.
death: (Julian) date of death or end of observation.
status: "A" (alive) or "D" (dead) at end of observation.
T.categ: Reported transmission category.
age: Age (years) at diagnosis.

Note

This data set has been slightly jittered as a condition of its release, to ensure patient confidentiality.

Source

Dr P. J. Solomon and the Australian National Centre in HIV Epidemiology and Clinical Research.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Brain and Body Weights for 28 Species

Description

Average brain and body weights for 28 species of land animals.

Usage

Animals
Animals

Format

body: body weight in kg.
brain: brain weight in g.

Note

The name Animals avoided conflicts with a system dataset animals in S-PLUS 4.5 and later.

Source

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley, p. 57.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Anorexia Data on Weight Change

Description

The anorexia data frame has 72 rows and 3 columns. Weight change data for young female anorexia patients.

Usage

anorexia
anorexia

Format

This data frame contains the following columns:

Treat: Factor of three levels: "Cont" (control), "CBT" (Cognitive Behavioural treatment) and "FT" (family treatment).
Prewt: Weight of patient before study period, in lbs.
Postwt: Weight of patient after study period, in lbs.

Source

Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, Data set 285 (p. 229)

(Note that the original source mistakenly says that weights are in kg.)

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Likelihood Ratio Tests for Negative Binomial GLMs

Description

Method function to perform sequential likelihood ratio tests for Negative Binomial generalized linear models.

Usage

## S3 method for class 'negbin'
anova(object, ..., test = "Chisq")
## S3 method for class 'negbin'
anova(object, ..., test = "Chisq")

Arguments

`object`	Fitted model object of class `"negbin"`, inheriting from classes `"glm"` and `"lm"`, specifying a Negative Binomial fitted GLM. Typically the output of `glm.nb()`.
`...`	Zero or more additional fitted model objects of class `"negbin"`. They should form a nested sequence of models, but need not be specified in any particular order.
`test`	Argument to match the `test` argument of `anova.glm`. Ignored (with a warning if changed) if a sequence of two or more Negative Binomial fitted model objects is specified, but possibly used if only one object is specified.

Details

This function is a method for the generic function anova() for class "negbin". It can be invoked by calling anova(x) for an object x of the appropriate class, or directly by calling anova.negbin(x) regardless of the class of the object.

Note

If only one fitted model object is specified, a sequential analysis of deviance table is given for the fitted model. The theta parameter is kept fixed. If more than one fitted model object is specified they must all be of class "negbin" and likelihood ratio tests are done of each model within the next. In this case theta is assumed to have been re-estimated for each model.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

m1 <- glm.nb(Days ~ Eth*Age*Lrn*Sex, quine, link = log)
m2 <- update(m1, . ~ . - Eth:Age:Lrn:Sex)
anova(m2, m1)
anova(m2)
m1 <- glm.nb(Days ~ Eth*Age*Lrn*Sex, quine, link = log)
m2 <- update(m1, . ~ . - Eth:Age:Lrn:Sex)
anova(m2, m1)
anova(m2)

Adaptive Numerical Integration

Description

Integrate a function of one variable over a finite range using a recursive adaptive method. This function is mainly for demonstration purposes.

Usage

area(f, a, b, ..., fa = f(a, ...), fb = f(b, ...),
     limit = 10, eps = 1e-05)
area(f, a, b, ..., fa = f(a, ...), fb = f(b, ...),
     limit = 10, eps = 1e-05)

Arguments

`f`	The integrand as an `S` function object. The variable of integration must be the first argument.
`a`	Lower limit of integration.
`b`	Upper limit of integration.
`...`	Additional arguments needed by the integrand.
`fa`	Function value at the lower limit.
`fb`	Function value at the upper limit.
`limit`	Limit on the depth to which recursion is allowed to go.
`eps`	Error tolerance to control the process.

Details

The method divides the interval in two and compares the values given by Simpson's rule and the trapezium rule. If these are within eps of each other the Simpson's rule result is given, otherwise the process is applied separately to each half of the interval and the results added together.

Value

The integral from a to b of f(x).

References

Venables, W. N. and Ripley, B. D. (1994) Modern Applied Statistics with S-Plus. Springer. pp. 105–110.

Examples

area(sin, 0, pi)  # integrate the sin function from 0 to pi.
area(sin, 0, pi)  # integrate the sin function from 0 to pi.

Presence of Bacteria after Drug Treatments

Description

Tests of the presence of the bacteria H. influenzae in children with otitis media in the Northern Territory of Australia.

Usage

bacteria
bacteria

Format

This data frame has 220 rows and the following columns:

y: presence or absence: a factor with levels n and y.
ap: active/placebo: a factor with levels a and p.
hilo: hi/low compliance: a factor with levels hi amd lo.
week: numeric: week of test.
ID: subject ID: a factor.
trt: a factor with levels placebo, drug and drug+, a re-coding of ap and hilo.

Details

Dr A. Leach tested the effects of a drug on 50 children with a history of otitis media in the Northern Territory of Australia. The children were randomized to the drug or the a placebo, and also to receive active encouragement to comply with taking the drug.

The presence of H. influenzae was checked at weeks 0, 2, 4, 6 and 11: 30 of the checks were missing and are not included in this data frame.

Source

Dr Amanda Leach via Mr James McBroom.

References

Menzies School of Health Research 1999–2000 Annual Report. p.20. https://www.menzies.edu.au/icms_docs/172302_2000_Annual_report.pdf.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

contrasts(bacteria$trt) <- structure(contr.sdif(3),
     dimnames = list(NULL, c("drug", "encourage")))
## fixed effects analyses
## IGNORE_RDIFF_BEGIN
summary(glm(y ~ trt * week, binomial, data = bacteria))
summary(glm(y ~ trt + week, binomial, data = bacteria))
summary(glm(y ~ trt + I(week > 2), binomial, data = bacteria))
## IGNORE_RDIFF_END

# conditional random-effects analysis
library(survival)
bacteria$Time <- rep(1, nrow(bacteria))
coxph(Surv(Time, unclass(y)) ~ week + strata(ID),
      data = bacteria, method = "exact")
coxph(Surv(Time, unclass(y)) ~ factor(week) + strata(ID),
      data = bacteria, method = "exact")
coxph(Surv(Time, unclass(y)) ~ I(week > 2) + strata(ID),
      data = bacteria, method = "exact")

# PQL glmm analysis
library(nlme)
## IGNORE_RDIFF_BEGIN
summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))
## IGNORE_RDIFF_END
contrasts(bacteria$trt) <- structure(contr.sdif(3),
     dimnames = list(NULL, c("drug", "encourage")))
## fixed effects analyses
## IGNORE_RDIFF_BEGIN
summary(glm(y ~ trt * week, binomial, data = bacteria))
summary(glm(y ~ trt + week, binomial, data = bacteria))
summary(glm(y ~ trt + I(week > 2), binomial, data = bacteria))
## IGNORE_RDIFF_END

# conditional random-effects analysis
library(survival)
bacteria$Time <- rep(1, nrow(bacteria))
coxph(Surv(Time, unclass(y)) ~ week + strata(ID),
      data = bacteria, method = "exact")
coxph(Surv(Time, unclass(y)) ~ factor(week) + strata(ID),
      data = bacteria, method = "exact")
coxph(Surv(Time, unclass(y)) ~ I(week > 2) + strata(ID),
      data = bacteria, method = "exact")

# PQL glmm analysis
library(nlme)
## IGNORE_RDIFF_BEGIN
summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))
## IGNORE_RDIFF_END

Bandwidth for density() via Normal Reference Distribution

Description

A well-supported rule-of-thumb for choosing the bandwidth of a Gaussian kernel density estimator.

Usage

bandwidth.nrd(x)
bandwidth.nrd(x)

Arguments

`x`	A data vector.

Value

A bandwidth on a scale suitable for the width argument of density.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer, equation (5.5) on page 130.

Examples

# The function is currently defined as
function(x)
{
    r <- quantile(x, c(0.25, 0.75))
    h <- (r[2] - r[1])/1.34
    4 * 1.06 * min(sqrt(var(x)), h) * length(x)^(-1/5)
}
# The function is currently defined as
function(x)
{
    r <- quantile(x, c(0.25, 0.75))
    h <- (r[2] - r[1])/1.34
    4 * 1.06 * min(sqrt(var(x)), h) * length(x)^(-1/5)
}

Biased Cross-Validation for Bandwidth Selection

Description

Uses biased cross-validation to select the bandwidth of a Gaussian kernel density estimator.

Usage

bcv(x, nb = 1000, lower, upper)
bcv(x, nb = 1000, lower, upper)

Arguments

`x`	a numeric vector
`nb`	number of bins to use.
`lower`, `upper`	Range over which to minimize. The default is almost always satisfactory.

Value

a bandwidth

References

Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

bcv(geyser$duration)
bcv(geyser$duration)

Body Temperature Series of Beaver 1

Description

Reynolds (1994) describes a small part of a study of the long-term temperature dynamics of beaver Castor canadensis in north-central Wisconsin. Body temperature was measured by telemetry every 10 minutes for four females, but data from a one period of less than a day for each of two animals is used there.

Usage

beav1
beav1

Format

The beav1 data frame has 114 rows and 4 columns. This data frame contains the following columns:

day: Day of observation (in days since the beginning of 1990), December 12–13.
time: Time of observation, in the form 0330 for 3.30am.
temp: Measured body temperature in degrees Celsius.
activ: Indicator of activity outside the retreat.

Note

The observation at 22:20 is missing.

Source

P. S. Reynolds (1994) Time-series analyses of beaver body temperatures. Chapter 11 of Lange, N., Ryan, L., Billard, L., Brillinger, D., Conquest, L. and Greenhouse, J. eds (1994) Case Studies in Biometry. New York: John Wiley and Sons.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

beav1 <- within(beav1,
               hours <- 24*(day-346) + trunc(time/100) + (time%%100)/60)
plot(beav1$hours, beav1$temp, type="l", xlab="time",
   ylab="temperature", main="Beaver 1")
usr <- par("usr"); usr[3:4] <- c(-0.2, 8); par(usr=usr)
lines(beav1$hours, beav1$activ, type="s", lty=2)
temp <- ts(c(beav1$temp[1:82], NA, beav1$temp[83:114]),
           start = 9.5, frequency = 6)
activ <- ts(c(beav1$activ[1:82], NA, beav1$activ[83:114]),
            start = 9.5, frequency = 6)

acf(temp[1:53])
acf(temp[1:53], type = "partial")
ar(temp[1:53])
act <- c(rep(0, 10), activ)
X <- cbind(1, act = act[11:125], act1 = act[10:124],
          act2 = act[9:123], act3 = act[8:122])
alpha <- 0.80
stemp <- as.vector(temp - alpha*lag(temp, -1))
sX <- X[-1, ] - alpha * X[-115,]
beav1.ls <- lm(stemp ~ -1 + sX, na.action = na.omit)
summary(beav1.ls, correlation = FALSE)
rm(temp, activ)
beav1 <- within(beav1,
               hours <- 24*(day-346) + trunc(time/100) + (time%%100)/60)
plot(beav1$hours, beav1$temp, type="l", xlab="time",
   ylab="temperature", main="Beaver 1")
usr <- par("usr"); usr[3:4] <- c(-0.2, 8); par(usr=usr)
lines(beav1$hours, beav1$activ, type="s", lty=2)
temp <- ts(c(beav1$temp[1:82], NA, beav1$temp[83:114]),
           start = 9.5, frequency = 6)
activ <- ts(c(beav1$activ[1:82], NA, beav1$activ[83:114]),
            start = 9.5, frequency = 6)

acf(temp[1:53])
acf(temp[1:53], type = "partial")
ar(temp[1:53])
act <- c(rep(0, 10), activ)
X <- cbind(1, act = act[11:125], act1 = act[10:124],
          act2 = act[9:123], act3 = act[8:122])
alpha <- 0.80
stemp <- as.vector(temp - alpha*lag(temp, -1))
sX <- X[-1, ] - alpha * X[-115,]
beav1.ls <- lm(stemp ~ -1 + sX, na.action = na.omit)
summary(beav1.ls, correlation = FALSE)
rm(temp, activ)

Body Temperature Series of Beaver 2

Description

Usage

beav2
beav2

Format

The beav2 data frame has 100 rows and 4 columns. This data frame contains the following columns:

day: Day of observation (in days since the beginning of 1990), November 3–4.
time: Time of observation, in the form 0330 for 3.30am.
temp: Measured body temperature in degrees Celsius.
activ: Indicator of activity outside the retreat.

Source

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

attach(beav2)
beav2$hours <- 24*(day-307) + trunc(time/100) + (time%%100)/60
plot(beav2$hours, beav2$temp, type = "l", xlab = "time",
   ylab = "temperature", main = "Beaver 2")
usr <- par("usr"); usr[3:4] <- c(-0.2, 8); par(usr = usr)
lines(beav2$hours, beav2$activ, type = "s", lty = 2)

temp <- ts(temp, start = 8+2/3, frequency = 6)
activ <- ts(activ, start = 8+2/3, frequency = 6)
acf(temp[activ == 0]); acf(temp[activ == 1]) # also look at PACFs
ar(temp[activ == 0]); ar(temp[activ == 1])

arima(temp, order = c(1,0,0), xreg = activ)
dreg <- cbind(sin = sin(2*pi*beav2$hours/24), cos = cos(2*pi*beav2$hours/24))
arima(temp, order = c(1,0,0), xreg = cbind(active=activ, dreg))

## IGNORE_RDIFF_BEGIN
library(nlme) # for gls and corAR1
beav2.gls <- gls(temp ~ activ, data = beav2, correlation = corAR1(0.8),
                 method = "ML")
summary(beav2.gls)
summary(update(beav2.gls, subset = 6:100))
detach("beav2"); rm(temp, activ)
## IGNORE_RDIFF_END
attach(beav2)
beav2$hours <- 24*(day-307) + trunc(time/100) + (time%%100)/60
plot(beav2$hours, beav2$temp, type = "l", xlab = "time",
   ylab = "temperature", main = "Beaver 2")
usr <- par("usr"); usr[3:4] <- c(-0.2, 8); par(usr = usr)
lines(beav2$hours, beav2$activ, type = "s", lty = 2)

temp <- ts(temp, start = 8+2/3, frequency = 6)
activ <- ts(activ, start = 8+2/3, frequency = 6)
acf(temp[activ == 0]); acf(temp[activ == 1]) # also look at PACFs
ar(temp[activ == 0]); ar(temp[activ == 1])

arima(temp, order = c(1,0,0), xreg = activ)
dreg <- cbind(sin = sin(2*pi*beav2$hours/24), cos = cos(2*pi*beav2$hours/24))
arima(temp, order = c(1,0,0), xreg = cbind(active=activ, dreg))

## IGNORE_RDIFF_BEGIN
library(nlme) # for gls and corAR1
beav2.gls <- gls(temp ~ activ, data = beav2, correlation = corAR1(0.8),
                 method = "ML")
summary(beav2.gls)
summary(update(beav2.gls, subset = 6:100))
detach("beav2"); rm(temp, activ)
## IGNORE_RDIFF_END

Belgium Phone Calls 1950-1973

Description

A list object with the annual numbers of telephone calls, in Belgium. The components are:

year: last two digits of the year.
calls: number of telephone calls made (in millions of calls).

Usage

phones
phones

Source

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression & Outlier Detection. Wiley.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Biopsy Data on Breast Cancer Patients

Description

This breast cancer database was obtained from the University of Wisconsin Hospitals, Madison from Dr. William H. Wolberg. He assessed biopsies of breast tumours for 699 patients up to 15 July 1992; each of nine attributes has been scored on a scale of 1 to 10, and the outcome is also known. There are 699 rows and 11 columns.

Usage

biopsy
biopsy

Format

This data frame contains the following columns:

ID: sample code number (not unique).
V1: clump thickness.
V2: uniformity of cell size.
V3: uniformity of cell shape.
V4: marginal adhesion.
V5: single epithelial cell size.
V6: bare nuclei (16 values are missing).
V7: bland chromatin.
V8: normal nucleoli.
V9: mitoses.
class: "benign" or "malignant".

Source

P. M. Murphy and D. W. Aha (1992). UCI Repository of machine learning databases. [Machine-readable data repository]. Irvine, CA: University of California, Department of Information and Computer Science.

O. L. Mangasarian and W. H. Wolberg (1990) Cancer diagnosis via linear programming. SIAM News 23, pp 1 & 18.

William H. Wolberg and O.L. Mangasarian (1990) Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, U.S.A. 87, pp. 9193–9196.

O. L. Mangasarian, R. Setiono and W.H. Wolberg (1990) Pattern recognition via linear programming: Theory and application to medical diagnosis. In Large-scale Numerical Optimization eds Thomas F. Coleman and Yuying Li, SIAM Publications, Philadelphia, pp 22–30.

K. P. Bennett and O. L. Mangasarian (1992) Robust linear programming discrimination of two linearly inseparable sets. Optimization Methods and Software 1, pp. 23–34 (Gordon & Breach Science Publishers).

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Risk Factors Associated with Low Infant Birth Weight

Description

The birthwt data frame has 189 rows and 10 columns. The data were collected at Baystate Medical Center, Springfield, Mass during 1986.

Usage

birthwt
birthwt

Format

This data frame contains the following columns:

low: indicator of birth weight less than 2.5 kg.
age: mother's age in years.
lwt: mother's weight in pounds at last menstrual period.
race: mother's race (1 = white, 2 = black, 3 = other).
smoke: smoking status during pregnancy.
ptl: number of previous premature labours.
ht: history of hypertension.
ui: presence of uterine irritability.
ftv: number of physician visits during the first trimester.
bwt: birth weight in grams.

Source

Hosmer, D.W. and Lemeshow, S. (1989) Applied Logistic Regression. New York: Wiley

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

bwt <- with(birthwt, {
race <- factor(race, labels = c("white", "black", "other"))
ptd <- factor(ptl > 0)
ftv <- factor(ftv)
levels(ftv)[-(1:2)] <- "2+"
data.frame(low = factor(low), age, lwt, race, smoke = (smoke > 0),
           ptd, ht = (ht > 0), ui = (ui > 0), ftv)
})
options(contrasts = c("contr.treatment", "contr.poly"))
glm(low ~ ., binomial, bwt)
bwt <- with(birthwt, {
race <- factor(race, labels = c("white", "black", "other"))
ptd <- factor(ptl > 0)
ftv <- factor(ftv)
levels(ftv)[-(1:2)] <- "2+"
data.frame(low = factor(low), age, lwt, race, smoke = (smoke > 0),
           ptd, ht = (ht > 0), ui = (ui > 0), ftv)
})
options(contrasts = c("contr.treatment", "contr.poly"))
glm(low ~ ., binomial, bwt)

Housing Values in Suburbs of Boston

Description

The Boston data frame has 506 rows and 14 columns.

Usage

Boston
Boston

Format

This data frame contains the following columns:

crim: per capita crime rate by town.
zn: proportion of residential land zoned for lots over 25,000 sq.ft.
indus: proportion of non-retail business acres per town.
chas: Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).
nox: nitrogen oxides concentration (parts per 10 million).
rm: average number of rooms per dwelling.
age: proportion of owner-occupied units built prior to 1940.
dis: weighted mean of distances to five Boston employment centres.
rad: index of accessibility to radial highways.
tax: full-value property-tax rate per $10,000.
ptratio: pupil-teacher ratio by town.
black: $1000(Bk - 0.63)^2$ where $Bk$ is the proportion of blacks by town.
lstat: lower status of the population (percent).
medv: median value of owner-occupied homes in $1000s.

Source

Harrison, D. and Rubinfeld, D.L. (1978) Hedonic prices and the demand for clean air. J. Environ. Economics and Management 5, 81–102.

Belsley D.A., Kuh, E. and Welsch, R.E. (1980) Regression Diagnostics. Identifying Influential Data and Sources of Collinearity. New York: Wiley.

Box-Cox Transformations for Linear Models

Description

Computes and optionally plots profile log-likelihoods for the parameter of the Box-Cox power transformation.

Usage

boxcox(object, ...)

## Default S3 method:
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'formula'
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'lm'
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)
boxcox(object, ...)

## Default S3 method:
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'formula'
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

## S3 method for class 'lm'
boxcox(object, lambda = seq(-2, 2, 1/10), plotit = TRUE,
       interp, eps = 1/50, xlab = expression(lambda),
       ylab = "log-Likelihood", ...)

Arguments

`object`	a formula or fitted model object. Currently only `lm` and `aov` objects are handled.
`lambda`	vector of values of `lambda` – default $(-2, 2)$ in steps of 0.1.
`plotit`	logical which controls whether the result should be plotted.
`interp`	logical which controls whether spline interpolation is used. Default to `TRUE` if plotting with `lambda` of length less than 100.
`eps`	Tolerance for `lambda = 0`; defaults to 0.02.
`xlab`	defaults to `"lambda"`.
`ylab`	defaults to `"log-Likelihood"`.
`...`	additional parameters to be used in the model fitting.

Value

A list of the lambda vector and the computed profile log-likelihood vector, invisibly if the result is plotted.

Side Effects

If plotit = TRUE plots log-likelihood vs lambda and indicates a 95% confidence interval about the maximum observed value of lambda. If interp = TRUE, spline interpolation is used to give a smoother plot.

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations (with discussion). Journal of the Royal Statistical Society B, 26, 211–252.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

boxcox(Volume ~ log(Height) + log(Girth), data = trees,
       lambda = seq(-0.25, 0.25, length.out = 10))

boxcox(Days+1 ~ Eth*Sex*Age*Lrn, data = quine,
       lambda = seq(-0.05, 0.45, length.out = 20))
boxcox(Volume ~ log(Height) + log(Girth), data = trees,
       lambda = seq(-0.25, 0.25, length.out = 10))

boxcox(Days+1 ~ Eth*Sex*Age*Lrn, data = quine,
       lambda = seq(-0.05, 0.45, length.out = 20))

Data from a cabbage field trial

Description

The cabbages data set has 60 observations and 4 variables

Usage

cabbages
cabbages

Format

This data frame contains the following columns:

Cult: Factor giving the cultivar of the cabbage, two levels: c39 and c52.
Date: Factor specifying one of three planting dates: d16, d20 or d21.
HeadWt: Weight of the cabbage head, presumably in kg.
VitC: Ascorbic acid content, in undefined units.

Source

Rawlings, J. O. (1988) Applied Regression Analysis: A Research Tool. Wadsworth and Brooks/Cole. Example 8.4, page 219. (Rawlings cites the original source as the files of the late Dr Gertrude M Cox.)

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Colours of Eyes and Hair of People in Caithness

Description

Data on the cross-classification of people in Caithness, Scotland, by eye and hair colour. The region of the UK is particularly interesting as there is a mixture of people of Nordic, Celtic and Anglo-Saxon origin.

Usage

caith
caith

Format

A 4 by 5 table with rows the eye colours (blue, light, medium, dark) and columns the hair colours (fair, red, medium, dark, black).

Source

Fisher, R.A. (1940) The precision of discriminant functions. Annals of Eugenics (London) 10, 422–429.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

## IGNORE_RDIFF_BEGIN
## The signs can vary by platform
corresp(caith)
## IGNORE_RDIFF_END
dimnames(caith)[[2]] <- c("F", "R", "M", "D", "B")
par(mfcol=c(1,3))
plot(corresp(caith, nf=2)); title("symmetric")
plot(corresp(caith, nf=2), type="rows"); title("rows")
plot(corresp(caith, nf=2), type="col"); title("columns")
par(mfrow=c(1,1))
## IGNORE_RDIFF_BEGIN
## The signs can vary by platform
corresp(caith)
## IGNORE_RDIFF_END
dimnames(caith)[[2]] <- c("F", "R", "M", "D", "B")
par(mfcol=c(1,3))
plot(corresp(caith, nf=2)); title("symmetric")
plot(corresp(caith, nf=2), type="rows"); title("rows")
plot(corresp(caith, nf=2), type="col"); title("columns")
par(mfrow=c(1,1))

Data from 93 Cars on Sale in the USA in 1993

Description

The Cars93 data frame has 93 rows and 27 columns.

Usage

Cars93
Cars93

Format

This data frame contains the following columns:

Manufacturer: Manufacturer.
Model: Model.
Type: Type: a factor with levels "Small", "Sporty", "Compact", "Midsize", "Large" and "Van".
Min.Price: Minimum Price (in $1,000): price for a basic version.
Price: Midrange Price (in $1,000): average of Min.Price and Max.Price.
Max.Price: Maximum Price (in $1,000): price for “a premium version”.
MPG.city: City MPG (miles per US gallon by EPA rating).
MPG.highway: Highway MPG.
AirBags: Air Bags standard. Factor: none, driver only, or driver & passenger.
DriveTrain: Drive train type: rear wheel, front wheel or 4WD; (factor).
Cylinders: Number of cylinders (missing for Mazda RX-7, which has a rotary engine).
EngineSize: Engine size (litres).
Horsepower: Horsepower (maximum).
RPM: RPM (revs per minute at maximum horsepower).
Rev.per.mile: Engine revolutions per mile (in highest gear).
Man.trans.avail: Is a manual transmission version available? (yes or no, Factor).
Fuel.tank.capacity: Fuel tank capacity (US gallons).
Passengers: Passenger capacity (persons)
Length: Length (inches).
Wheelbase: Wheelbase (inches).
Width: Width (inches).
Turn.circle: U-turn space (feet).
Rear.seat.room: Rear seat room (inches) (missing for 2-seater vehicles).
Luggage.room: Luggage capacity (cubic feet) (missing for vans).
Weight: Weight (pounds).
Origin: Of non-USA or USA company origins? (factor).
Make: Combination of Manufacturer and Model (character).

Details

Cars were selected at random from among 1993 passenger car models that were listed in both the Consumer Reports issue and the PACE Buying Guide. Pickup trucks and Sport/Utility vehicles were eliminated due to incomplete information in the Consumer Reports source. Duplicate models (e.g., Dodge Shadow and Plymouth Sundance) were listed at most once.

Further description can be found in Lock (1993).

Source

Lock, R. H. (1993) 1993 New Car Data. Journal of Statistics Education 1(1). doi:10.1080/10691898.1993.11910459

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Anatomical Data from Domestic Cats

Description

The heart and body weights of samples of male and female cats used for digitalis experiments. The cats were all adult, over 2 kg body weight.

Usage

cats
cats

Format

This data frame contains the following columns:

Sex: sex: Factor with levels "F" and "M".
Bwt: body weight in kg.
Hwt: heart weight in g.

Source

R. A. Fisher (1947) The analysis of covariance method for the relation between a part and the whole, Biometrics 3, 65–68.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Heat Evolved by Setting Cements

Description

Experiment on the heat evolved in the setting of each of 13 cements.

Usage

cement
cement

Format

x1, x2, x3, x4: Proportions (%) of active ingredients.
y: heat evolved in cals/gm.

Details

Thirteen samples of Portland cement were set. For each sample, the percentages of the four main chemical ingredients was accurately measured. While the cement was setting the amount of heat evolved was also measured.

Source

Woods, H., Steinour, H.H. and Starke, H.R. (1932) Effect of composition of Portland cement on heat evolved during hardening. Industrial Engineering and Chemistry, 24, 1207–1214.

References

Hald, A. (1957) Statistical Theory with Engineering Applications. Wiley, New York.

Examples

lm(y ~ x1 + x2 + x3 + x4, cement)
lm(y ~ x1 + x2 + x3 + x4, cement)

Copper in Wholemeal Flour

Description

A numeric vector of 24 determinations of copper in wholemeal flour, in parts per million.

Usage

chem
chem

Source

Analytical Methods Committee (1989) Robust statistics – how not to reject outliers. The Analyst 114, 1693–1702.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Convert Lists to Data Frames for use by lattice

Description

Convert lists to data frames for use by lattice.

Usage

con2tr(obj)
con2tr(obj)

Arguments

obj

A list of components x, y and z as passed to contour.

Details

con2tr repeats the x and y components suitably to match the vector z.

Value

A data frame suitable for passing to lattice (formerly trellis) functions.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Confidence Intervals for Model Parameters

Description

Computes confidence intervals for one or more parameters in a fitted model. Package MASS added methods for glm and nls fits. As fron R 4.4.0 these have been migrated to package stats.

It also adds a method for polr fits.

Successive Differences Contrast Coding

Description

A coding for factors based on successive differences.

Usage

contr.sdif(n, contrasts = TRUE, sparse = FALSE)
contr.sdif(n, contrasts = TRUE, sparse = FALSE)

Arguments

`n`	The number of levels required.
`contrasts`	logical: Should there be `n - 1` columns orthogonal to the mean (the default) or `n` columns spanning the space?
`sparse`	logical. If true and the result would be sparse (only true for `contrasts = FALSE`), return a sparse matrix.

Details

The contrast coefficients are chosen so that the coded coefficients in a one-way layout are the differences between the means of the second and first levels, the third and second levels, and so on. This makes most sense for ordered factors, but does not assume that the levels are equally spaced.

Value

If contrasts is TRUE, a matrix with n rows and n - 1 columns, and the n by n identity matrix if contrasts is FALSE.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition, Springer.

Examples

(A <- contr.sdif(6))
zapsmall(ginv(A))
(A <- contr.sdif(6))
zapsmall(ginv(A))

Co-operative Trial in Analytical Chemistry

Description

Seven specimens were sent to 6 laboratories in 3 separate batches and each analysed for Analyte. Each analysis was duplicated.

Usage

coop
coop

Format

This data frame contains the following columns:

Lab: Laboratory, L1, L2, ..., L6.
Spc: Specimen, S1, S2, ..., S7.
Bat: Batch, B1, B2, B3 (nested within Spc/Lab),
Conc: Concentration of Analyte in $g/kg$ .

Source

Analytical Methods Committee (1987) Recommendations for the conduct and interpretation of co-operative trials, The Analyst 112, 679–686.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Simple Correspondence Analysis

Description

Find the principal canonical correlation and corresponding row- and column-scores from a correspondence analysis of a two-way contingency table.

Usage

corresp(x, ...)

## S3 method for class 'matrix'
corresp(x, nf = 1, ...)

## S3 method for class 'factor'
corresp(x, y, ...)

## S3 method for class 'data.frame'
corresp(x, ...)

## S3 method for class 'xtabs'
corresp(x, ...)

## S3 method for class 'formula'
corresp(formula, data, ...)
corresp(x, ...)

## S3 method for class 'matrix'
corresp(x, nf = 1, ...)

## S3 method for class 'factor'
corresp(x, y, ...)

## S3 method for class 'data.frame'
corresp(x, ...)

## S3 method for class 'xtabs'
corresp(x, ...)

## S3 method for class 'formula'
corresp(formula, data, ...)

Arguments

`x`, `formula`	The function is generic, accepting various forms of the principal argument for specifying a two-way frequency table. Currently accepted forms are matrices, data frames (coerced to frequency tables), objects of class `"xtabs"` and formulae of the form `~ F1 + F2`, where `F1` and `F2` are factors.
`nf`	The number of factors to be computed. Note that although 1 is the most usual, one school of thought takes the first two singular vectors for a sort of biplot.
`y`	a second factor for a cross-classification.
`data`	an optional data frame, list or environment against which to preferentially resolve variables in the formula.
`...`	If the principal argument is a formula, a data frame may be specified as well from which variables in the formula are preferentially satisfied.

Details

See Venables & Ripley (2002). The plot method produces a graphical representation of the table if nf=1, with the areas of circles representing the numbers of points. If nf is two or more the biplot method is called, which plots the second and third columns of the matrices A = Dr^(-1/2) U L and B = Dc^(-1/2) V L where the singular value decomposition is U L V. Thus the x-axis is the canonical correlation times the row and column scores. Although this is called a biplot, it does not have any useful inner product relationship between the row and column scores. Think of this as an equally-scaled plot with two unrelated sets of labels. The origin is marked on the plot with a cross. (For other versions of this plot see the book.)

Value

An list object of class "correspondence" for which print, plot and biplot methods are supplied. The main components are the canonical correlation(s) and the row and column scores.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Gower, J. C. and Hand, D. J. (1996) Biplots. Chapman & Hall.

Examples

## IGNORE_RDIFF_BEGIN
## The signs can vary by platform
(ct <- corresp(~ Age + Eth, data = quine))
plot(ct)

corresp(caith)
biplot(corresp(caith, nf = 2))
## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN
## The signs can vary by platform
(ct <- corresp(~ Age + Eth, data = quine))
plot(ct)

corresp(caith)
biplot(corresp(caith, nf = 2))
## IGNORE_RDIFF_END

Resistant Estimation of Multivariate Location and Scatter

Description

Compute a multivariate location and scale estimate with a high breakdown point – this can be thought of as estimating the mean and covariance of the good part of the data. cov.mve and cov.mcd are compatibility wrappers.

Usage

cov.rob(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
        method = c("mve", "mcd", "classical"),
        nsamp = "best", seed)

cov.mve(...)
cov.mcd(...)
cov.rob(x, cor = FALSE, quantile.used = floor((n + p + 1)/2),
        method = c("mve", "mcd", "classical"),
        nsamp = "best", seed)

cov.mve(...)
cov.mcd(...)

Arguments

`x`	a matrix or data frame.
`cor`	should the returned result include a correlation matrix?
`quantile.used`	the minimum number of the data points regarded as `good` points.
`method`	the method to be used – minimum volume ellipsoid, minimum covariance determinant or classical product-moment. Using `cov.mve` or `cov.mcd` forces `mve` or `mcd` respectively.
`nsamp`	the number of samples or `"best"` or `"exact"` or `"sample"`. The limit If `"sample"` the number chosen is `min(5*p, 3000)`, taken from Rousseeuw and Hubert (1997). If `"best"` exhaustive enumeration is done up to 5000 samples: if `"exact"` exhaustive enumeration will be attempted.
`seed`	the seed to be used for random sampling: see `RNGkind`. The current value of `.Random.seed` will be preserved if it is set.
`...`	arguments to `cov.rob` other than `method`.

Details

For method "mve", an approximate search is made of a subset of size quantile.used with an enclosing ellipsoid of smallest volume; in method "mcd" it is the volume of the Gaussian confidence ellipsoid, equivalently the determinant of the classical covariance matrix, that is minimized. The mean of the subset provides a first estimate of the location, and the rescaled covariance matrix a first estimate of scatter. The Mahalanobis distances of all the points from the location estimate for this covariance matrix are calculated, and those points within the 97.5% point under Gaussian assumptions are declared to be good. The final estimates are the mean and rescaled covariance of the good points.

The rescaling is by the appropriate percentile under Gaussian data; in addition the first covariance matrix has an ad hoc finite-sample correction given by Marazzi.

For method "mve" the search is made over ellipsoids determined by the covariance matrix of p of the data points. For method "mcd" an additional improvement step suggested by Rousseeuw and van Driessen (1999) is used, in which once a subset of size quantile.used is selected, an ellipsoid based on its covariance is tested (as this will have no larger a determinant, and may be smaller).

There is a hard limit on the allowed number of samples, $2^{31} - 1$ . However, practical limits are likely to be much lower and one might check the number of samples used for exhaustive enumeration, combn(NROW(x), NCOL(x) + 1), before attempting it.

Value

A list with components

`center`	the final estimate of location.
`cov`	the final estimate of scatter.
`cor`	(only is `cor = TRUE`) the estimate of the correlation matrix.
`sing`	message giving number of singular samples out of total
`crit`	the value of the criterion on log scale. For MCD this is the determinant, and for MVE it is proportional to the volume.
`best`	the subset used. For MVE the best sample, for MCD the best set of size `quantile.used`.
`n.obs`	total number of observations.

References

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth and Brooks/Cole.

P. J. Rousseeuw and B. C. van Zomeren (1990) Unmasking multivariate outliers and leverage points, Journal of the American Statistical Association, 85, 633–639.

P. J. Rousseeuw and K. van Driessen (1999) A fast algorithm for the minimum covariance determinant estimator. Technometrics 41, 212–223.

P. Rousseeuw and M. Hubert (1997) Recent developments in PROGRESS. In L1-Statistical Procedures and Related Topics ed Y. Dodge, IMS Lecture Notes volume 31, pp. 201–214.

Examples

set.seed(123)
cov.rob(stackloss)
cov.rob(stack.x, method = "mcd", nsamp = "exact")
set.seed(123)
cov.rob(stackloss)
cov.rob(stack.x, method = "mcd", nsamp = "exact")

Covariance Estimation for Multivariate t Distribution

Description

Estimates a covariance or correlation matrix assuming the data came from a multivariate t distribution: this provides some degree of robustness to outlier without giving a high breakdown point.

Usage

cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5,
         maxit = 25, tol = 0.01)
cov.trob(x, wt = rep(1, n), cor = FALSE, center = TRUE, nu = 5,
         maxit = 25, tol = 0.01)

Arguments

`x`	data matrix. Missing values (NAs) are not allowed.
`wt`	A vector of weights for each case: these are treated as if the case `i` actually occurred `wt[i]` times.
`cor`	Flag to choose between returning the correlation (`cor = TRUE`) or covariance (`cor = FALSE`) matrix.
`center`	a logical value or a numeric vector providing the location about which the covariance is to be taken. If `center = FALSE`, no centering is done; if `center = TRUE` the MLE of the location vector is used.
`nu`	‘degrees of freedom’ for the multivariate t distribution. Must exceed 2 (so that the covariance matrix is finite).
`maxit`	Maximum number of iterations in fitting.
`tol`	Convergence tolerance for fitting.

Value

A list with the following components

`cov`	the fitted covariance matrix.
`center`	the estimated or specified location vector.
`wt`	the specified weights: only returned if the `wt` argument was given.
`n.obs`	the number of cases used in the fitting.
`cor`	the fitted correlation matrix: only returned if `cor = TRUE`.
`call`	The matched call.
`iter`	The number of iterations used.

References

J. T. Kent, D. E. Tyler and Y. Vardi (1994) A curious likelihood identity for the multivariate t-distribution. Communications in Statistics—Simulation and Computation 23, 441–453.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

cov.trob(stackloss)
cov.trob(stackloss)

Performance of Computer CPUs

Description

A relative performance measure and characteristics of 209 CPUs.

Usage

cpus
cpus

Format

The components are:

name: manufacturer and model.
syct: cycle time in nanoseconds.
mmin: minimum main memory in kilobytes.
mmax: maximum main memory in kilobytes.
cach: cache size in kilobytes.
chmin: minimum number of channels.
chmax: maximum number of channels.
perf: published performance on a benchmark mix relative to an IBM 370/158-3.
estperf: estimated performance (by Ein-Dor & Feldmesser).

Source

P. Ein-Dor and J. Feldmesser (1987) Attributes of the performance of central processing units: a relative performance prediction model. Comm. ACM. 30, 308–317.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Morphological Measurements on Leptograpsus Crabs

Description

The crabs data frame has 200 rows and 8 columns, describing 5 morphological measurements on 50 crabs each of two colour forms and both sexes, of the species Leptograpsus variegatus collected at Fremantle, W. Australia.

Usage

crabs
crabs

Format

This data frame contains the following columns:

sp: species - "B" or "O" for blue or orange.
sex: as it says.
index: index 1:50 within each of the four groups.
FL: frontal lobe size (mm).
RW: rear width (mm).
CL: carapace length (mm).
CW: carapace width (mm).
BD: body depth (mm).

Source

Campbell, N.A. and Mahon, R.J. (1974) A multivariate study of variation in two species of rock crab of genus Leptograpsus. Australian Journal of Zoology 22, 417–425.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Diagnostic Tests on Patients with Cushing's Syndrome

Description

Cushing's syndrome is a hypertensive disorder associated with over-secretion of cortisol by the adrenal gland. The observations are urinary excretion rates of two steroid metabolites.

Usage

Cushings
Cushings

Format

The Cushings data frame has 27 rows and 3 columns:

Tetrahydrocortisone: urinary excretion rate (mg/24hr) of Tetrahydrocortisone.
Pregnanetriol: urinary excretion rate (mg/24hr) of Pregnanetriol.
Type: underlying type of syndrome, coded a (adenoma) , b (bilateral hyperplasia), c (carcinoma) or u for unknown.

Source

J. Aitchison and I. R. Dunsmore (1975) Statistical Prediction Analysis. Cambridge University Press, Tables 11.1–3.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

DDT in Kale

Description

A numeric vector of 15 measurements by different laboratories of the pesticide DDT in kale, in ppm (parts per million) using the multiple pesticide residue measurement.

Usage

DDT
DDT

Source

C. E. Finsterwalder (1976) Collaborative study of an extension of the Mills et al method for the determination of pesticide residues in food. J. Off. Anal. Chem. 59, 169–171

R. G. Staudte and S. J. Sheather (1990) Robust Estimation and Testing. Wiley

Monthly Deaths from Lung Diseases in the UK

Description

A time series giving the monthly deaths from bronchitis, emphysema and asthma in the UK, 1974-1979, both sexes (deaths),

Usage

deaths
deaths

Source

P. J. Diggle (1990) Time Series: A Biostatistical Introduction. Oxford, table A.3

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Transform an Allowable Formula for 'loglm' into one for 'terms'

Description

loglm allows dimension numbers to be used in place of names in the formula. denumerate modifies such a formula into one that terms can process.

Usage

denumerate(x)
denumerate(x)

Arguments

`x`	A formula conforming to the conventions of `loglm`, that is, it may allow dimension numbers to stand in for names when specifying a log-linear model.

Details

The model fitting function loglm fits log-linear models to frequency data using iterative proportional scaling. To specify the model the user must nominate the margins in the data that remain fixed under the log-linear model. It is convenient to allow the user to use dimension numbers, 1, 2, 3, ... for the first, second, third, ..., margins in a similar way to variable names. As the model formula has to be parsed by terms, which treats 1 in a special way and requires parseable variable names, these formulae have to be modified by giving genuine names for these margin, or dimension numbers. denumerate replaces these numbers with names of a special form, namely n is replaced by .vn. This allows terms to parse the formula in the usual way.

Value

A linear model formula like that presented, except that where dimension numbers, say n, have been used to specify fixed margins these are replaced by names of the form .vn which may be processed by terms.

Examples

denumerate(~(1+2+3)^3 + a/b)
## which gives ~ (.v1 + .v2 + .v3)^3 + a/b
denumerate(~(1+2+3)^3 + a/b)
## which gives ~ (.v1 + .v2 + .v3)^3 + a/b

Predict Doses for Binomial Assay model

Description

Calibrate binomial assays, generalizing the calculation of LD50.

Usage

dose.p(obj, cf = 1:2, p = 0.5)
dose.p(obj, cf = 1:2, p = 0.5)

Arguments

`obj`	A fitted model object of class inheriting from `"glm"`.
`cf`	The terms in the coefficient vector giving the intercept and coefficient of (log-)dose
`p`	Probabilities at which to predict the dose needed.

Value

An object of class "glm.dose" giving the prediction (attribute "p" and standard error (attribute "SE") at each response probability.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.

Examples

ldose <- rep(0:5, 2)
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- cbind(numdead, numalive = 20 - numdead)
budworm.lg0 <- glm(SF ~ sex + ldose - 1, family = binomial)

dose.p(budworm.lg0, cf = c(1,3), p = 1:3/4)
dose.p(update(budworm.lg0, family = binomial(link=probit)),
       cf = c(1,3), p = 1:3/4)
ldose <- rep(0:5, 2)
numdead <- c(1, 4, 9, 13, 18, 20, 0, 2, 6, 10, 12, 16)
sex <- factor(rep(c("M", "F"), c(6, 6)))
SF <- cbind(numdead, numalive = 20 - numdead)
budworm.lg0 <- glm(SF ~ sex + ldose - 1, family = binomial)

dose.p(budworm.lg0, cf = c(1,3), p = 1:3/4)
dose.p(update(budworm.lg0, family = binomial(link=probit)),
       cf = c(1,3), p = 1:3/4)

Deaths of Car Drivers in Great Britain 1969-84

Description

A regular time series giving the monthly totals of car drivers in Great Britain killed or seriously injured Jan 1969 to Dec 1984. Compulsory wearing of seat belts was introduced on 31 Jan 1983

Usage

drivers
drivers

Source

Harvey, A.C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, pp. 519–523.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Try All One-Term Deletions from a Model

Description

Try fitting all models that differ from the current model by dropping a single term, maintaining marginality.

This function is generic; there exist methods for classes lm and glm and the default method will work for many other classes.

Usage

dropterm (object, ...)

## Default S3 method:
dropterm(object, scope, scale = 0, test = c("none", "Chisq"),
         k = 2, sorted = FALSE, trace = FALSE, ...)

## S3 method for class 'lm'
dropterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
         k = 2, sorted = FALSE, ...)

## S3 method for class 'glm'
dropterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
         k = 2, sorted = FALSE, trace = FALSE, ...)
dropterm (object, ...)

## Default S3 method:
dropterm(object, scope, scale = 0, test = c("none", "Chisq"),
         k = 2, sorted = FALSE, trace = FALSE, ...)

## S3 method for class 'lm'
dropterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
         k = 2, sorted = FALSE, ...)

## S3 method for class 'glm'
dropterm(object, scope, scale = 0, test = c("none", "Chisq", "F"),
         k = 2, sorted = FALSE, trace = FALSE, ...)

Arguments

`object`	A object fitted by some model-fitting function.
`scope`	a formula giving terms which might be dropped. By default, the model formula. Only terms that can be dropped and maintain marginality are actually tried.
`scale`	used in the definition of the AIC statistic for selecting the models, currently only for `lm`, `aov` and `glm` models. Specifying `scale` asserts that the residual standard error or dispersion is known.
`test`	should the results include a test statistic relative to the original model? The F test is only appropriate for `lm` and `aov` models, and perhaps for some over-dispersed `glm` models. The Chisq test can be an exact test (`lm` models with known scale) or a likelihood-ratio test depending on the method.
`k`	the multiple of the number of degrees of freedom used for the penalty. Only `k = 2` gives the genuine AIC: `k = log(n)` is sometimes referred to as BIC or SBC.
`sorted`	should the results be sorted on the value of AIC?
`trace`	if `TRUE` additional information may be given on the fits as they are tried.
`...`	arguments passed to or from other methods.

Details

Value

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
dropterm(quine.nxt, test=  "F")
quine.stp <- stepAIC(quine.nxt,
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1),
    trace = FALSE)
dropterm(quine.stp, test = "F")
quine.3 <- update(quine.stp, . ~ . - Eth:Age:Lrn)
dropterm(quine.3, test = "F")
quine.4 <- update(quine.3, . ~ . - Eth:Age)
dropterm(quine.4, test = "F")
quine.5 <- update(quine.4, . ~ . - Age:Lrn)
dropterm(quine.5, test = "F")

house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family=poisson,
                   data = housing)
house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
dropterm(house.glm1, test = "Chisq")
quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
dropterm(quine.nxt, test=  "F")
quine.stp <- stepAIC(quine.nxt,
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1),
    trace = FALSE)
dropterm(quine.stp, test = "F")
quine.3 <- update(quine.stp, . ~ . - Eth:Age:Lrn)
dropterm(quine.3, test = "F")
quine.4 <- update(quine.3, . ~ . - Eth:Age)
dropterm(quine.4, test = "F")
quine.5 <- update(quine.4, . ~ . - Age:Lrn)
dropterm(quine.5, test = "F")

house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family=poisson,
                   data = housing)
house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
dropterm(house.glm1, test = "Chisq")

Foraging Ecology of Bald Eagles

Description

Knight and Skagen collected during a field study on the foraging behaviour of wintering Bald Eagles in Washington State, USA data concerning 160 attempts by one (pirating) Bald Eagle to steal a chum salmon from another (feeding) Bald Eagle.

Usage

eagles
eagles

Format

The eagles data frame has 8 rows and 5 columns.

y: Number of successful attempts.
n: Total number of attempts.
P: Size of pirating eagle (L = large, S = small).
A: Age of pirating eagle (I = immature, A = adult).
V: Size of victim eagle (L = large, S = small).

Source

Knight, R. L. and Skagen, S. K. (1988) Agonistic asymmetries and the foraging ecology of Bald Eagles. Ecology 69, 1188–1194.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

eagles.glm <- glm(cbind(y, n - y) ~ P*A + V, data = eagles,
                  family = binomial)
dropterm(eagles.glm)
prof <- profile(eagles.glm)
plot(prof)
pairs(prof)
eagles.glm <- glm(cbind(y, n - y) ~ P*A + V, data = eagles,
                  family = binomial)
dropterm(eagles.glm)
prof <- profile(eagles.glm)
plot(prof)
pairs(prof)

Seizure Counts for Epileptics

Description

Thall and Vail (1990) give a data set on two-week seizure counts for 59 epileptics. The number of seizures was recorded for a baseline period of 8 weeks, and then patients were randomly assigned to a treatment group or a control group. Counts were then recorded for four successive two-week periods. The subject's age is the only covariate.

Usage

epil
epil

Format

This data frame has 236 rows and the following 9 columns:

y: the count for the 2-week period.
trt: treatment, "placebo" or "progabide".
base: the counts in the baseline 8-week period.
age: subject's age, in years.
V4: 0/1 indicator variable of period 4.
subject: subject number, 1 to 59.
period: period, 1 to 4.
lbase: log-counts for the baseline period, centred to have zero mean.
lage: log-ages, centred to have zero mean.

Source

Thall, P. F. and Vail, S. C. (1990) Some covariance models for longitudinal count data with over-dispersion. Biometrics 46, 657–671.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer.

Examples

## IGNORE_RDIFF_BEGIN
summary(glm(y ~ lbase*trt + lage + V4, family = poisson,
            data = epil), correlation = FALSE)
## IGNORE_RDIFF_END
epil2 <- epil[epil$period == 1, ]
epil2["period"] <- rep(0, 59); epil2["y"] <- epil2["base"]
epil["time"] <- 1; epil2["time"] <- 4
epil2 <- rbind(epil, epil2)
epil2$pred <- unclass(epil2$trt) * (epil2$period > 0)
epil2$subject <- factor(epil2$subject)
epil3 <- aggregate(epil2, list(epil2$subject, epil2$period > 0),
   function(x) if(is.numeric(x)) sum(x) else x[1])
epil3$pred <- factor(epil3$pred,
   labels = c("base", "placebo", "drug"))

contrasts(epil3$pred) <- structure(contr.sdif(3),
    dimnames = list(NULL, c("placebo-base", "drug-placebo")))
## IGNORE_RDIFF_BEGIN
summary(glm(y ~ pred + factor(subject) + offset(log(time)),
            family = poisson, data = epil3), correlation = FALSE)
## IGNORE_RDIFF_END

summary(glmmPQL(y ~ lbase*trt + lage + V4,
                random = ~ 1 | subject,
                family = poisson, data = epil))
summary(glmmPQL(y ~ pred, random = ~1 | subject,
                family = poisson, data = epil3))
## IGNORE_RDIFF_BEGIN
summary(glm(y ~ lbase*trt + lage + V4, family = poisson,
            data = epil), correlation = FALSE)
## IGNORE_RDIFF_END
epil2 <- epil[epil$period == 1, ]
epil2["period"] <- rep(0, 59); epil2["y"] <- epil2["base"]
epil["time"] <- 1; epil2["time"] <- 4
epil2 <- rbind(epil, epil2)
epil2$pred <- unclass(epil2$trt) * (epil2$period > 0)
epil2$subject <- factor(epil2$subject)
epil3 <- aggregate(epil2, list(epil2$subject, epil2$period > 0),
   function(x) if(is.numeric(x)) sum(x) else x[1])
epil3$pred <- factor(epil3$pred,
   labels = c("base", "placebo", "drug"))

contrasts(epil3$pred) <- structure(contr.sdif(3),
    dimnames = list(NULL, c("placebo-base", "drug-placebo")))
## IGNORE_RDIFF_BEGIN
summary(glm(y ~ pred + factor(subject) + offset(log(time)),
            family = poisson, data = epil3), correlation = FALSE)
## IGNORE_RDIFF_END

summary(glmmPQL(y ~ lbase*trt + lage + V4,
                random = ~ 1 | subject,
                family = poisson, data = epil))
summary(glmmPQL(y ~ pred, random = ~1 | subject,
                family = poisson, data = epil3))

Plots with Geometrically Equal Scales

Description

Version of a scatterplot with scales chosen to be equal on both axes, that is 1cm represents the same units on each

Usage

eqscplot(x, y, ratio = 1, tol = 0.04, uin, ...)
eqscplot(x, y, ratio = 1, tol = 0.04, uin, ...)

Arguments

`x`	vector of x values, or a 2-column matrix, or a list with components `x` and `y`
`y`	vector of y values
`ratio`	desired ratio of units on the axes. Units on the y axis are drawn at `ratio` times the size of units on the x axis. Ignored if `uin` is specified and of length 2.
`tol`	proportion of white space at the margins of plot.
`uin`	desired values for the units-per-inch parameter. If of length 1, the desired units per inch on the x axis.
`...`	further arguments for `plot` and graphical parameters. Note that `par(xaxs="i", yaxs="i")` is enforced, and `xlim` and `ylim` will be adjusted accordingly.

Details

Limits for the x and y axes are chosen so that they include the data. One of the sets of limits is then stretched from the midpoint to make the units in the ratio given by ratio. Finally both are stretched by 1 + tol to move points away from the axes, and the points plotted.

Value

invisibly, the values of uin used for the plot.

Side Effects

performs the plot.

Note

This was originally written for S: R's plot.window has an argument asp with a similar effect (including to this function's ratio) and can be passed from the default plot function.

Arguments ratio and uin were suggested by Bill Dunlap.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Ecological Factors in Farm Management

Description

The farms data frame has 20 rows and 4 columns. The rows are farms on the Dutch island of Terschelling and the columns are factors describing the management of grassland.

Usage

farms
farms

Format

This data frame contains the following columns:

Mois: Five levels of soil moisture – level 3 does not occur at these 20 farms.
Manag: Grassland management type (SF = standard, BF = biological, HF = hobby farming, NM = nature conservation).
Use: Grassland use (U1 = hay production, U2 = intermediate, U3 = grazing).
Manure: Manure usage – classes C0 to C4.

Source

J.C. Gower and D.J. Hand (1996) Biplots. Chapman & Hall, Table 4.6.

Quoted as from:
R.H.G. Jongman, C.J.F. ter Braak and O.F.R. van Tongeren (1987) Data Analysis in Community and Landscape Ecology. PUDOC, Wageningen.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

farms.mca <- mca(farms, abbrev = TRUE)  # Use levels as names
eqscplot(farms.mca$cs, type = "n")
text(farms.mca$rs, cex = 0.7)
text(farms.mca$cs, labels = dimnames(farms.mca$cs)[[1]], cex = 0.7)
farms.mca <- mca(farms, abbrev = TRUE)  # Use levels as names
eqscplot(farms.mca$cs, type = "n")
text(farms.mca$rs, cex = 0.7)
text(farms.mca$cs, labels = dimnames(farms.mca$cs)[[1]], cex = 0.7)

Measurements of Forensic Glass Fragments

Description

The fgl data frame has 214 rows and 10 columns. It was collected by B. German on fragments of glass collected in forensic work.

Usage

fgl
fgl

Format

This data frame contains the following columns:

RI

refractive index; more precisely the refractive index is 1.518xxxx.

The next 8 measurements are percentages by weight of oxides.

Na

sodium.

Mg

manganese.

Al

aluminium.

Si

silicon.

K

potassium.

Ca

calcium.

Ba

barium.

Fe

iron.

type

The fragments were originally classed into seven types, one of which was absent in this dataset. The categories which occur are window float glass (WinF: 70), window non-float glass (WinNF: 76), vehicle window glass (Veh: 17), containers (Con: 13), tableware (Tabl: 9) and vehicle headlamps (Head: 29).

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Maximum-likelihood Fitting of Univariate Distributions

Description

Maximum-likelihood fitting of univariate distributions, allowing parameters to be held fixed if desired.

Usage

fitdistr(x, densfun, start, ...)
fitdistr(x, densfun, start, ...)

Arguments

`x`	A numeric vector of length at least one containing only finite values.
`densfun`	Either a character string or a function returning a density evaluated at its first argument. Distributions `"beta"`, `"cauchy"`, `"chi-squared"`, `"exponential"`, `"gamma"`, `"geometric"`, `"log-normal"`, `"lognormal"`, `"logistic"`, `"negative binomial"`, `"normal"`, `"Poisson"`, `"t"` and `"weibull"` are recognised, case being ignored.
`start`	A named list giving the parameters to be optimized with initial values. This can be omitted for some of the named distributions and must be for others (see Details).
`...`	Additional parameters, either for `densfun` or for `optim`. In particular, it can be used to specify bounds via `lower` or `upper` or both. If arguments of `densfun` (or the density function corresponding to a character-string specification) are included they will be held fixed.

Details

For the Normal, log-Normal, geometric, exponential and Poisson distributions the closed-form MLEs (and exact standard errors) are used, and start should not be supplied.

For all other distributions, direct optimization of the log-likelihood is performed using optim. The estimated standard errors are taken from the observed information matrix, calculated by a numerical approximation. For one-dimensional problems the Nelder-Mead method is used and for multi-dimensional problems the BFGS method, unless arguments named lower or upper are supplied (when L-BFGS-B is used) or method is supplied explicitly.

For the "t" named distribution the density is taken to be the location-scale family with location m and scale s.

For the following named distributions, reasonable starting values will be computed if start is omitted or only partially specified: "cauchy", "gamma", "logistic", "negative binomial" (parametrized by mu and size), "t" and "weibull". Note that these starting values may not be good enough if the fit is poor: in particular they are not resistant to outliers unless the fitted distribution is long-tailed.

There are print, coef, vcov and logLik methods for class "fitdistr".

Value

An object of class "fitdistr", a list with four components,

`estimate`	the parameter estimates,
`sd`	the estimated standard errors,
`vcov`	the estimated variance-covariance matrix, and
`loglik`	the log-likelihood.

Note

Numerical optimization cannot work miracles: please note the comments in optim on scaling data. If the fitted parameters are far away from one, consider re-fitting specifying the control parameter parscale.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

## avoid spurious accuracy
op <- options(digits = 3)
set.seed(123)
x <- rgamma(100, shape = 5, rate = 0.1)
fitdistr(x, "gamma")
## now do this directly with more control.
fitdistr(x, dgamma, list(shape = 1, rate = 0.1), lower = 0.001)

set.seed(123)
x2 <- rt(250, df = 9)
fitdistr(x2, "t", df = 9)
## allow df to vary: not a very good idea!
fitdistr(x2, "t")
## now do fixed-df fit directly with more control.
mydt <- function(x, m, s, df) dt((x-m)/s, df)/s
fitdistr(x2, mydt, list(m = 0, s = 1), df = 9, lower = c(-Inf, 0))

set.seed(123)
x3 <- rweibull(100, shape = 4, scale = 100)
fitdistr(x3, "weibull")

set.seed(123)
x4 <- rnegbin(500, mu = 5, theta = 4)
fitdistr(x4, "Negative Binomial")
options(op)
## avoid spurious accuracy
op <- options(digits = 3)
set.seed(123)
x <- rgamma(100, shape = 5, rate = 0.1)
fitdistr(x, "gamma")
## now do this directly with more control.
fitdistr(x, dgamma, list(shape = 1, rate = 0.1), lower = 0.001)

set.seed(123)
x2 <- rt(250, df = 9)
fitdistr(x2, "t", df = 9)
## allow df to vary: not a very good idea!
fitdistr(x2, "t")
## now do fixed-df fit directly with more control.
mydt <- function(x, m, s, df) dt((x-m)/s, df)/s
fitdistr(x2, mydt, list(m = 0, s = 1), df = 9, lower = c(-Inf, 0))

set.seed(123)
x3 <- rweibull(100, shape = 4, scale = 100)
fitdistr(x3, "weibull")

set.seed(123)
x4 <- rnegbin(500, mu = 5, theta = 4)
fitdistr(x4, "Negative Binomial")
options(op)

Forbes' Data on Boiling Points in the Alps

Description

A data frame with 17 observations on boiling point of water and barometric pressure in inches of mercury.

Usage

forbes
forbes

Format

bp: boiling point (degrees Farenheit).
pres: barometric pressure in inches of mercury.

Source

A. C. Atkinson (1985) Plots, Transformations and Regression. Oxford.

S. Weisberg (1980) Applied Linear Regression. Wiley.

Rational Approximation

Description

Find rational approximations to the components of a real numeric object using a standard continued fraction method.

Usage

fractions(x, cycles = 10, max.denominator = 2000, ...)

as.fractions(x)

is.fractions(f)
fractions(x, cycles = 10, max.denominator = 2000, ...)

as.fractions(x)

is.fractions(f)

Arguments

`x`	Any object of mode numeric. Missing values are now allowed.
`cycles`	The maximum number of steps to be used in the continued fraction approximation process.
`max.denominator`	An early termination criterion. If any partial denominator exceeds `max.denominator` the continued fraction stops at that point.
`...`	arguments passed to or from other methods.
`f`	an R object.

Details

Each component is first expanded in a continued fraction of the form

x = floor(x) + 1/(p1 + 1/(p2 + ...)))

where p1, p2, ... are positive integers, terminating either at cycles terms or when a pj > max.denominator. The continued fraction is then re-arranged to retrieve the numerator and denominator as integers.

The numerators and denominators are then combined into a character vector that becomes the "fracs" attribute and used in printed representations.

Arithmetic operations on "fractions" objects have full floating point accuracy, but the character representation printed out may not.

Value

An object of class "fractions". A structure with .Data component the same as the input numeric x, but with the rational approximations held as a character vector attribute, "fracs". Arithmetic operations on "fractions" objects are possible.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer.

Examples

X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
fractions(solve(X, X/5))
fractions(solve(X, X/5)) + 1
X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
fractions(solve(X, X/5))
fractions(solve(X, X/5)) + 1

Level of GAG in Urine of Children

Description

Data were collected on the concentration of a chemical GAG in the urine of 314 children aged from zero to seventeen years. The aim of the study was to produce a chart to help a paediatrican to assess if a child's GAG concentration is ‘normal’.

Usage

GAGurine
GAGurine

Format

This data frame contains the following columns:

Age: age of child in years.
GAG: concentration of GAG (the units have been lost).

Source

Mrs Susan Prosser, Paediatrics Department, University of Oxford, via Department of Statistics Consulting Service.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Velocities for 82 Galaxies

Description

A numeric vector of velocities in km/sec of 82 galaxies from 6 well-separated conic sections of an unfilled survey of the Corona Borealis region. Multimodality in such surveys is evidence for voids and superclusters in the far universe.

Usage

galaxies
galaxies

Note

There is an 83rd measurement of 5607 km/sec in the Postman et al. paper which is omitted in Roeder (1990) and from the dataset here.

There is also a typo: this dataset has 78th observation 26690 which should be 26960.

Source

Roeder, K. (1990) Density estimation with confidence sets exemplified by superclusters and voids in galaxies. Journal of the American Statistical Association 85, 617–624.

Postman, M., Huchra, J. P. and Geller, M. J. (1986) Probes of large-scale structures in the Corona Borealis region. Astronomical Journal 92, 1238–1247.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

gal <- galaxies/1000
c(width.SJ(gal, method = "dpi"), width.SJ(gal))
plot(x = c(0, 40), y = c(0, 0.3), type = "n", bty = "l",
     xlab = "velocity of galaxy (1000km/s)", ylab = "density")
rug(gal)
lines(density(gal, width = 3.25, n = 200), lty = 1)
lines(density(gal, width = 2.56, n = 200), lty = 3)
gal <- galaxies/1000
c(width.SJ(gal, method = "dpi"), width.SJ(gal))
plot(x = c(0, 40), y = c(0, 0.3), type = "n", bty = "l",
     xlab = "velocity of galaxy (1000km/s)", ylab = "density")
rug(gal)
lines(density(gal, width = 3.25, n = 200), lty = 1)
lines(density(gal, width = 2.56, n = 200), lty = 3)

Calculate the MLE of the Gamma Dispersion Parameter in a GLM Fit

Description

A front end to gamma.shape for convenience. Finds the reciprocal of the estimate of the shape parameter only.

Usage

gamma.dispersion(object, ...)
gamma.dispersion(object, ...)

Arguments

`object`	Fitted model object giving the gamma fit.
`...`	Additional arguments passed on to `gamma.shape`.

Value

The MLE of the dispersion parameter of the gamma distribution.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Estimate the Shape Parameter of the Gamma Distribution in a GLM Fit

Description

Find the maximum likelihood estimate of the shape parameter of the gamma distribution after fitting a Gamma generalized linear model.

Usage

gamma.shape(object, ...)

## S3 method for class 'glm'
gamma.shape(object, it.lim = 10,
            eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)
gamma.shape(object, ...)

## S3 method for class 'glm'
gamma.shape(object, it.lim = 10,
            eps.max = .Machine$double.eps^0.25, verbose = FALSE, ...)

Arguments

`object`	Fitted model object from a `Gamma` family or `quasi` family with `variance = "mu^2"`.
`it.lim`	Upper limit on the number of iterations.
`eps.max`	Maximum discrepancy between approximations for the iteration process to continue.
`verbose`	If `TRUE`, causes successive iterations to be printed out. The initial estimate is taken from the deviance.
`...`	further arguments passed to or from other methods.

Details

A glm fit for a Gamma family correctly calculates the maximum likelihood estimate of the mean parameters but provides only a crude estimate of the dispersion parameter. This function takes the results of the glm fit and solves the maximum likelihood equation for the reciprocal of the dispersion parameter, which is usually called the shape (or exponent) parameter.

Value

List of two components

`alpha`	the maximum likelihood estimate
`SE`	the approximate standard error, the square-root of the reciprocal of the observed information.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

clotting <- data.frame(
    u = c(5,10,15,20,30,40,60,80,100),
    lot1 = c(118,58,42,35,27,25,21,19,18),
    lot2 = c(69,35,26,21,18,16,13,12,12))
clot1 <- glm(lot1 ~ log(u), data = clotting, family = Gamma)
gamma.shape(clot1)

gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn,
          quasi(link=log, variance="mu^2"), quine,
          start = c(3, rep(0,31)))
gamma.shape(gm, verbose = TRUE)
## IGNORE_RDIFF_BEGIN
summary(gm, dispersion = gamma.dispersion(gm))  # better summary
## IGNORE_RDIFF_END
clotting <- data.frame(
    u = c(5,10,15,20,30,40,60,80,100),
    lot1 = c(118,58,42,35,27,25,21,19,18),
    lot2 = c(69,35,26,21,18,16,13,12,12))
clot1 <- glm(lot1 ~ log(u), data = clotting, family = Gamma)
gamma.shape(clot1)

gm <- glm(Days + 0.1 ~ Age*Eth*Sex*Lrn,
          quasi(link=log, variance="mu^2"), quine,
          start = c(3, rep(0,31)))
gamma.shape(gm, verbose = TRUE)
## IGNORE_RDIFF_BEGIN
summary(gm, dispersion = gamma.dispersion(gm))  # better summary
## IGNORE_RDIFF_END

Remission Times of Leukaemia Patients

Description

A data frame from a trial of 42 leukaemia patients. Some were treated with the drug 6-mercaptopurine and the rest are controls. The trial was designed as matched pairs, both withdrawn from the trial when either came out of remission.

Usage

gehan
gehan

Format

This data frame contains the following columns:

pair: label for pair.
time: remission time in weeks.
cens: censoring, 0/1.
treat: treatment, control or 6-MP.

Source

Cox, D. R. and Oakes, D. (1984) Analysis of Survival Data. Chapman & Hall, p. 7. Taken from

Gehan, E.A. (1965) A generalized Wilcoxon test for comparing arbitrarily single-censored samples. Biometrika 52, 203–233.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(survival)
gehan.surv <- survfit(Surv(time, cens) ~ treat, data = gehan,
     conf.type = "log-log")
summary(gehan.surv)
survreg(Surv(time, cens) ~ factor(pair) + treat, gehan, dist = "exponential")
summary(survreg(Surv(time, cens) ~ treat, gehan, dist = "exponential"))
summary(survreg(Surv(time, cens) ~ treat, gehan))
gehan.cox <- coxph(Surv(time, cens) ~ treat, gehan)
summary(gehan.cox)
library(survival)
gehan.surv <- survfit(Surv(time, cens) ~ treat, data = gehan,
     conf.type = "log-log")
summary(gehan.surv)
survreg(Surv(time, cens) ~ factor(pair) + treat, gehan, dist = "exponential")
summary(survreg(Surv(time, cens) ~ treat, gehan, dist = "exponential"))
summary(survreg(Surv(time, cens) ~ treat, gehan))
gehan.cox <- coxph(Surv(time, cens) ~ treat, gehan)
summary(gehan.cox)

Rat Genotype Data

Description

Data from a foster feeding experiment with rat mothers and litters of four different genotypes: A, B, I and J. Rat litters were separated from their natural mothers at birth and given to foster mothers to rear.

Usage

genotype
genotype

Format

The data frame has the following components:

Litter: genotype of the litter.
Mother: genotype of the foster mother.
Wt: Litter average weight gain of the litter, in grams at age 28 days. (The source states that the within-litter variability is negligible.)

Source

Scheffe, H. (1959) The Analysis of Variance Wiley p. 140.

Bailey, D. W. (1953) The Inheritance of Maternal Influences on the Growth of the Rat. Unpublished Ph.D. thesis, University of California. Table B of the Appendix.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Old Faithful Geyser Data

Description

A version of the eruptions data from the ‘Old Faithful’ geyser in Yellowstone National Park, Wyoming. This version comes from Azzalini and Bowman (1990) and is of continuous measurement from August 1 to August 15, 1985.

Some nocturnal duration measurements were coded as 2, 3 or 4 minutes, having originally been described as ‘short’, ‘medium’ or ‘long’.

Usage

geyser
geyser

Format

A data frame with 299 observations on 2 variables.

`duration`	numeric	Eruption time in mins
`waiting`	numeric	Waiting time for this eruption

Note

The waiting time was incorrectly described as the time to the next eruption in the original files, and corrected for MASS version 7.3-30.

References

Azzalini, A. and Bowman, A. W. (1990) A look at some data on the Old Faithful geyser. Applied Statistics 39, 357–365.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Line Transect of Soil in Gilgai Territory

Description

This dataset was collected on a line transect survey in gilgai territory in New South Wales, Australia. Gilgais are natural gentle depressions in otherwise flat land, and sometimes seem to be regularly distributed. The data collection was stimulated by the question: are these patterns reflected in soil properties? At each of 365 sampling locations on a linear grid of 4 meters spacing, samples were taken at depths 0-10 cm, 30-40 cm and 80-90 cm below the surface. pH, electrical conductivity and chloride content were measured on a 1:5 soil:water extract from each sample.

Usage

gilgais
gilgais

Format

This data frame contains the following columns:

pH00: pH at depth 0–10 cm.
pH30: pH at depth 30–40 cm.
pH80: pH at depth 80–90 cm.
e00: electrical conductivity in mS/cm (0–10 cm).
e30: electrical conductivity in mS/cm (30–40 cm).
e80: electrical conductivity in mS/cm (80–90 cm).
c00: chloride content in ppm (0–10 cm).
c30: chloride content in ppm (30–40 cm).
c80: chloride content in ppm (80–90 cm).

Source

Webster, R. (1977) Spectral analysis of gilgai soil. Australian Journal of Soil Research 15, 191–204.

Laslett, G. M. (1989) Kriging and splines: An empirical comparison of their predictive performance in some applications (with discussion). Journal of the American Statistical Association 89, 319–409

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Generalized Inverse of a Matrix

Description

Calculates the Moore-Penrose generalized inverse of a matrix X.

Usage

ginv(X, tol = sqrt(.Machine$double.eps))
ginv(X, tol = sqrt(.Machine$double.eps))

Arguments

`X`	Matrix for which the Moore-Penrose inverse is required.
`tol`	A relative tolerance to detect zero singular values.

Value

A MP generalized inverse matrix for X.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Change a Negative Binomial fit to a GLM fit

Description

This function modifies an output object from glm.nb() to one that looks like the output from glm() with a negative binomial family. This allows it to be updated keeping the theta parameter fixed.

Usage

glm.convert(object)
glm.convert(object)

Arguments

object

An object of class "negbin", typically the output from glm.nb().

Details

Convenience function needed to effect some low level changes to the structure of the fitted model object.

Value

An object of class "glm" with negative binomial family. The theta parameter is then fixed at its present estimate.

Examples

quine.nb1 <- glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)
quine.nbA <- glm.convert(quine.nb1)
quine.nbB <- update(quine.nb1, . ~ . + Sex:Age:Lrn)
anova(quine.nbA, quine.nbB)
quine.nb1 <- glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)
quine.nbA <- glm.convert(quine.nb1)
quine.nbB <- update(quine.nb1, . ~ . + Sex:Age:Lrn)
anova(quine.nbA, quine.nbB)

Fit a Negative Binomial Generalized Linear Model

Description

A modification of the system function glm() to include estimation of the additional parameter, theta, for a Negative Binomial generalized linear model.

Usage

glm.nb(formula, data, weights, subset, na.action,
       start = NULL, etastart, mustart,
       control = glm.control(...), method = "glm.fit",
       model = TRUE, x = FALSE, y = TRUE, contrasts = NULL, ...,
       init.theta, link = log)
glm.nb(formula, data, weights, subset, na.action,
       start = NULL, etastart, mustart,
       control = glm.control(...), method = "glm.fit",
       model = TRUE, x = FALSE, y = TRUE, contrasts = NULL, ...,
       init.theta, link = log)

Arguments

`formula`, `data`, `weights`, `subset`, `na.action`, `start`, `etastart`, `mustart`, `control`, `method`, `model`, `x`, `y`, `contrasts`, `...`	arguments for the `glm()` function. Note that these exclude `family` and `offset` (but `offset()` can be used).
`init.theta`	Optional initial value for the theta parameter. If omitted a moment estimator after an initial fit using a Poisson GLM is used.
`link`	The link function. Currently must be one of `log`, `sqrt` or `identity`.

Details

An alternating iteration process is used. For given theta the GLM is fitted using the same process as used by glm(). For fixed means the theta parameter is estimated using score and information iterations. The two are alternated until convergence of both. (The number of alternations and the number of iterations when estimating theta are controlled by the maxit parameter of glm.control.)

Setting trace > 0 traces the alternating iteration process. Setting trace > 1 traces the glm fit, and setting trace > 2 traces the estimation of theta.

Value

A fitted model object of class negbin inheriting from glm and lm. The object is like the output of glm but contains three additional components, namely theta for the ML estimate of theta, SE.theta for its approximate standard error (using observed rather than expected information), and twologlik for twice the log-likelihood function.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

quine.nb1 <- glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)
quine.nb2 <- update(quine.nb1, . ~ . + Sex:Age:Lrn)
quine.nb3 <- update(quine.nb2, Days ~ .^4)
anova(quine.nb1, quine.nb2, quine.nb3)
quine.nb1 <- glm.nb(Days ~ Sex/(Age + Eth*Lrn), data = quine)
quine.nb2 <- update(quine.nb1, . ~ . + Sex:Age:Lrn)
quine.nb3 <- update(quine.nb2, Days ~ .^4)
anova(quine.nb1, quine.nb2, quine.nb3)

Fit Generalized Linear Mixed Models via PQL

Description

Fit a GLMM model with multivariate normal random effects, using Penalized Quasi-Likelihood.

Usage

glmmPQL(fixed, random, family, data, correlation, weights,
        control, niter = 10, verbose = TRUE, ...)
glmmPQL(fixed, random, family, data, correlation, weights,
        control, niter = 10, verbose = TRUE, ...)

Arguments

`fixed`	a two-sided linear formula giving fixed-effects part of the model.
`random`	a formula or list of formulae describing the random effects.
`family`	a GLM family.
`data`	an optional data frame, list or environment used as the first place to find variables in the formulae, `weights` and if present in `...`, `subset`.
`correlation`	an optional correlation structure.
`weights`	optional case weights as in `glm`.
`control`	an optional argument to be passed to `lme`.
`niter`	maximum number of iterations.
`verbose`	logical: print out record of iterations?
`...`	Further arguments for `lme`.

Details

glmmPQL works by repeated calls to lme, so namespace nlme will be loaded at first use. (Before 2015 it used to attach nlme but nowadays only loads the namespace.)

Unlike lme, offset terms are allowed in fixed – this is done by pre- and post-processing the calls to lme.

Note that the returned object inherits from class "lme" and that most generics will use the method for that class. As from version 3.1-158, the fitted values have any offset included, as do the results of calling predict.

Value

A object of class c("glmmPQL", "lme"): see lmeObject.

References

Schall, R. (1991) Estimation in generalized linear models with random effects. Biometrika 78, 719–727.

Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9–25.

Wolfinger, R. and O'Connell, M. (1993) Generalized linear mixed models: a pseudo-likelihood approach. Journal of Statistical Computation and Simulation 48, 233–243.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))

## an example of an offset: the coefficient of 'week' changes by one.
summary(glmmPQL(y ~ trt + week, random = ~ 1 | ID,
               family = binomial, data = bacteria))
summary(glmmPQL(y ~ trt + week + offset(week), random = ~ 1 | ID,
                family = binomial, data = bacteria))
summary(glmmPQL(y ~ trt + I(week > 2), random = ~ 1 | ID,
                family = binomial, data = bacteria))

## an example of an offset: the coefficient of 'week' changes by one.
summary(glmmPQL(y ~ trt + week, random = ~ 1 | ID,
               family = binomial, data = bacteria))
summary(glmmPQL(y ~ trt + week + offset(week), random = ~ 1 | ID,
                family = binomial, data = bacteria))

Record Times in Scottish Hill Races

Description

The record times in 1984 for 35 Scottish hill races.

Usage

hills
hills

Format

The components are:

dist: distance in miles (on the map).
climb: total height gained during the route, in feet.
time: record time in minutes.

Source

A.C. Atkinson (1986) Comment: Aspects of diagnostic regression analysis. Statistical Science 1, 397–402.

[A.C. Atkinson (1988) Transformations unmasked. Technometrics 30, 311–318 “corrects” the time for Knock Hill from 78.65 to 18.65. It is unclear if this based on the original records.]

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Plot a Histogram with Automatic Bin Width Selection

Description

Plot a histogram with automatic bin width selection, using the Scott or Freedman–Diaconis formulae.

Usage

hist.scott(x, prob = TRUE, xlab = deparse(substitute(x)), ...)
hist.FD(x, prob = TRUE, xlab = deparse(substitute(x)), ...)
hist.scott(x, prob = TRUE, xlab = deparse(substitute(x)), ...)
hist.FD(x, prob = TRUE, xlab = deparse(substitute(x)), ...)

Arguments

`x`	A data vector
`prob`	Should the plot have unit area, so be a density estimate?
`xlab`, `...`	Further arguments to `hist`.

Value

For the nclass.* functions, the suggested number of classes.

Side Effects

Plot a histogram.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.

Frequency Table from a Copenhagen Housing Conditions Survey

Description

The housing data frame has 72 rows and 5 variables.

Usage

housing
housing

Format

Sat: Satisfaction of householders with their present housing circumstances, (High, Medium or Low, ordered factor).
Infl: Perceived degree of influence householders have on the management of the property (High, Medium, Low).
Type: Type of rental accommodation, (Tower, Atrium, Apartment, Terrace).
Cont: Contact residents are afforded with other residents, (Low, High).
Freq: Frequencies: the numbers of residents in each class.

Source

Madsen, M. (1976) Statistical analysis of multiple contingency tables. Two examples. Scand. J. Statist. 3, 97–106.

Cox, D. R. and Snell, E. J. (1984) Applied Statistics, Principles and Examples. Chapman & Hall.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

options(contrasts = c("contr.treatment", "contr.poly"))

# Surrogate Poisson models
house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family = poisson,
                  data = housing)
## IGNORE_RDIFF_BEGIN
summary(house.glm0, correlation = FALSE)
## IGNORE_RDIFF_END

addterm(house.glm0, ~. + Sat:(Infl+Type+Cont), test = "Chisq")

house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
## IGNORE_RDIFF_BEGIN
summary(house.glm1, correlation = FALSE)
## IGNORE_RDIFF_END

1 - pchisq(deviance(house.glm1), house.glm1$df.residual)

dropterm(house.glm1, test = "Chisq")

addterm(house.glm1, ~. + Sat:(Infl+Type+Cont)^2, test  =  "Chisq")

hnames <- lapply(housing[, -5], levels) # omit Freq
newData <- expand.grid(hnames)
newData$Sat <- ordered(newData$Sat)
house.pm <- predict(house.glm1, newData,
                    type = "response")  # poisson means
house.pm <- matrix(house.pm, ncol = 3, byrow = TRUE,
                   dimnames = list(NULL, hnames[[1]]))
house.pr <- house.pm/drop(house.pm %*% rep(1, 3))
cbind(expand.grid(hnames[-1]), round(house.pr, 2))

# Iterative proportional scaling
loglm(Freq ~ Infl*Type*Cont + Sat*(Infl+Type+Cont), data = housing)


# multinomial model
library(nnet)
(house.mult<- multinom(Sat ~ Infl + Type + Cont, weights = Freq,
                       data = housing))
house.mult2 <- multinom(Sat ~ Infl*Type*Cont, weights = Freq,
                        data = housing)
anova(house.mult, house.mult2)

house.pm <- predict(house.mult, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pm, 2))

# proportional odds model
house.cpr <- apply(house.pr, 1, cumsum)
logit <- function(x) log(x/(1-x))
house.ld <- logit(house.cpr[2, ]) - logit(house.cpr[1, ])
(ratio <- sort(drop(house.ld)))
mean(ratio)

(house.plr <- polr(Sat ~ Infl + Type + Cont,
                   data = housing, weights = Freq))

house.pr1 <- predict(house.plr, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pr1, 2))

Fr <- matrix(housing$Freq, ncol  =  3, byrow = TRUE)
2*sum(Fr*log(house.pr/house.pr1))

house.plr2 <- stepAIC(house.plr, ~.^2)
house.plr2$anova
options(contrasts = c("contr.treatment", "contr.poly"))

# Surrogate Poisson models
house.glm0 <- glm(Freq ~ Infl*Type*Cont + Sat, family = poisson,
                  data = housing)
## IGNORE_RDIFF_BEGIN
summary(house.glm0, correlation = FALSE)
## IGNORE_RDIFF_END

addterm(house.glm0, ~. + Sat:(Infl+Type+Cont), test = "Chisq")

house.glm1 <- update(house.glm0, . ~ . + Sat*(Infl+Type+Cont))
## IGNORE_RDIFF_BEGIN
summary(house.glm1, correlation = FALSE)
## IGNORE_RDIFF_END

1 - pchisq(deviance(house.glm1), house.glm1$df.residual)

dropterm(house.glm1, test = "Chisq")

addterm(house.glm1, ~. + Sat:(Infl+Type+Cont)^2, test  =  "Chisq")

hnames <- lapply(housing[, -5], levels) # omit Freq
newData <- expand.grid(hnames)
newData$Sat <- ordered(newData$Sat)
house.pm <- predict(house.glm1, newData,
                    type = "response")  # poisson means
house.pm <- matrix(house.pm, ncol = 3, byrow = TRUE,
                   dimnames = list(NULL, hnames[[1]]))
house.pr <- house.pm/drop(house.pm %*% rep(1, 3))
cbind(expand.grid(hnames[-1]), round(house.pr, 2))

# Iterative proportional scaling
loglm(Freq ~ Infl*Type*Cont + Sat*(Infl+Type+Cont), data = housing)


# multinomial model
library(nnet)
(house.mult<- multinom(Sat ~ Infl + Type + Cont, weights = Freq,
                       data = housing))
house.mult2 <- multinom(Sat ~ Infl*Type*Cont, weights = Freq,
                        data = housing)
anova(house.mult, house.mult2)

house.pm <- predict(house.mult, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pm, 2))

# proportional odds model
house.cpr <- apply(house.pr, 1, cumsum)
logit <- function(x) log(x/(1-x))
house.ld <- logit(house.cpr[2, ]) - logit(house.cpr[1, ])
(ratio <- sort(drop(house.ld)))
mean(ratio)

(house.plr <- polr(Sat ~ Infl + Type + Cont,
                   data = housing, weights = Freq))

house.pr1 <- predict(house.plr, expand.grid(hnames[-1]), type = "probs")
cbind(expand.grid(hnames[-1]), round(house.pr1, 2))

Fr <- matrix(housing$Freq, ncol  =  3, byrow = TRUE)
2*sum(Fr*log(house.pr/house.pr1))

house.plr2 <- stepAIC(house.plr, ~.^2)
house.plr2$anova

Huber M-estimator of Location with MAD Scale

Description

Finds the Huber M-estimator of location with MAD scale.

Usage

huber(y, k = 1.5, tol = 1e-06)
huber(y, k = 1.5, tol = 1e-06)

Arguments

`y`	vector of data values
`k`	Winsorizes at `k` standard deviations
`tol`	convergence tolerance

Value

list of location and scale parameters

`mu`	location estimate
`s`	MAD scale estimate

References

Huber, P. J. (1981) Robust Statistics. Wiley.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

huber(chem)
huber(chem)

Huber Proposal 2 Robust Estimator of Location and/or Scale

Description

Finds the Huber M-estimator for location with scale specified, scale with location specified, or both if neither is specified.

Usage

hubers(y, k = 1.5, mu, s, initmu = median(y), tol = 1e-06)
hubers(y, k = 1.5, mu, s, initmu = median(y), tol = 1e-06)

Arguments

`y`	vector y of data values
`k`	Winsorizes at `k` standard deviations
`mu`	specified location
`s`	specified scale
`initmu`	initial value of `mu`
`tol`	convergence tolerance

Value

list of location and scale estimates

`mu`	location estimate
`s`	scale estimate

References

Huber, P. J. (1981) Robust Statistics. Wiley.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

hubers(chem)
hubers(chem, mu=3.68)
hubers(chem)
hubers(chem, mu=3.68)

Yields from a Barley Field Trial

Description

The immer data frame has 30 rows and 4 columns. Five varieties of barley were grown in six locations in each of 1931 and 1932.

Usage

immer
immer

Format

This data frame contains the following columns:

Loc: The location.
Var: The variety of barley ("manchuria", "svansota", "velvet", "trebi" and "peatland").
Y1: Yield in 1931.
Y2: Yield in 1932.

Source

Immer, F.R., Hayes, H.D. and LeRoy Powers (1934) Statistical determination of barley varietal adaptation. Journal of the American Society for Agronomy 26, 403–419.

Fisher, R.A. (1947) The Design of Experiments. 4th edition. Edinburgh: Oliver and Boyd.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

immer.aov <- aov(cbind(Y1,Y2) ~ Loc + Var, data = immer)
summary(immer.aov)

immer.aov <- aov((Y1+Y2)/2 ~ Var + Loc, data = immer)
summary(immer.aov)
model.tables(immer.aov, type = "means", se = TRUE, cterms = "Var")
immer.aov <- aov(cbind(Y1,Y2) ~ Loc + Var, data = immer)
summary(immer.aov)

immer.aov <- aov((Y1+Y2)/2 ~ Var + Loc, data = immer)
summary(immer.aov)
model.tables(immer.aov, type = "means", se = TRUE, cterms = "Var")

Numbers of Car Insurance claims

Description

The data given in data frame Insurance consist of the numbers of policyholders of an insurance company who were exposed to risk, and the numbers of car insurance claims made by those policyholders in the third quarter of 1973.

Usage

Insurance
Insurance

Format

This data frame contains the following columns:

District: factor: district of residence of policyholder (1 to 4): 4 is major cities.
Group: an ordered factor: group of car with levels <1 litre, 1–1.5 litre, 1.5–2 litre, >2 litre.
Age: an ordered factor: the age of the insured in 4 groups labelled <25, 25–29, 30–35, >35.
Holders: numbers of policyholders.
Claims: numbers of claims

Source

L. A. Baxter, S. M. Coutts and G. A. F. Ross (1980) Applications of linear models in motor insurance. Proceedings of the 21st International Congress of Actuaries, Zurich pp. 11–29.

M. Aitkin, D. Anderson, B. Francis and J. Hinde (1989) Statistical Modelling in GLIM. Oxford University Press.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

## main-effects fit as Poisson GLM with offset
glm(Claims ~ District + Group + Age + offset(log(Holders)),
    data = Insurance, family = poisson)

# same via loglm
loglm(Claims ~ District + Group + Age + offset(log(Holders)),
      data = Insurance)
## main-effects fit as Poisson GLM with offset
glm(Claims ~ District + Group + Age + offset(log(Holders)),
    data = Insurance, family = poisson)

# same via loglm
loglm(Claims ~ District + Group + Age + offset(log(Holders)),
      data = Insurance)

Kruskal's Non-metric Multidimensional Scaling

Description

One form of non-metric multidimensional scaling

Usage

isoMDS(d, y = cmdscale(d, k), k = 2, maxit = 50, trace = TRUE,
       tol = 1e-3, p = 2)

Shepard(d, x, p = 2)
isoMDS(d, y = cmdscale(d, k), k = 2, maxit = 50, trace = TRUE,
       tol = 1e-3, p = 2)

Shepard(d, x, p = 2)

Arguments

`d`	distance structure of the form returned by `dist`, or a full, symmetric matrix. Data are assumed to be dissimilarities or relative distances, but must be positive except for self-distance. Both missing and infinite values are allowed.
`y`	An initial configuration. If none is supplied, `cmdscale` is used to provide the classical solution, unless there are missing or infinite dissimilarities.
`k`	The desired dimension for the solution, passed to `cmdscale`.
`maxit`	The maximum number of iterations.
`trace`	Logical for tracing optimization. Default `TRUE`.
`tol`	convergence tolerance.
`p`	Power for Minkowski distance in the configuration space.
`x`	A final configuration.

Details

This chooses a k-dimensional (default k = 2) configuration to minimize the stress, the square root of the ratio of the sum of squared differences between the input distances and those of the configuration to the sum of configuration distances squared. However, the input distances are allowed a monotonic transformation.

An iterative algorithm is used, which will usually converge in around 10 iterations. As this is necessarily an $O(n^2)$ calculation, it is slow for large datasets. Further, since for the default $p = 2$ the configuration is only determined up to rotations and reflections (by convention the centroid is at the origin), the result can vary considerably from machine to machine.

Value

Two components:

`points`	A k-column vector of the fitted configuration.
`stress`	The final stress achieved (in percent).

Side Effects

If trace is true, the initial stress and the current stress are printed out every 5 iterations.

References

T. F. Cox and M. A. A. Cox (1994, 2001) Multidimensional Scaling. Chapman & Hall.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

swiss.x <- as.matrix(swiss[, -1])
swiss.dist <- dist(swiss.x)
swiss.mds <- isoMDS(swiss.dist)
plot(swiss.mds$points, type = "n")
text(swiss.mds$points, labels = as.character(1:nrow(swiss.x)))
swiss.sh <- Shepard(swiss.dist, swiss.mds$points)
plot(swiss.sh, pch = ".")
lines(swiss.sh$x, swiss.sh$yf, type = "S")
swiss.x <- as.matrix(swiss[, -1])
swiss.dist <- dist(swiss.x)
swiss.mds <- isoMDS(swiss.dist)
plot(swiss.mds$points, type = "n")
text(swiss.mds$points, labels = as.character(1:nrow(swiss.x)))
swiss.sh <- Shepard(swiss.dist, swiss.mds$points)
plot(swiss.sh, pch = ".")
lines(swiss.sh$x, swiss.sh$yf, type = "S")

Two-Dimensional Kernel Density Estimation

Description

Two-dimensional kernel density estimation with an axis-aligned bivariate normal kernel, evaluated on a square grid.

Usage

kde2d(x, y, h, n = 25, lims = c(range(x), range(y)))
kde2d(x, y, h, n = 25, lims = c(range(x), range(y)))

Arguments

`x`	x coordinate of data
`y`	y coordinate of data
`h`	vector of bandwidths for x and y directions. Defaults to normal reference bandwidth (see `bandwidth.nrd`). A scalar value will be taken to apply to both directions.
`n`	Number of grid points in each direction. Can be scalar or a length-2 integer vector.
`lims`	The limits of the rectangle covered by the grid as `c(xl, xu, yl, yu)`.

Value

A list of three components.

`x`, `y`	The x and y coordinates of the grid points, vectors of length `n`.
`z`	An `n[1]` by `n[2]` matrix of the estimated density: rows correspond to the value of `x`, columns to the value of `y`.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

attach(geyser)
plot(duration, waiting, xlim = c(0.5,6), ylim = c(40,100))
f1 <- kde2d(duration, waiting, n = 50, lims = c(0.5, 6, 40, 100))
image(f1, zlim = c(0, 0.05))
f2 <- kde2d(duration, waiting, n = 50, lims = c(0.5, 6, 40, 100),
            h = c(width.SJ(duration), width.SJ(waiting)) )
image(f2, zlim = c(0, 0.05))
persp(f2, phi = 30, theta = 20, d = 5)

plot(duration[-272], duration[-1], xlim = c(0.5, 6),
     ylim = c(1, 6),xlab = "previous duration", ylab = "duration")
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(1.5, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(0.6, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(0.4, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
detach("geyser")
attach(geyser)
plot(duration, waiting, xlim = c(0.5,6), ylim = c(40,100))
f1 <- kde2d(duration, waiting, n = 50, lims = c(0.5, 6, 40, 100))
image(f1, zlim = c(0, 0.05))
f2 <- kde2d(duration, waiting, n = 50, lims = c(0.5, 6, 40, 100),
            h = c(width.SJ(duration), width.SJ(waiting)) )
image(f2, zlim = c(0, 0.05))
persp(f2, phi = 30, theta = 20, d = 5)

plot(duration[-272], duration[-1], xlim = c(0.5, 6),
     ylim = c(1, 6),xlab = "previous duration", ylab = "duration")
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(1.5, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(0.6, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
f1 <- kde2d(duration[-272], duration[-1],
            h = rep(0.4, 2), n = 50, lims = c(0.5, 6, 0.5, 6))
contour(f1, xlab = "previous duration",
        ylab = "duration", levels  =  c(0.05, 0.1, 0.2, 0.4) )
detach("geyser")

Linear Discriminant Analysis

Description

Linear discriminant analysis.

Usage

lda(x, ...)

## S3 method for class 'formula'
lda(formula, data, ..., subset, na.action)

## Default S3 method:
lda(x, grouping, prior = proportions, tol = 1.0e-4,
    method, CV = FALSE, nu, ...)

## S3 method for class 'data.frame'
lda(x, ...)

## S3 method for class 'matrix'
lda(x, grouping, ..., subset, na.action)
lda(x, ...)

## S3 method for class 'formula'
lda(formula, data, ..., subset, na.action)

## Default S3 method:
lda(x, grouping, prior = proportions, tol = 1.0e-4,
    method, CV = FALSE, nu, ...)

## S3 method for class 'data.frame'
lda(x, ...)

## S3 method for class 'matrix'
lda(x, grouping, ..., subset, na.action)

Arguments

`formula`	A formula of the form `groups ~ x1 + x2 + ...` That is, the response is the grouping factor and the right hand side specifies the (non-factor) discriminators.
`data`	An optional data frame, list or environment from which variables specified in `formula` are preferentially to be taken.
`x`	(required if no formula is given as the principal argument.) a matrix or data frame or Matrix containing the explanatory variables.
`grouping`	(required if no formula principal argument is given.) a factor specifying the class for each observation.
`prior`	the prior probabilities of class membership. If unspecified, the class proportions for the training set are used. If present, the probabilities should be specified in the order of the factor levels.
`tol`	A tolerance to decide if a matrix is singular; it will reject variables and linear combinations of unit-variance variables whose variance is less than `tol^2`.
`subset`	An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
`na.action`	A function to specify the action to be taken if `NA`s are found. The default action is for the procedure to fail. An alternative is `na.omit`, which leads to rejection of cases with missing values on any required variable. (NOTE: If given, this argument must be named.)
`method`	`"moment"` for standard estimators of the mean and variance, `"mle"` for MLEs, `"mve"` to use `cov.mve`, or `"t"` for robust estimates based on a $t$ distribution.
`CV`	If true, returns results (classes and posterior probabilities) for leave-one-out cross-validation. Note that if the prior is estimated, the proportions in the whole dataset are used.
`nu`	degrees of freedom for `method = "t"`.
`...`	arguments passed to or from other methods.

Details

The function tries hard to detect if the within-class covariance matrix is singular. If any variable has within-group variance less than tol^2 it will stop and report the variable as constant. This could result from poor scaling of the problem, but is more likely to result from constant variables.

Specifying the prior will affect the classification unless over-ridden in predict.lda. Unlike in most statistical packages, it will also affect the rotation of the linear discriminants within their space, as a weighted between-groups covariance matrix is used. Thus the first few linear discriminants emphasize the differences between groups with the weights given by the prior, which may differ from their prevalence in the dataset.

If one or more groups is missing in the supplied data, they are dropped with a warning, but the classifications produced are with respect to the original set of levels.

Value

If CV = TRUE the return value is a list with components class, the MAP classification (a factor), and posterior, posterior probabilities for the classes.

Otherwise it is an object of class "lda" containing the following components:

`prior`	the prior probabilities used.
`means`	the group means.
`scaling`	a matrix which transforms observations to discriminant functions, normalized so that within groups covariance matrix is spherical.
`svd`	the singular values, which give the ratio of the between- and within-group standard deviations on the linear discriminant variables. Their squares are the canonical F-statistics.
`N`	The number of observations used.
`call`	The (matched) function call.

Note

This function may be called giving either a formula and optional data frame, or a matrix and grouping factor as the first two arguments. All other arguments are optional, but subset= and na.action=, if required, must be fully named.

If a formula is given as the principal argument the object may be modified using update() in the usual way.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Examples

Iris <- data.frame(rbind(iris3[,,1], iris3[,,2], iris3[,,3]),
                   Sp = rep(c("s","c","v"), rep(50,3)))
train <- sample(1:150, 75)
table(Iris$Sp[train])
## your answer may differ
##  c  s  v
## 22 23 30
z <- lda(Sp ~ ., Iris, prior = c(1,1,1)/3, subset = train)
predict(z, Iris[-train, ])$class
##  [1] s s s s s s s s s s s s s s s s s s s s s s s s s s s c c c
## [31] c c c c c c c v c c c c v c c c c c c c c c c c c v v v v v
## [61] v v v v v v v v v v v v v v v
(z1 <- update(z, . ~ . - Petal.W.))
Iris <- data.frame(rbind(iris3[,,1], iris3[,,2], iris3[,,3]),
                   Sp = rep(c("s","c","v"), rep(50,3)))
train <- sample(1:150, 75)
table(Iris$Sp[train])
## your answer may differ
##  c  s  v
## 22 23 30
z <- lda(Sp ~ ., Iris, prior = c(1,1,1)/3, subset = train)
predict(z, Iris[-train, ])$class
##  [1] s s s s s s s s s s s s s s s s s s s s s s s s s s s c c c
## [31] c c c c c c c v c c c c v c c c c c c c c c c c c v v v v v
## [61] v v v v v v v v v v v v v v v
(z1 <- update(z, . ~ . - Petal.W.))

Histograms or Density Plots of Multiple Groups

Description

Plot histograms or density plots of data on a single Fisher linear discriminant.

Usage

ldahist(data, g, nbins = 25, h, x0 = - h/1000, breaks,
        xlim = range(breaks), ymax = 0, width,
        type = c("histogram", "density", "both"),
        sep = (type != "density"),
        col = 5, xlab = deparse(substitute(data)), bty = "n", ...)
ldahist(data, g, nbins = 25, h, x0 = - h/1000, breaks,
        xlim = range(breaks), ymax = 0, width,
        type = c("histogram", "density", "both"),
        sep = (type != "density"),
        col = 5, xlab = deparse(substitute(data)), bty = "n", ...)

Arguments

`data`	vector of data. Missing values (`NA`s) are allowed and omitted.
`g`	factor or vector giving groups, of the same length as `data`.
`nbins`	Suggested number of bins to cover the whole range of the data.
`h`	The bin width (takes precedence over `nbins`).
`x0`	Shift for the bins - the breaks are at `x0 + h * (..., -1, 0, 1, ...)`
`breaks`	The set of breakpoints to be used. (Usually omitted, takes precedence over `h` and `nbins`).
`xlim`	The limits for the x-axis.
`ymax`	The upper limit for the y-axis.
`width`	Bandwidth for density estimates. If missing, the Sheather-Jones selector is used for each group separately.
`type`	Type of plot.
`sep`	Whether there is a separate plot for each group, or one combined plot.
`col`	The colour number for the bar fill.
`xlab`	label for the plot x-axis. By default, this will be the name of `data`.
`bty`	The box type for the plot - defaults to none.
`...`	additional arguments to `polygon`.

Side Effects

Histogram and/or density plots are plotted on the current device.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Survival Times and White Blood Counts for Leukaemia Patients

Description

A data frame of data from 33 leukaemia patients.

Usage

leuk
leuk

Format

A data frame with columns:

wbc: white blood count.
ag: a test result, "present" or "absent".
time: survival time in weeks.

Details

Survival times are given for 33 patients who died from acute myelogenous leukaemia. Also measured was the patient's white blood cell count at the time of diagnosis. The patients were also factored into 2 groups according to the presence or absence of a morphologic characteristic of white blood cells. Patients termed AG positive were identified by the presence of Auer rods and/or significant granulation of the leukaemic cells in the bone marrow at the time of diagnosis.

Source

Cox, D. R. and Oakes, D. (1984) Analysis of Survival Data. Chapman & Hall, p. 9.

Taken from

Feigl, P. & Zelen, M. (1965) Estimation of exponential survival probabilities with concomitant information. Biometrics 21, 826–838.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(survival)
plot(survfit(Surv(time) ~ ag, data = leuk), lty = 2:3, col = 2:3)

# now Cox models
leuk.cox <- coxph(Surv(time) ~ ag + log(wbc), leuk)
summary(leuk.cox)
library(survival)
plot(survfit(Surv(time) ~ ag, data = leuk), lty = 2:3, col = 2:3)

# now Cox models
leuk.cox <- coxph(Surv(time) ~ ag + log(wbc), leuk)
summary(leuk.cox)

Fit Linear Models by Generalized Least Squares

Description

Fit linear models by Generalized Least Squares

Usage

lm.gls(formula, data, W, subset, na.action, inverse = FALSE,
       method = "qr", model = FALSE, x = FALSE, y = FALSE,
       contrasts = NULL, ...)
lm.gls(formula, data, W, subset, na.action, inverse = FALSE,
       method = "qr", model = FALSE, x = FALSE, y = FALSE,
       contrasts = NULL, ...)

Arguments

`formula`	a formula expression as for regression models, of the form `response ~ predictors`. See the documentation of `formula` for other details.
`data`	an optional data frame, list or environment in which to interpret the variables occurring in `formula`.
`W`	a weight matrix.
`subset`	expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
`na.action`	a function to filter missing data.
`inverse`	logical: if true `W` specifies the inverse of the weight matrix: this is appropriate if a variance matrix is used.
`method`	method to be used by `lm.fit`.
`model`	should the model frame be returned?
`x`	should the design matrix be returned?
`y`	should the response be returned?
`contrasts`	a list of contrasts to be used for some or all of
`...`	additional arguments to `lm.fit`.

Details

The problem is transformed to uncorrelated form and passed to lm.fit.

Value

An object of class "lm.gls", which is similar to an "lm" object. There is no "weights" component, and only a few "lm" methods will work correctly. As from version 7.1-22 the residuals and fitted values refer to the untransformed problem.

Ridge Regression

Description

Fit a linear model by ridge regression.

Usage

lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
         x = FALSE, y = FALSE, contrasts = NULL, ...)
select(obj)
lm.ridge(formula, data, subset, na.action, lambda = 0, model = FALSE,
         x = FALSE, y = FALSE, contrasts = NULL, ...)
select(obj)

Arguments

`formula`	a formula expression as for regression models, of the form `response ~ predictors`. See the documentation of `formula` for other details. `offset` terms are allowed.
`data`	an optional data frame, list or environment in which to interpret the variables occurring in `formula`.
`subset`	expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
`na.action`	a function to filter missing data.
`lambda`	A scalar or vector of ridge constants.
`model`	should the model frame be returned? Not implemented.
`x`	should the design matrix be returned? Not implemented.
`y`	should the response be returned? Not implemented.
`contrasts`	a list of contrasts to be used for some or all of factor terms in the formula. See the `contrasts.arg` of `model.matrix.default`.
`...`	additional arguments to `lm.fit`.
`obj`	an R object, such as an `"lm.ridge"` fit.

Details

If an intercept is present in the model, its coefficient is not penalized. (If you want to penalize an intercept, put in your own constant term and remove the intercept.)

Value

A list with components

`coef`	matrix of coefficients, one row for each value of `lambda`. Note that these are not on the original scale and are for use by the `coef` method.
`scales`	scalings used on the X matrix.
`Inter`	was intercept included?
`lambda`	vector of lambda values
`ym`	mean of `y`
`xm`	column means of `x` matrix
`GCV`	vector of GCV values
`kHKB`	HKB estimate of the ridge constant.
`kLW`	L-W estimate of the ridge constant.

References

Brown, P. J. (1994) Measurement, Regression and Calibration Oxford.

Examples

longley # not the same as the S-PLUS dataset
names(longley)[1] <- "y"
lm.ridge(y ~ ., longley)
plot(lm.ridge(y ~ ., longley,
              lambda = seq(0,0.1,0.001)))
select(lm.ridge(y ~ ., longley,
               lambda = seq(0,0.1,0.0001)))
longley # not the same as the S-PLUS dataset
names(longley)[1] <- "y"
lm.ridge(y ~ ., longley)
plot(lm.ridge(y ~ ., longley,
              lambda = seq(0,0.1,0.001)))
select(lm.ridge(y ~ ., longley,
               lambda = seq(0,0.1,0.0001)))

Fit Log-Linear Models by Iterative Proportional Scaling

Description

This function provides a front-end to the standard function, loglin, to allow log-linear models to be specified and fitted in a manner similar to that of other fitting functions, such as glm.

Usage

loglm(formula, data, subset, na.action, ...)
loglm(formula, data, subset, na.action, ...)

Arguments

`formula`	A linear model formula specifying the log-linear model. If the left-hand side is empty, the `data` argument is required and must be a (complete) array of frequencies. In this case the variables on the right-hand side may be the names of the `dimnames` attribute of the frequency array, or may be the positive integers: 1, 2, 3, ... used as alternative names for the 1st, 2nd, 3rd, ... dimension (classifying factor). If the left-hand side is not empty it specifies a vector of frequencies. In this case the data argument, if present, must be a data frame from which the left-hand side vector and the classifying factors on the right-hand side are (preferentially) obtained. The usual abbreviation of a `.` to stand for ‘all other variables in the data frame’ is allowed. Any non-factors on the right-hand side of the formula are coerced to factor.
`data`	Numeric array or data frame (or list or environment). In the first case it specifies the array of frequencies; in the second it provides the data frame from which the variables occurring in the formula are preferentially obtained in the usual way. This argument may be the result of a call to `xtabs`.
`subset`	Specifies a subset of the rows in the data frame to be used. The default is to take all rows.
`na.action`	Specifies a method for handling missing observations. The default is to fail if missing values are present.
`...`	May supply other arguments to the function `loglm1`.

Details

If the left-hand side of the formula is empty the data argument supplies the frequency array and the right-hand side of the formula is used to construct the list of fixed faces as required by loglin. Structural zeros may be specified by giving a start argument with those entries set to zero, as described in the help information for loglin.

If the left-hand side is not empty, all variables on the right-hand side are regarded as classifying factors and an array of frequencies is constructed. If some cells in the complete array are not specified they are treated as structural zeros. The right-hand side of the formula is again used to construct the list of faces on which the observed and fitted totals must agree, as required by loglin. Hence terms such as a:b, a*b and a/b are all equivalent.

Value

An object of class "loglm" conveying the results of the fitted log-linear model. Methods exist for the generic functions print, summary, deviance, fitted, coef, resid, anova and update, which perform the expected tasks. Only log-likelihood ratio tests are allowed using anova.

The deviance is simply an alternative name for the log-likelihood ratio statistic for testing the current model within a saturated model, in accordance with standard usage in generalized linear models.

Warning

If structural zeros are present, the calculation of degrees of freedom may not be correct. loglin itself takes no action to allow for structural zeros. loglm deducts one degree of freedom for each structural zero, but cannot make allowance for gains in error degrees of freedom due to loss of dimension in the model space. (This would require checking the rank of the model matrix, but since iterative proportional scaling methods are developed largely to avoid constructing the model matrix explicitly, the computation is at least difficult.)

When structural zeros (or zero fitted values) are present the estimated coefficients will not be available due to infinite estimates. The deviances will normally continue to be correct, though.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

# The data frames  Cars93, minn38 and quine are available
# in the MASS package.

# Case 1: frequencies specified as an array.
sapply(minn38, function(x) length(levels(x)))
## hs phs fol sex f
##  3   4   7   2 0
##minn38a <- array(0, c(3,4,7,2), lapply(minn38[, -5], levels))
##minn38a[data.matrix(minn38[,-5])] <- minn38$f

## or more simply
minn38a <- xtabs(f ~ ., minn38)

fm <- loglm(~ 1 + 2 + 3 + 4, minn38a)  # numerals as names.
deviance(fm)
## [1] 3711.9
fm1 <- update(fm, .~.^2)
fm2 <- update(fm, .~.^3, print = TRUE)
## 5 iterations: deviation 0.075
anova(fm, fm1, fm2)

# Case 1. An array generated with xtabs.

loglm(~ Type + Origin, xtabs(~ Type + Origin, Cars93))

# Case 2.  Frequencies given as a vector in a data frame
names(quine)
## [1] "Eth"  "Sex"  "Age"  "Lrn"  "Days"
fm <- loglm(Days ~ .^2, quine)
gm <- glm(Days ~ .^2, poisson, quine)  # check glm.
c(deviance(fm), deviance(gm))          # deviances agree
## [1] 1368.7 1368.7
c(fm$df, gm$df)                        # resid df do not!
c(fm$df, gm$df.residual)               # resid df do not!
## [1] 127 128
# The loglm residual degrees of freedom is wrong because of
# a non-detectable redundancy in the model matrix.
# The data frames  Cars93, minn38 and quine are available
# in the MASS package.

# Case 1: frequencies specified as an array.
sapply(minn38, function(x) length(levels(x)))
## hs phs fol sex f
##  3   4   7   2 0
##minn38a <- array(0, c(3,4,7,2), lapply(minn38[, -5], levels))
##minn38a[data.matrix(minn38[,-5])] <- minn38$f

## or more simply
minn38a <- xtabs(f ~ ., minn38)

fm <- loglm(~ 1 + 2 + 3 + 4, minn38a)  # numerals as names.
deviance(fm)
## [1] 3711.9
fm1 <- update(fm, .~.^2)
fm2 <- update(fm, .~.^3, print = TRUE)
## 5 iterations: deviation 0.075
anova(fm, fm1, fm2)

# Case 1. An array generated with xtabs.

loglm(~ Type + Origin, xtabs(~ Type + Origin, Cars93))

# Case 2.  Frequencies given as a vector in a data frame
names(quine)
## [1] "Eth"  "Sex"  "Age"  "Lrn"  "Days"
fm <- loglm(Days ~ .^2, quine)
gm <- glm(Days ~ .^2, poisson, quine)  # check glm.
c(deviance(fm), deviance(gm))          # deviances agree
## [1] 1368.7 1368.7
c(fm$df, gm$df)                        # resid df do not!
c(fm$df, gm$df.residual)               # resid df do not!
## [1] 127 128
# The loglm residual degrees of freedom is wrong because of
# a non-detectable redundancy in the model matrix.

Estimate log Transformation Parameter

Description

Find and optionally plot the marginal (profile) likelihood for alpha for a transformation model of the form log(y + alpha) ~ x1 + x2 + ....

Usage

logtrans(object, ...)

## Default S3 method:
logtrans(object, ..., alpha = seq(0.5, 6, by = 0.25) - min(y),
         plotit = TRUE, interp =, xlab = "alpha",
         ylab = "log Likelihood")

## S3 method for class 'formula'
logtrans(object, data, ...)

## S3 method for class 'lm'
logtrans(object, ...)
logtrans(object, ...)

## Default S3 method:
logtrans(object, ..., alpha = seq(0.5, 6, by = 0.25) - min(y),
         plotit = TRUE, interp =, xlab = "alpha",
         ylab = "log Likelihood")

## S3 method for class 'formula'
logtrans(object, data, ...)

## S3 method for class 'lm'
logtrans(object, ...)

Arguments

`object`	Fitted linear model object, or formula defining the untransformed model that is `y ~ x1 + x2 + ...`. The function is generic.
`...`	If `object` is a formula, this argument may specify a data frame as for `lm`.
`alpha`	Set of values for the transformation parameter, alpha.
`plotit`	Should plotting be done?
`interp`	Should the marginal log-likelihood be interpolated with a spline approximation? (Default is `TRUE` if plotting is to be done and the number of real points is less than 100.)
`xlab`	as for `plot`.
`ylab`	as for `plot`.
`data`	optional `data` argument for `lm` fit.

Value

List with components x (for alpha) and y (for the marginal log-likelihood values).

Side Effects

A plot of the marginal log-likelihood is produced, if requested, together with an approximate mle and 95% confidence interval.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

logtrans(Days ~ Age*Sex*Eth*Lrn, data = quine,
         alpha = seq(0.75, 6.5, length.out = 20))
logtrans(Days ~ Age*Sex*Eth*Lrn, data = quine,
         alpha = seq(0.75, 6.5, length.out = 20))

Resistant Regression

Description

Fit a regression to the good points in the dataset, thereby achieving a regression estimator with a high breakdown point. lmsreg and ltsreg are compatibility wrappers.

Usage

lqs(x, ...)

## S3 method for class 'formula'
lqs(formula, data, ...,
    method = c("lts", "lqs", "lms", "S", "model.frame"),
    subset, na.action, model = TRUE,
    x.ret = FALSE, y.ret = FALSE, contrasts = NULL)

## Default S3 method:
lqs(x, y, intercept = TRUE, method = c("lts", "lqs", "lms", "S"),
    quantile, control = lqs.control(...), k0 = 1.548, seed, ...)

lmsreg(...)
ltsreg(...)
lqs(x, ...)

## S3 method for class 'formula'
lqs(formula, data, ...,
    method = c("lts", "lqs", "lms", "S", "model.frame"),
    subset, na.action, model = TRUE,
    x.ret = FALSE, y.ret = FALSE, contrasts = NULL)

## Default S3 method:
lqs(x, y, intercept = TRUE, method = c("lts", "lqs", "lms", "S"),
    quantile, control = lqs.control(...), k0 = 1.548, seed, ...)

lmsreg(...)
ltsreg(...)

Arguments

`formula`	a formula of the form `y ~ x1 + x2 + ...`.
`data`	an optional data frame, list or environemnt from which variables specified in `formula` are preferentially to be taken.
`subset`	an index vector specifying the cases to be used in fitting. (NOTE: If given, this argument must be named exactly.)
`na.action`	function to specify the action to be taken if `NA`s are found. The default action is for the procedure to fail. Alternatives include `na.omit` and `na.exclude`, which lead to omission of cases with missing values on any required variable. (NOTE: If given, this argument must be named exactly.)
`model`, `x.ret`, `y.ret`	logical. If `TRUE` the model frame, the model matrix and the response are returned, respectively.
`contrasts`	an optional list. See the `contrasts.arg` of `model.matrix.default`.
`x`	a matrix or data frame containing the explanatory variables.
`y`	the response: a vector of length the number of rows of `x`.
`intercept`	should the model include an intercept?
`method`	the method to be used. `model.frame` returns the model frame: for the others see the `Details` section. Using `lmsreg` or `ltsreg` forces `"lms"` and `"lts"` respectively.
`quantile`	the quantile to be used: see `Details`. This is over-ridden if `method = "lms"`.
`control`	additional control items: see `Details`.
`k0`	the cutoff / tuning constant used for $\chi()$ and $\psi()$ functions when `method = "S"`, currently corresponding to Tukey's ‘biweight’.
`seed`	the seed to be used for random sampling: see `.Random.seed`. The current value of `.Random.seed` will be preserved if it is set..
`...`	arguments to be passed to `lqs.default` or `lqs.control`, see `control` above and `Details`.

Details

Suppose there are n data points and p regressors, including any intercept.

The first three methods minimize some function of the sorted squared residuals. For methods "lqs" and "lms" is the quantile squared residual, and for "lts" it is the sum of the quantile smallest squared residuals. "lqs" and "lms" differ in the defaults for quantile, which are floor((n+p+1)/2) and floor((n+1)/2) respectively. For "lts" the default is floor(n/2) + floor((p+1)/2).

The "S" estimation method solves for the scale s such that the average of a function chi of the residuals divided by s is equal to a given constant.

The control argument is a list with components

psamp:: the size of each sample. Defaults to p.
nsamp:: the number of samples or "best" (the default) or "exact" or "sample". If "sample" the number chosen is min(5*p, 3000), taken from Rousseeuw and Hubert (1997). If "best" exhaustive enumeration is done up to 5000 samples; if "exact" exhaustive enumeration will be attempted however many samples are needed.
adjust:: should the intercept be optimized for each sample? Defaults to TRUE.

Value

An object of class "lqs". This is a list with components

`crit`	the value of the criterion for the best solution found, in the case of `method == "S"` before IWLS refinement.
`sing`	character. A message about the number of samples which resulted in singular fits.
`coefficients`	of the fitted linear model
`bestone`	the indices of those points fitted by the best sample found (prior to adjustment of the intercept, if requested).
`fitted.values`	the fitted values.
`residuals`	the residuals.
`scale`	estimate(s) of the scale of the error. The first is based on the fit criterion. The second (not present for `method == "S"`) is based on the variance of those residuals whose absolute value is less than 2.5 times the initial estimate.

Note

There seems no reason other than historical to use the lms and lqs options. LMS estimation is of low efficiency (converging at rate $n^{-1/3}$ ) whereas LTS has the same asymptotic efficiency as an M estimator with trimming at the quartiles (Marazzi, 1993, p.201). LQS and LTS have the same maximal breakdown value of (floor((n-p)/2) + 1)/n attained if floor((n+p)/2) <= quantile <= floor((n+p+1)/2). The only drawback mentioned of LTS is greater computation, as a sort was thought to be required (Marazzi, 1993, p.201) but this is not true as a partial sort can be used (and is used in this implementation).

Adjusting the intercept for each trial fit does need the residuals to be sorted, and may be significant extra computation if n is large and p small.

Opinions differ over the choice of psamp. Rousseeuw and Hubert (1997) only consider p; Marazzi (1993) recommends p+1 and suggests that more samples are better than adjustment for a given computational limit.

The computations are exact for a model with just an intercept and adjustment, and for LQS for a model with an intercept plus one regressor and exhaustive search with adjustment. For all other cases the minimization is only known to be approximate.

References

P. J. Rousseeuw and A. M. Leroy (1987) Robust Regression and Outlier Detection. Wiley.

A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth and Brooks/Cole.

P. Rousseeuw and M. Hubert (1997) Recent developments in PROGRESS. In L1-Statistical Procedures and Related Topics, ed Y. Dodge, IMS Lecture Notes volume 31, pp. 201–214.

Examples

## IGNORE_RDIFF_BEGIN
set.seed(123) # make reproducible
lqs(stack.loss ~ ., data = stackloss)
lqs(stack.loss ~ ., data = stackloss, method = "S", nsamp = "exact")
## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN
set.seed(123) # make reproducible
lqs(stack.loss ~ ., data = stackloss)
lqs(stack.loss ~ ., data = stackloss, method = "S", nsamp = "exact")
## IGNORE_RDIFF_END

Brain and Body Weights for 62 Species of Land Mammals

Description

A data frame with average brain and body weights for 62 species of land mammals.

Usage

mammals
mammals

Format

body: body weight in kg.
brain: brain weight in g.
name: Common name of species. (Rock hyrax-a = Heterohyrax brucci, Rock hyrax-b = Procavia habessinic..)

Source

Weisberg, S. (1985) Applied Linear Regression. 2nd edition. Wiley, pp. 144–5.

Selected from: Allison, T. and Cicchetti, D. V. (1976) Sleep in mammals: ecological and constitutional correlates. Science 194, 732–734.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Multiple Correspondence Analysis

Description

Computes a multiple correspondence analysis of a set of factors.

Usage

mca(df, nf = 2, abbrev = FALSE)
mca(df, nf = 2, abbrev = FALSE)

Arguments

`df`	A data frame containing only factors
`nf`	The number of dimensions for the MCA. Rarely 3 might be useful.
`abbrev`	Should the vertex names be abbreviated? By default these are of the form ‘factor.level’ but if `abbrev = TRUE` they are just ‘level’ which will suffice if the factors have distinct levels.

Value

An object of class "mca", with components

`rs`	The coordinates of the rows, in `nf` dimensions.
`cs`	The coordinates of the column vertices, one for each level of each factor.
`fs`	Weights for each row, used to interpolate additional factors in `predict.mca`.
`p`	The number of factors
`d`	The singular values for the `nf` dimensions.
`call`	The matched call.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

farms.mca <- mca(farms, abbrev=TRUE)
farms.mca
plot(farms.mca)
farms.mca <- mca(farms, abbrev=TRUE)
farms.mca
plot(farms.mca)

Data from a Simulated Motorcycle Accident

Description

A data frame giving a series of measurements of head acceleration in a simulated motorcycle accident, used to test crash helmets.

Usage

mcycle
mcycle

Format

times: in milliseconds after impact.
accel: in g.

Source

Silverman, B. W. (1985) Some aspects of the spline smoothing approach to non-parametric curve fitting. Journal of the Royal Statistical Society series B 47, 1–52.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Survival from Malignant Melanoma

Description

The Melanoma data frame has data on 205 patients in Denmark with malignant melanoma.

Usage

Melanoma
Melanoma

Format

This data frame contains the following columns:

time: survival time in days, possibly censored.
status: 1 died from melanoma, 2 alive, 3 dead from other causes.
sex: 1 = male, 0 = female.
age: age in years.
year: of operation.
thickness: tumour thickness in mm.
ulcer: 1 = presence, 0 = absence.

Source

P. K. Andersen, O. Borgan, R. D. Gill and N. Keiding (1993) Statistical Models based on Counting Processes. Springer.

Age of Menarche in Warsaw

Description

Proportions of female children at various ages during adolescence who have reached menarche.

Usage

menarche
menarche

Format

This data frame contains the following columns:

Age: Average age of the group. (The groups are reasonably age homogeneous.)
Total: Total number of children in the group.
Menarche: Number who have reached menarche.

Source

Milicer, H. and Szczotka, F. (1966) Age at Menarche in Warsaw girls in 1965. Human Biology 38, 199–203.

The data are also given in
Aranda-Ordaz, F.J. (1981) On two families of transformations to additivity for binary response data. Biometrika 68, 357–363.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

mprob <- glm(cbind(Menarche, Total - Menarche) ~ Age,
             binomial(link = probit), data = menarche)
mprob <- glm(cbind(Menarche, Total - Menarche) ~ Age,
             binomial(link = probit), data = menarche)

Michelson's Speed of Light Data

Description

Measurements of the speed of light in air, made between 5th June and 2nd July, 1879. The data consists of five experiments, each consisting of 20 consecutive runs. The response is the speed of light in km/s, less 299000. The currently accepted value, on this scale of measurement, is 734.5.

Usage

michelson
michelson

Format

The data frame contains the following components:

Expt: The experiment number, from 1 to 5.
Run: The run number within each experiment.
Speed: Speed-of-light measurement.

Source

A.J. Weekes (1986) A Genstat Primer. Edward Arnold.

S. M. Stigler (1977) Do robust estimators work with real data? Annals of Statistics 5, 1055–1098.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Minnesota High School Graduates of 1938

Description

The Minnesota high school graduates of 1938 were classified according to four factors, described below. The minn38 data frame has 168 rows and 5 columns.

Usage

minn38
minn38

Format

This data frame contains the following columns:

hs: high school rank: "L", "M" and "U" for lower, middle and upper third.
phs: post high school status: Enrolled in college, ("C"), enrolled in non-collegiate school, ("N"), employed full-time, ("E") and other, ("O").
fol: father's occupational level, (seven levels, "F1", "F2", ..., "F7").
sex: sex: factor with levels"F" or "M".
f: frequency.

Source

From R. L. Plackett, (1974) The Analysis of Categorical Data. London: Griffin

who quotes the data from

Hoyt, C. J., Krishnaiah, P. R. and Torrance, E. P. (1959) Analysis of complex contingency tables, J. Exp. Ed. 27, 187–194.

Accelerated Life Testing of Motorettes

Description

The motors data frame has 40 rows and 3 columns. It describes an accelerated life test at each of four temperatures of 10 motorettes, and has rather discrete times.

Usage

motors
motors

Format

This data frame contains the following columns:

temp: the temperature (degrees C) of the test.
time: the time in hours to failure or censoring at 8064 hours (= 336 days).
cens: an indicator variable for death.

Source

Kalbfleisch, J. D. and Prentice, R. L. (1980) The Statistical Analysis of Failure Time Data. New York: Wiley.

taken from

Nelson, W. D. and Hahn, G. J. (1972) Linear regression of a regression relationship from censored data. Part 1 – simple methods and their application. Technometrics, 14, 247–276.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(survival)
plot(survfit(Surv(time, cens) ~ factor(temp), motors), conf.int = FALSE)
# fit Weibull model
motor.wei <- survreg(Surv(time, cens) ~ temp, motors)
summary(motor.wei)
# and predict at 130C
unlist(predict(motor.wei, data.frame(temp=130), se.fit = TRUE))

motor.cox <- coxph(Surv(time, cens) ~ temp, motors)
summary(motor.cox)
# predict at temperature 200
plot(survfit(motor.cox, newdata = data.frame(temp=200),
     conf.type = "log-log"))
summary( survfit(motor.cox, newdata = data.frame(temp=130)) )
library(survival)
plot(survfit(Surv(time, cens) ~ factor(temp), motors), conf.int = FALSE)
# fit Weibull model
motor.wei <- survreg(Surv(time, cens) ~ temp, motors)
summary(motor.wei)
# and predict at 130C
unlist(predict(motor.wei, data.frame(temp=130), se.fit = TRUE))

motor.cox <- coxph(Surv(time, cens) ~ temp, motors)
summary(motor.cox)
# predict at temperature 200
plot(survfit(motor.cox, newdata = data.frame(temp=200),
     conf.type = "log-log"))
summary( survfit(motor.cox, newdata = data.frame(temp=130)) )

Effect of Calcium Chloride on Muscle Contraction in Rat Hearts

Description

The purpose of this experiment was to assess the influence of calcium in solution on the contraction of heart muscle in rats. The left auricle of 21 rat hearts was isolated and on several occasions a constant-length strip of tissue was electrically stimulated and dipped into various concentrations of calcium chloride solution, after which the shortening of the strip was accurately measured as the response.

Usage

muscle
muscle

Format

This data frame contains the following columns:

Strip: which heart muscle strip was used?
Conc: concentration of calcium chloride solution, in multiples of 2.2 mM.
Length: the change in length (shortening) of the strip, (allegedly) in mm.

Source

Linder, A., Chakravarti, I. M. and Vuagnat, P. (1964) Fitting asymptotic regression curves with different asymptotes. In Contributions to Statistics. Presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday, ed. C. R. Rao, pp. 221–228. Oxford: Pergamon Press.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer.

Examples

## IGNORE_RDIFF_BEGIN
A <- model.matrix(~ Strip - 1, data=muscle)
rats.nls1 <- nls(log(Length) ~ cbind(A, rho^Conc),
   data = muscle, start = c(rho=0.1), algorithm="plinear")
(B <- coef(rats.nls1))

st <- list(alpha = B[2:22], beta = B[23], rho = B[1])
(rats.nls2 <- nls(log(Length) ~ alpha[Strip] + beta*rho^Conc,
                  data = muscle, start = st))
## IGNORE_RDIFF_END

Muscle <- with(muscle, {
Muscle <- expand.grid(Conc = sort(unique(Conc)), Strip = levels(Strip))
Muscle$Yhat <- predict(rats.nls2, Muscle)
Muscle <- cbind(Muscle, logLength = rep(as.numeric(NA), 126))
ind <- match(paste(Strip, Conc),
            paste(Muscle$Strip, Muscle$Conc))
Muscle$logLength[ind] <- log(Length)
Muscle})

lattice::xyplot(Yhat ~ Conc | Strip, Muscle, as.table = TRUE,
   ylim = range(c(Muscle$Yhat, Muscle$logLength), na.rm = TRUE),
   subscripts = TRUE, xlab = "Calcium Chloride concentration (mM)",
   ylab = "log(Length in mm)", panel =
   function(x, y, subscripts, ...) {
      panel.xyplot(x, Muscle$logLength[subscripts], ...)
      llines(spline(x, y))
   })
## IGNORE_RDIFF_BEGIN
A <- model.matrix(~ Strip - 1, data=muscle)
rats.nls1 <- nls(log(Length) ~ cbind(A, rho^Conc),
   data = muscle, start = c(rho=0.1), algorithm="plinear")
(B <- coef(rats.nls1))

st <- list(alpha = B[2:22], beta = B[23], rho = B[1])
(rats.nls2 <- nls(log(Length) ~ alpha[Strip] + beta*rho^Conc,
                  data = muscle, start = st))
## IGNORE_RDIFF_END

Muscle <- with(muscle, {
Muscle <- expand.grid(Conc = sort(unique(Conc)), Strip = levels(Strip))
Muscle$Yhat <- predict(rats.nls2, Muscle)
Muscle <- cbind(Muscle, logLength = rep(as.numeric(NA), 126))
ind <- match(paste(Strip, Conc),
            paste(Muscle$Strip, Muscle$Conc))
Muscle$logLength[ind] <- log(Length)
Muscle})

lattice::xyplot(Yhat ~ Conc | Strip, Muscle, as.table = TRUE,
   ylim = range(c(Muscle$Yhat, Muscle$logLength), na.rm = TRUE),
   subscripts = TRUE, xlab = "Calcium Chloride concentration (mM)",
   ylab = "log(Length in mm)", panel =
   function(x, y, subscripts, ...) {
      panel.xyplot(x, Muscle$logLength[subscripts], ...)
      llines(spline(x, y))
   })

Simulate from a Multivariate Normal Distribution

Description

Produces one or more samples from the specified multivariate normal distribution.

Usage

mvrnorm(n = 1, mu, Sigma, tol = 1e-6, empirical = FALSE, EISPACK = FALSE)
mvrnorm(n = 1, mu, Sigma, tol = 1e-6, empirical = FALSE, EISPACK = FALSE)

Arguments

`n`	the number of samples required.
`mu`	a vector giving the means of the variables.
`Sigma`	a positive-definite symmetric matrix specifying the covariance matrix of the variables.
`tol`	tolerance (relative to largest variance) for numerical lack of positive-definiteness in `Sigma`.
`empirical`	logical. If true, mu and Sigma specify the empirical not population mean and covariance matrix.
`EISPACK`	logical: values other than `FALSE` are an error.

Details

The matrix decomposition is done via eigen; although a Choleski decomposition might be faster, the eigendecomposition is stabler.

Value

If n = 1 a vector of the same length as mu, otherwise an n by length(mu) matrix with one sample in each row.

Side Effects

Causes creation of the dataset .Random.seed if it does not already exist, otherwise its value is updated.

References

B. D. Ripley (1987) Stochastic Simulation. Wiley. Page 98.

Examples

Sigma <- matrix(c(10,3,3,2),2,2)
Sigma
var(mvrnorm(n = 1000, rep(0, 2), Sigma))
var(mvrnorm(n = 1000, rep(0, 2), Sigma, empirical = TRUE))
Sigma <- matrix(c(10,3,3,2),2,2)
Sigma
var(mvrnorm(n = 1000, rep(0, 2), Sigma))
var(mvrnorm(n = 1000, rep(0, 2), Sigma, empirical = TRUE))

Family function for Negative Binomial GLMs

Description

Specifies the information required to fit a Negative Binomial generalized linear model, with known theta parameter, using glm().

Usage

negative.binomial(theta = stop("'theta' must be specified"), link = "log")
negative.binomial(theta = stop("'theta' must be specified"), link = "log")

Arguments

`theta`	The known value of the additional parameter, `theta`.
`link`	The link function, as a character string, name or one-element character vector specifying one of `log`, `sqrt` or `identity`, or an object of class `"link-glm"`.

Value

An object of class "family", a list of functions and expressions needed by glm() to fit a Negative Binomial generalized linear model.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

# Fitting a Negative Binomial model to the quine data
#   with theta = 2 assumed known.
#
glm(Days ~ .^4, family = negative.binomial(2), data = quine)
# Fitting a Negative Binomial model to the quine data
#   with theta = 2 assumed known.
#
glm(Days ~ .^4, family = negative.binomial(2), data = quine)

Newcomb's Measurements of the Passage Time of Light

Description

A numeric vector giving the ‘Third Series’ of measurements of the passage time of light recorded by Newcomb in 1882. The given values divided by 1000 plus 24.8 give the time in millionths of a second for light to traverse a known distance. The ‘true’ value is now considered to be 33.02.

The dataset is given in the order in Staudte and Sheather. Stigler (1977, Table 5) gives the dataset as

    28 26 33 24 34 -44 27 16 40 -2 29 22 24 21 25 30 23 29 31 19
    24 20 36 32 36 28 25 21 28 29 37 25 28 26 30 32 36 26 30 22
    36 23 27 27 28 27 31 27 26 33 26 32 32 24 39 28 24 25 32 25
    29 27 28 29 16 23

However, order is not relevant to its use as an example of robust estimation. (Thanks to Anthony Unwin for bringing this difference to our attention.)

Usage

newcomb
newcomb

Source

S. M. Stigler (1973) Simon Newcomb, Percy Daniell, and the history of robust estimation 1885–1920. Journal of the American Statistical Association 68, 872–879.

S. M. Stigler (1977) Do robust estimators work with real data? Annals of Statistics, 5, 1055–1098.

R. G. Staudte and S. J. Sheather (1990) Robust Estimation and Testing. Wiley.

Eighth-Grade Pupils in the Netherlands

Description

Snijders and Bosker (1999) use as a running example a study of 2287 eighth-grade pupils (aged about 11) in 132 classes in 131 schools in the Netherlands. Only the variables used in our examples are supplied.

Usage

nlschools
nlschools

Format

This data frame contains 2287 rows and the following columns:

lang: language test score.
IQ: verbal IQ.
class: class ID.
GS: class size: number of eighth-grade pupils recorded in the class (there may be others: see COMB, and some may have been omitted with missing values).
SES: social-economic status of pupil's family.
COMB: were the pupils taught in a multi-grade class (0/1)? Classes which contained pupils from grades 7 and 8 are coded 1, but only eighth-graders were tested.

Source

Snijders, T. A. B. and Bosker, R. J. (1999) Multilevel Analysis. An Introduction to Basic and Advanced Multilevel Modelling. London: Sage.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples


nl1 <- within(nlschools, {
IQave <- tapply(IQ, class, mean)[as.character(class)]
IQ <- IQ - IQave
})
cen <- c("IQ", "IQave", "SES")
nl1[cen] <- scale(nl1[cen], center = TRUE, scale = FALSE)

nl.lme <- nlme::lme(lang ~ IQ*COMB + IQave + SES,
                    random = ~ IQ | class, data = nl1)
## IGNORE_RDIFF_BEGIN
summary(nl.lme)
## IGNORE_RDIFF_END

nl1 <- within(nlschools, {
IQave <- tapply(IQ, class, mean)[as.character(class)]
IQ <- IQ - IQave
})
cen <- c("IQ", "IQave", "SES")
nl1[cen] <- scale(nl1[cen], center = TRUE, scale = FALSE)

nl.lme <- nlme::lme(lang ~ IQ*COMB + IQave + SES,
                    random = ~ IQ | class, data = nl1)
## IGNORE_RDIFF_BEGIN
summary(nl.lme)
## IGNORE_RDIFF_END

Classical N, P, K Factorial Experiment

Description

A classical N, P, K (nitrogen, phosphate, potassium) factorial experiment on the growth of peas conducted on 6 blocks. Each half of a fractional factorial design confounding the NPK interaction was used on 3 of the plots.

Usage

npk
npk

Format

The npk data frame has 24 rows and 5 columns:

block: which block (label 1 to 6).
N: indicator (0/1) for the application of nitrogen.
P: indicator (0/1) for the application of phosphate.
K: indicator (0/1) for the application of potassium.
yield: Yield of peas, in pounds/plot (the plots were (1/70) acre).

Note

This dataset is also contained in R 3.0.2 and later.

Source

Imperial College, London, M.Sc. exercise sheet.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

options(contrasts = c("contr.sum", "contr.poly"))
npk.aov <- aov(yield ~ block + N*P*K, npk)
## IGNORE_RDIFF_BEGIN
npk.aov
summary(npk.aov)
alias(npk.aov)
coef(npk.aov)
options(contrasts = c("contr.treatment", "contr.poly"))
npk.aov1 <- aov(yield ~ block + N + K, data = npk)
summary.lm(npk.aov1)
se.contrast(npk.aov1, list(N=="0", N=="1"), data = npk)
model.tables(npk.aov1, type = "means", se = TRUE)
## IGNORE_RDIFF_ENDoptions(contrasts = c("contr.sum", "contr.poly"))
npk.aov <- aov(yield ~ block + N*P*K, npk)
## IGNORE_RDIFF_BEGIN
npk.aov
summary(npk.aov)
alias(npk.aov)
coef(npk.aov)
options(contrasts = c("contr.treatment", "contr.poly"))
npk.aov1 <- aov(yield ~ block + N + K, data = npk)
summary.lm(npk.aov1)
se.contrast(npk.aov1, list(N=="0", N=="1"), data = npk)
model.tables(npk.aov1, type = "means", se = TRUE)
## IGNORE_RDIFF_END

US Naval Petroleum Reserve No. 1 data

Description

Data on the locations, porosity and permeability (a measure of oil flow) on 104 oil wells in the US Naval Petroleum Reserve No. 1 in California.

Usage

npr1
npr1

Format

This data frame contains the following columns:

x: x coordinates, in miles (origin unspecified)..
y: y coordinates, in miles.
perm: permeability in milli-Darcies.
por: porosity (%).

Source

Maher, J.C., Carter, R.D. and Lantz, R.J. (1975) Petroleum geology of Naval Petroleum Reserve No. 1, Elk Hills, Kern County, California. USGS Professional Paper 912.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Null Spaces of Matrices

Description

Given a matrix, M, find a matrix N giving a basis for the (left) null space. That is crossprod(N, M) = t(N) %*% M is an all-zero matrix and N has the maximum number of linearly independent columns.

Usage

Null(M)
Null(M)

Arguments

`M`	Input matrix. A vector is coerced to a 1-column matrix.

Details

For a basis for the (right) null space $\{x : Mx = 0\}$ , use Null(t(M)).

Value

The matrix N with the basis for the (left) null space, or a matrix with zero columns if the matrix M is square and of maximal rank.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

# The function is currently defined as
function(M)
{
    tmp <- qr(M)
    set <- if(tmp$rank == 0L) seq_len(ncol(M)) else  -seq_len(tmp$rank)
    qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
}
# The function is currently defined as
function(M)
{
    tmp <- qr(M)
    set <- if(tmp$rank == 0L) seq_len(ncol(M)) else  -seq_len(tmp$rank)
    qr.Q(tmp, complete = TRUE)[, set, drop = FALSE]
}

Data from an Oats Field Trial

Description

The yield of oats from a split-plot field trial using three varieties and four levels of manurial treatment. The experiment was laid out in 6 blocks of 3 main plots, each split into 4 sub-plots. The varieties were applied to the main plots and the manurial treatments to the sub-plots.

Usage

oats
oats

Format

This data frame contains the following columns:

B: Blocks, levels I, II, III, IV, V and VI.
V: Varieties, 3 levels.
N: Nitrogen (manurial) treatment, levels 0.0cwt, 0.2cwt, 0.4cwt and 0.6cwt, showing the application in cwt/acre.
Y: Yields in 1/4lbs per sub-plot, each of area 1/80 acre.

Source

Yates, F. (1935) Complex experiments, Journal of the Royal Statistical Society Suppl. 2, 181–247.

Also given in Yates, F. (1970) Experimental design: Selected papers of Frank Yates, C.B.E, F.R.S. London: Griffin.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

oats$Nf <- ordered(oats$N, levels = sort(levels(oats$N)))
oats.aov <- aov(Y ~ Nf*V + Error(B/V), data = oats, qr = TRUE)
## IGNORE_RDIFF_BEGIN
summary(oats.aov)
summary(oats.aov, split = list(Nf=list(L=1, Dev=2:3)))
## IGNORE_RDIFF_END
par(mfrow = c(1,2), pty = "s")
plot(fitted(oats.aov[[4]]), studres(oats.aov[[4]]))
abline(h = 0, lty = 2)
oats.pr <- proj(oats.aov)
qqnorm(oats.pr[[4]][,"Residuals"], ylab = "Stratum 4 residuals")
qqline(oats.pr[[4]][,"Residuals"])

par(mfrow = c(1,1), pty = "m")
oats.aov2 <- aov(Y ~ N + V + Error(B/V), data = oats, qr = TRUE)
model.tables(oats.aov2, type = "means", se = TRUE)
oats$Nf <- ordered(oats$N, levels = sort(levels(oats$N)))
oats.aov <- aov(Y ~ Nf*V + Error(B/V), data = oats, qr = TRUE)
## IGNORE_RDIFF_BEGIN
summary(oats.aov)
summary(oats.aov, split = list(Nf=list(L=1, Dev=2:3)))
## IGNORE_RDIFF_END
par(mfrow = c(1,2), pty = "s")
plot(fitted(oats.aov[[4]]), studres(oats.aov[[4]]))
abline(h = 0, lty = 2)
oats.pr <- proj(oats.aov)
qqnorm(oats.pr[[4]][,"Residuals"], ylab = "Stratum 4 residuals")
qqline(oats.pr[[4]][,"Residuals"])

par(mfrow = c(1,1), pty = "m")
oats.aov2 <- aov(Y ~ N + V + Error(B/V), data = oats, qr = TRUE)
model.tables(oats.aov2, type = "means", se = TRUE)

Tests of Auditory Perception in Children with OME

Description

Experiments were performed on children on their ability to differentiate a signal in broad-band noise. The noise was played from a pair of speakers and a signal was added to just one channel; the subject had to turn his/her head to the channel with the added signal. The signal was either coherent (the amplitude of the noise was increased for a period) or incoherent (independent noise was added for the same period to form the same increase in power).

The threshold used in the original analysis was the stimulus loudness needs to get 75% correct responses. Some of the children had suffered from otitis media with effusion (OME).

Usage

OME
OME

Format

The OME data frame has 1129 rows and 7 columns:

ID: Subject ID (1 to 99, with some IDs missing). A few subjects were measured at different ages.
OME: "low" or "high" or "N/A" (at ages other than 30 and 60 months).
Age: Age of the subject (months).
Loud: Loudness of stimulus, in decibels.
Noise: Whether the signal in the stimulus was "coherent" or "incoherent".
Correct: Number of correct responses from Trials trials.
Trials: Number of trials performed.

Background

The experiment was to study otitis media with effusion (OME), a very common childhood condition where the middle ear space, which is normally air-filled, becomes congested by a fluid. There is a concomitant fluctuating, conductive hearing loss which can result in various language, cognitive and social deficits. The term ‘binaural hearing’ is used to describe the listening conditions in which the brain is processing information from both ears at the same time. The brain computes differences in the intensity and/or timing of signals arriving at each ear which contributes to sound localisation and also to our ability to hear in background noise.

Some years ago, it was found that children of 7–8 years with a history of significant OME had significantly worse binaural hearing than children without such a history, despite having equivalent sensitivity. The question remained as to whether it was the timing, the duration, or the degree of severity of the otitis media episodes during critical periods, which affected later binaural hearing. In an attempt to begin to answer this question, 95 children were monitored for the presence of effusion every month since birth. On the basis of OME experience in their first two years, the test population was split into one group of high OME prevalence and one of low prevalence.

Source

Sarah Hogan, Dept of Physiology, University of Oxford, via Dept of Statistics Consulting Service

Examples

# Fit logistic curve from p = 0.5 to p = 1.0
fp1 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/scal)),
             c("L75", "scal"),
             function(x,L75,scal)NULL)
nls(Correct/Trials ~ fp1(Loud, L75, scal), data = OME,
    start = c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
    data = OME[OME$Noise == "coherent",],
    start=c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, scal=3))

# individual fits for each experiment

aa <- factor(OME$Age)
ab <- 10*OME$ID + unclass(aa)
ac <- unclass(factor(ab))
OME$UID <- as.vector(ac)
OME$UIDn <- OME$UID + 0.1*(OME$Noise == "incoherent")
rm(aa, ab, ac)
OMEi <- OME

library(nlme)
fp2 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/2)),
            "L75", function(x,L75) NULL)
dec <- getOption("OutDec")
options(show.error.messages = FALSE, OutDec=".")
OMEi.nls <- nlsList(Correct/Trials ~ fp2(Loud, L75) | UIDn,
   data = OMEi, start = list(L75=45), control = list(maxiter=100))
options(show.error.messages = TRUE, OutDec=dec)
tmp <- sapply(OMEi.nls, function(X)
              {if(is.null(X)) NA else as.vector(coef(X))})
OMEif <- data.frame(UID = round(as.numeric((names(tmp)))),
         Noise = rep(c("coherent", "incoherent"), 110),
         L75 = as.vector(tmp), stringsAsFactors = TRUE)
OMEif$Age <- OME$Age[match(OMEif$UID, OME$UID)]
OMEif$OME <- OME$OME[match(OMEif$UID, OME$UID)]
OMEif <- OMEif[OMEif$L75 > 30,]
summary(lm(L75 ~ Noise/Age, data = OMEif, na.action = na.omit))
summary(lm(L75 ~ Noise/(Age + OME), data = OMEif,
           subset = (Age >= 30 & Age <= 60),
           na.action = na.omit), correlation = FALSE)

# Or fit by weighted least squares
fpl75 <- deriv(~ sqrt(n)*(r/n - 0.5 - 0.5/(1 + exp(-(x-L75)/scal))),
               c("L75", "scal"),
               function(r,n,x,L75,scal) NULL)
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
    data = OME[OME$Noise == "coherent",],
    start = c(L75=45, scal=3))
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, scal=3))

# Test to see if the curves shift with age
fpl75age <- deriv(~sqrt(n)*(r/n -  0.5 - 0.5/(1 +
                  exp(-(x-L75-slope*age)/scal))),
                  c("L75", "slope", "scal"),
                  function(r,n,x,age,L75,slope,scal) NULL)
OME.nls1 <-
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
    data = OME[OME$Noise == "coherent",],
    start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls1)))

OME.nls2 <-
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls2)))

# Now allow random effects by using NLME
OMEf <- OME[rep(1:nrow(OME), OME$Trials),]
OMEf$Resp <- with(OME, rep(rep(c(1,0), length(Trials)),
                          t(cbind(Correct, Trials-Correct))))
OMEf <- OMEf[, -match(c("Correct", "Trials"), names(OMEf))]

## Not run: ## these fail in R on most platforms
fp2 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/exp(lsc))),
             c("L75", "lsc"),
             function(x, L75, lsc) NULL)
try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
     fixed = list(L75 ~ Age, lsc ~ 1),
     random = L75 + lsc ~ 1 | UID,
     data = OMEf[OMEf$Noise == "coherent",], method = "ML",
     start = list(fixed=c(L75=c(48.7, -0.03), lsc=0.24)), verbose = TRUE)))

try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
     fixed = list(L75 ~ Age, lsc ~ 1),
     random = L75 + lsc ~ 1 | UID,
     data = OMEf[OMEf$Noise == "incoherent",], method = "ML",
     start = list(fixed=c(L75=c(41.5, -0.1), lsc=0)), verbose = TRUE)))

## End(Not run)# Fit logistic curve from p = 0.5 to p = 1.0
fp1 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/scal)),
             c("L75", "scal"),
             function(x,L75,scal)NULL)
nls(Correct/Trials ~ fp1(Loud, L75, scal), data = OME,
    start = c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
    data = OME[OME$Noise == "coherent",],
    start=c(L75=45, scal=3))
nls(Correct/Trials ~ fp1(Loud, L75, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, scal=3))

# individual fits for each experiment

aa <- factor(OME$Age)
ab <- 10*OME$ID + unclass(aa)
ac <- unclass(factor(ab))
OME$UID <- as.vector(ac)
OME$UIDn <- OME$UID + 0.1*(OME$Noise == "incoherent")
rm(aa, ab, ac)
OMEi <- OME

library(nlme)
fp2 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/2)),
            "L75", function(x,L75) NULL)
dec <- getOption("OutDec")
options(show.error.messages = FALSE, OutDec=".")
OMEi.nls <- nlsList(Correct/Trials ~ fp2(Loud, L75) | UIDn,
   data = OMEi, start = list(L75=45), control = list(maxiter=100))
options(show.error.messages = TRUE, OutDec=dec)
tmp <- sapply(OMEi.nls, function(X)
              {if(is.null(X)) NA else as.vector(coef(X))})
OMEif <- data.frame(UID = round(as.numeric((names(tmp)))),
         Noise = rep(c("coherent", "incoherent"), 110),
         L75 = as.vector(tmp), stringsAsFactors = TRUE)
OMEif$Age <- OME$Age[match(OMEif$UID, OME$UID)]
OMEif$OME <- OME$OME[match(OMEif$UID, OME$UID)]
OMEif <- OMEif[OMEif$L75 > 30,]
summary(lm(L75 ~ Noise/Age, data = OMEif, na.action = na.omit))
summary(lm(L75 ~ Noise/(Age + OME), data = OMEif,
           subset = (Age >= 30 & Age <= 60),
           na.action = na.omit), correlation = FALSE)

# Or fit by weighted least squares
fpl75 <- deriv(~ sqrt(n)*(r/n - 0.5 - 0.5/(1 + exp(-(x-L75)/scal))),
               c("L75", "scal"),
               function(r,n,x,L75,scal) NULL)
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
    data = OME[OME$Noise == "coherent",],
    start = c(L75=45, scal=3))
nls(0 ~ fpl75(Correct, Trials, Loud, L75, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, scal=3))

# Test to see if the curves shift with age
fpl75age <- deriv(~sqrt(n)*(r/n -  0.5 - 0.5/(1 +
                  exp(-(x-L75-slope*age)/scal))),
                  c("L75", "slope", "scal"),
                  function(r,n,x,age,L75,slope,scal) NULL)
OME.nls1 <-
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
    data = OME[OME$Noise == "coherent",],
    start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls1)))

OME.nls2 <-
nls(0 ~ fpl75age(Correct, Trials, Loud, Age, L75, slope, scal),
    data = OME[OME$Noise == "incoherent",],
    start = c(L75=45, slope=0, scal=2))
sqrt(diag(vcov(OME.nls2)))

# Now allow random effects by using NLME
OMEf <- OME[rep(1:nrow(OME), OME$Trials),]
OMEf$Resp <- with(OME, rep(rep(c(1,0), length(Trials)),
                          t(cbind(Correct, Trials-Correct))))
OMEf <- OMEf[, -match(c("Correct", "Trials"), names(OMEf))]

## Not run: ## these fail in R on most platforms
fp2 <- deriv(~ 0.5 + 0.5/(1 + exp(-(x-L75)/exp(lsc))),
             c("L75", "lsc"),
             function(x, L75, lsc) NULL)
try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
     fixed = list(L75 ~ Age, lsc ~ 1),
     random = L75 + lsc ~ 1 | UID,
     data = OMEf[OMEf$Noise == "coherent",], method = "ML",
     start = list(fixed=c(L75=c(48.7, -0.03), lsc=0.24)), verbose = TRUE)))

try(summary(nlme(Resp ~ fp2(Loud, L75, lsc),
     fixed = list(L75 ~ Age, lsc ~ 1),
     random = L75 + lsc ~ 1 | UID,
     data = OMEf[OMEf$Noise == "incoherent",], method = "ML",
     start = list(fixed=c(L75=c(41.5, -0.1), lsc=0)), verbose = TRUE)))

## End(Not run)

The Painter's Data of de Piles

Description

The subjective assessment, on a 0 to 20 integer scale, of 54 classical painters. The painters were assessed on four characteristics: composition, drawing, colour and expression. The data is due to the Eighteenth century art critic, de Piles.

Usage

painters
painters

Format

The row names of the data frame are the painters. The components are:

Composition: Composition score.
Drawing: Drawing score.
Colour: Colour score.
Expression: Expression score.
School: The school to which a painter belongs, as indicated by a factor level code as follows: "A": Renaissance; "B": Mannerist; "C": Seicento; "D": Venetian; "E": Lombard; "F": Sixteenth Century; "G": Seventeenth Century; "H": French.

Source

A. J. Weekes (1986) A Genstat Primer. Edward Arnold.

M. Davenport and G. Studdert-Kennedy (1972) The statistical analysis of aesthetic judgement: an exploration. Applied Statistics 21, 324–333.

I. T. Jolliffe (1986) Principal Component Analysis. Springer.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Produce Pairwise Scatterplots from an 'lda' Fit

Description

Pairwise scatterplot of the data on the linear discriminants.

Usage

## S3 method for class 'lda'
pairs(x, labels = colnames(x), panel = panel.lda,
     dimen, abbrev = FALSE, ..., cex=0.7, type = c("std", "trellis"))
## S3 method for class 'lda'
pairs(x, labels = colnames(x), panel = panel.lda,
     dimen, abbrev = FALSE, ..., cex=0.7, type = c("std", "trellis"))

Arguments

`x`	Object of class `"lda"`.
`labels`	vector of character strings for labelling the variables.
`panel`	panel function to plot the data in each panel.
`dimen`	The number of linear discriminants to be used for the plot; if this exceeds the number determined by `x` the smaller value is used.
`abbrev`	whether the group labels are abbreviated on the plots. If `abbrev > 0` this gives `minlength` in the call to `abbreviate`.
`...`	additional arguments for `pairs.default`.
`cex`	graphics parameter `cex` for labels on plots.
`type`	type of plot. The default is in the style of `pairs.default`; the style `"trellis"` uses the Trellis function `splom`.

Details

This function is a method for the generic function pairs() for class "lda". It can be invoked by calling pairs(x) for an object x of the appropriate class, or directly by calling pairs.lda(x) regardless of the class of the object.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Parallel Coordinates Plot

Description

Parallel coordinates plot

Usage

parcoord(x, col = 1, lty = 1, var.label = FALSE, ...)
parcoord(x, col = 1, lty = 1, var.label = FALSE, ...)

Arguments

`x`	a matrix or data frame who columns represent variables. Missing values are allowed.
`col`	A vector of colours, recycled as necessary for each observation.
`lty`	A vector of line types, recycled as necessary for each observation.
`var.label`	If `TRUE`, each variable's axis is labelled with maximum and minimum values.
`...`	Further graphics parameters which are passed to `matplot`.

Side Effects

a parallel coordinates plots is drawn.

Author(s)

B. D. Ripley. Enhancements based on ideas and code by Fabian Scheipl.

References

Wegman, E. J. (1990) Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association 85, 664–675.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

parcoord(state.x77[, c(7, 4, 6, 2, 5, 3)])

ir <- rbind(iris3[,,1], iris3[,,2], iris3[,,3])
parcoord(log(ir)[, c(3, 4, 2, 1)], col = 1 + (0:149)%/%50)
parcoord(state.x77[, c(7, 4, 6, 2, 5, 3)])

ir <- rbind(iris3[,,1], iris3[,,2], iris3[,,3])
parcoord(log(ir)[, c(3, 4, 2, 1)], col = 1 + (0:149)%/%50)

N. L. Prater's Petrol Refinery Data

Description

The yield of a petroleum refining process with four covariates. The crude oil appears to come from only 10 distinct samples.

These data were originally used by Prater (1956) to build an estimation equation for the yield of the refining process of crude oil to gasoline.

Usage

petrol
petrol

Format

The variables are as follows

No: crude oil sample identification label. (Factor.)
SG: specific gravity, degrees API. (Constant within sample.)
VP: vapour pressure in pounds per square inch. (Constant within sample.)
V10: volatility of crude; ASTM 10% point. (Constant within sample.)
EP: desired volatility of gasoline. (The end point. Varies within sample.)
Y: yield as a percentage of crude.

Source

N. H. Prater (1956) Estimate gasoline yields from crudes. Petroleum Refiner 35, 236–238.

This dataset is also given in D. J. Hand, F. Daly, K. McConway, D. Lunn and E. Ostrowski (eds) (1994) A Handbook of Small Data Sets. Chapman & Hall.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

library(nlme)
Petrol <- petrol
Petrol[, 2:5] <- scale(as.matrix(Petrol[, 2:5]), scale = FALSE)
pet3.lme <- lme(Y ~ SG + VP + V10 + EP,
                random = ~ 1 | No, data = Petrol)
pet3.lme <- update(pet3.lme, method = "ML")
pet4.lme <- update(pet3.lme, fixed. = Y ~ V10 + EP)
anova(pet4.lme, pet3.lme)
library(nlme)
Petrol <- petrol
Petrol[, 2:5] <- scale(as.matrix(Petrol[, 2:5]), scale = FALSE)
pet3.lme <- lme(Y ~ SG + VP + V10 + EP,
                random = ~ 1 | No, data = Petrol)
pet3.lme <- update(pet3.lme, method = "ML")
pet4.lme <- update(pet3.lme, fixed. = Y ~ V10 + EP)
anova(pet4.lme, pet3.lme)

Diabetes in Pima Indian Women

Description

A population of women who were at least 21 years old, of Pima Indian heritage and living near Phoenix, Arizona, was tested for diabetes according to World Health Organization criteria. The data were collected by the US National Institute of Diabetes and Digestive and Kidney Diseases. We used the 532 complete records after dropping the (mainly missing) data on serum insulin.

Usage

Pima.tr
Pima.tr2
Pima.te
Pima.tr
Pima.tr2
Pima.te

Format

These data frames contains the following columns:

npreg: number of pregnancies.
glu: plasma glucose concentration in an oral glucose tolerance test.
bp: diastolic blood pressure (mm Hg).
skin: triceps skin fold thickness (mm).
bmi: body mass index (weight in kg/(height in m) $^2$ ).
ped: diabetes pedigree function.
age: age in years.
type: Yes or No, for diabetic according to WHO criteria.

Details

The training set Pima.tr contains a randomly selected set of 200 subjects, and Pima.te contains the remaining 332 subjects. Pima.tr2 contains Pima.tr plus 100 subjects with missing values in the explanatory variables.

Source

Smith, J. W., Everhart, J. E., Dickson, W. C., Knowler, W. C. and Johannes, R. S. (1988) Using the ADAP learning algorithm to forecast the onset of diabetes mellitus. In Proceedings of the Symposium on Computer Applications in Medical Care (Washington, 1988), ed. R. A. Greenes, pp. 261–265. Los Alamitos, CA: IEEE Computer Society Press.

Ripley, B.D. (1996) Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.

Plot Method for Class 'lda'

Description

Plots a set of data on one, two or more linear discriminants.

Usage

## S3 method for class 'lda'
plot(x, panel = panel.lda, ..., cex = 0.7, dimen,
     abbrev = FALSE, xlab = "LD1", ylab = "LD2")
## S3 method for class 'lda'
plot(x, panel = panel.lda, ..., cex = 0.7, dimen,
     abbrev = FALSE, xlab = "LD1", ylab = "LD2")

Arguments

`x`	An object of class `"lda"`.
`panel`	the panel function used to plot the data.
`...`	additional arguments to `pairs`, `ldahist` or `eqscplot`.
`cex`	graphics parameter `cex` for labels on plots.
`dimen`	The number of linear discriminants to be used for the plot; if this exceeds the number determined by `x` the smaller value is used.
`abbrev`	whether the group labels are abbreviated on the plots. If `abbrev > 0` this gives `minlength` in the call to `abbreviate`.
`xlab`	label for the x axis
`ylab`	label for the y axis

Details

This function is a method for the generic function plot() for class "lda". It can be invoked by calling plot(x) for an object x of the appropriate class, or directly by calling plot.lda(x) regardless of the class of the object.

The behaviour is determined by the value of dimen. For dimen > 2, a pairs plot is used. For dimen = 2, an equiscaled scatter plot is drawn. For dimen = 1, a set of histograms or density plots are drawn. Use argument type to match "histogram" or "density" or "both".

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Plot Method for Objects of Class 'mca'

Description

Plot a multiple correspondence analysis.

Usage

## S3 method for class 'mca'
plot(x, rows = TRUE, col, cex = par("cex"), ...)
## S3 method for class 'mca'
plot(x, rows = TRUE, col, cex = par("cex"), ...)

Arguments

`x`	An object of class `"mca"`.
`rows`	Should the coordinates for the rows be plotted, or just the vertices for the levels?
`col`, `cex`	The colours and `cex` to be used for the row points and level vertices respectively.
`...`	Additional parameters to `plot`.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

plot(mca(farms, abbrev = TRUE))
plot(mca(farms, abbrev = TRUE))

Ordered Logistic or Probit Regression

Description

Fits a logistic or probit regression model to an ordered factor response. The default logistic case is proportional odds logistic regression, after which the function is named.

Usage

polr(formula, data, weights, start, ..., subset, na.action,
     contrasts = NULL, Hess = FALSE, model = TRUE,
     method = c("logistic", "probit", "loglog", "cloglog", "cauchit"))
polr(formula, data, weights, start, ..., subset, na.action,
     contrasts = NULL, Hess = FALSE, model = TRUE,
     method = c("logistic", "probit", "loglog", "cloglog", "cauchit"))

Arguments

`formula`	a formula expression as for regression models, of the form `response ~ predictors`. The response should be a factor (preferably an ordered factor), which will be interpreted as an ordinal response, with levels ordered as in the factor. The model must have an intercept: attempts to remove one will lead to a warning and be ignored. An offset may be used. See the documentation of `formula` for other details.
`data`	an optional data frame, list or environment in which to interpret the variables occurring in `formula`.
`weights`	optional case weights in fitting. Default to 1.
`start`	initial values for the parameters. This is in the format `c(coefficients, zeta)`: see the Values section.
`...`	additional arguments to be passed to `optim`, most often a `control` argument.
`subset`	expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.
`na.action`	a function to filter missing data.
`contrasts`	a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.
`Hess`	logical for whether the Hessian (the observed information matrix) should be returned. Use this if you intend to call `summary` or `vcov` on the fit.
`model`	logical for whether the model matrix should be returned.
`method`	logistic or probit or (complementary) log-log or cauchit (corresponding to a Cauchy latent variable).

Details

This model is what Agresti (2002) calls a cumulative link model. The basic interpretation is as a coarsened version of a latent variable $Y_i$ which has a logistic or normal or extreme-value or Cauchy distribution with scale parameter one and a linear model for the mean. The ordered factor which is observed is which bin $Y_i$ falls into with breakpoints

$\zeta_0 = -\infty < \zeta_1 < \cdots < \zeta_K = \infty$

This leads to the model

$\mbox{logit} P(Y \le k | x) = \zeta_k - \eta$

with logit replaced by probit for a normal latent variable, and $\eta$ being the linear predictor, a linear function of the explanatory variables (with no intercept). Note that it is quite common for other software to use the opposite sign for $\eta$ (and hence the coefficients beta).

In the logistic case, the left-hand side of the last display is the log odds of category $k$ or less, and since these are log odds which differ only by a constant for different $k$ , the odds are proportional. Hence the term proportional odds logistic regression.

The log-log and complementary log-log links are the increasing functions $F^{-1}(p) = -log(-log(p))$ and $F^{-1}(p) = log(-log(1-p))$ ; some call the first the ‘negative log-log’ link. These correspond to a latent variable with the extreme-value distribution for the maximum and minimum respectively.

A proportional hazards model for grouped survival times can be obtained by using the complementary log-log link with grouping ordered by increasing times.

predict, summary, vcov, anova, model.frame and an extractAIC method for use with stepAIC (and step). There are also profile and confint methods.

Value

A object of class "polr". This has components

`coefficients`	the coefficients of the linear predictor, which has no intercept.
`zeta`	the intercepts for the class boundaries.
`deviance`	the residual deviance.
`fitted.values`	a matrix, with a column for each level of the response.
`lev`	the names of the response levels.
`terms`	the `terms` structure describing the model.
`df.residual`	the number of residual degrees of freedoms, calculated using the weights.
`edf`	the (effective) number of degrees of freedom used by the model
`n`, `nobs`	the (effective) number of observations, calculated using the weights. (`nobs` is for use by `stepAIC`.
`call`	the matched call.
`method`	the matched method used.
`convergence`	the convergence code returned by `optim`.
`niter`	the number of function and gradient evaluations used by `optim`.
`lp`	the linear predictor (including any offset).
`Hessian`	(if `Hess` is true). Note that this is a numerical approximation derived from the optimization proces.
`model`	(if `model` is true).

Note

The vcov method uses the approximate Hessian: for reliable results the model matrix should be sensibly scaled with all columns having range the order of one.

Prior to version 7.3-32, method = "cloglog" confusingly gave the log-log link, implicitly assuming the first response level was the ‘best’.

References

Agresti, A. (2002) Categorical Data. Second edition. Wiley.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

options(contrasts = c("contr.treatment", "contr.poly"))
house.plr <- polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
house.plr
summary(house.plr, digits = 3)
## slightly worse fit from
summary(update(house.plr, method = "probit", Hess = TRUE), digits = 3)
## although it is not really appropriate, can fit
summary(update(house.plr, method = "loglog", Hess = TRUE), digits = 3)
summary(update(house.plr, method = "cloglog", Hess = TRUE), digits = 3)

predict(house.plr, housing, type = "p")
addterm(house.plr, ~.^2, test = "Chisq")
house.plr2 <- stepAIC(house.plr, ~.^2)
house.plr2$anova
anova(house.plr, house.plr2)

house.plr <- update(house.plr, Hess=TRUE)
pr <- profile(house.plr)
confint(pr)
plot(pr)
pairs(pr)
options(contrasts = c("contr.treatment", "contr.poly"))
house.plr <- polr(Sat ~ Infl + Type + Cont, weights = Freq, data = housing)
house.plr
summary(house.plr, digits = 3)
## slightly worse fit from
summary(update(house.plr, method = "probit", Hess = TRUE), digits = 3)
## although it is not really appropriate, can fit
summary(update(house.plr, method = "loglog", Hess = TRUE), digits = 3)
summary(update(house.plr, method = "cloglog", Hess = TRUE), digits = 3)

predict(house.plr, housing, type = "p")
addterm(house.plr, ~.^2, test = "Chisq")
house.plr2 <- stepAIC(house.plr, ~.^2)
house.plr2$anova
anova(house.plr, house.plr2)

house.plr <- update(house.plr, Hess=TRUE)
pr <- profile(house.plr)
confint(pr)
plot(pr)
pairs(pr)

Predict Method for glmmPQL Fits

Description

Obtains predictions from a fitted generalized linear model with random effects.

Usage

## S3 method for class 'glmmPQL'
predict(object, newdata = NULL, type = c("link", "response"),
       level, na.action = na.pass, ...)
## S3 method for class 'glmmPQL'
predict(object, newdata = NULL, type = c("link", "response"),
       level, na.action = na.pass, ...)

Arguments

`object`	a fitted object of class inheriting from `"glmmPQL"`.
`newdata`	optionally, a data frame in which to look for variables with which to predict.
`type`	the type of prediction required. The default is on the scale of the linear predictors; the alternative `"response"` is on the scale of the response variable. Thus for a default binomial model the default predictions are of log-odds (probabilities on logit scale) and `type = "response"` gives the predicted probabilities.
`level`	an optional integer vector giving the level(s) of grouping to be used in obtaining the predictions. Level values increase from outermost to innermost grouping, with level zero corresponding to the population predictions. Defaults to the highest or innermost level of grouping.
`na.action`	function determining what should be done with missing values in `newdata`. The default is to predict `NA`.
`...`	further arguments passed to or from other methods.

Value

If level is a single integer, a vector otherwise a data frame.

Examples

fit <- glmmPQL(y ~ trt + I(week > 2), random = ~1 |  ID,
               family = binomial, data = bacteria)
predict(fit, bacteria, level = 0, type="response")
predict(fit, bacteria, level = 1, type="response")
fit <- glmmPQL(y ~ trt + I(week > 2), random = ~1 |  ID,
               family = binomial, data = bacteria)
predict(fit, bacteria, level = 0, type="response")
predict(fit, bacteria, level = 1, type="response")

Classify Multivariate Observations by Linear Discrimination

Description

Classify multivariate observations in conjunction with lda, and also project data onto the linear discriminants.

Usage

## S3 method for class 'lda'
predict(object, newdata, prior = object$prior, dimen,
        method = c("plug-in", "predictive", "debiased"), ...)
## S3 method for class 'lda'
predict(object, newdata, prior = object$prior, dimen,
        method = c("plug-in", "predictive", "debiased"), ...)

Arguments

`object`	object of class `"lda"`
`newdata`	data frame of cases to be classified or, if `object` has a formula, a data frame with columns of the same names as the variables used. A vector will be interpreted as a row vector. If newdata is missing, an attempt will be made to retrieve the data used to fit the `lda` object.
`prior`	The prior probabilities of the classes, by default the proportions in the training set or what was set in the call to `lda`.
`dimen`	the dimension of the space to be used. If this is less than `min(p, ng-1)`, only the first `dimen` discriminant components are used (except for `method="predictive"`), and only those dimensions are returned in `x`.
`method`	This determines how the parameter estimation is handled. With `"plug-in"` (the default) the usual unbiased parameter estimates are used and assumed to be correct. With `"debiased"` an unbiased estimator of the log posterior probabilities is used, and with `"predictive"` the parameter estimates are integrated out using a vague prior.
`...`	arguments based from or to other methods

Details

This function is a method for the generic function predict() for class "lda". It can be invoked by calling predict(x) for an object x of the appropriate class, or directly by calling predict.lda(x) regardless of the class of the object.

Missing values in newdata are handled by returning NA if the linear discriminants cannot be evaluated. If newdata is omitted and the na.action of the fit omitted cases, these will be omitted on the prediction.

This version centres the linear discriminants so that the weighted mean (weighted by prior) of the group centroids is at the origin.

Value

a list with components

`class`	The MAP classification (a factor)
`posterior`	posterior probabilities for the classes
`x`	the scores of test cases on up to `dimen` discriminant variables

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
z <- lda(train, cl)
predict(z, test)$class
tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
z <- lda(train, cl)
predict(z, test)$class

Predict from an lqs Fit

Description

Predict from an resistant regression fitted by lqs.

Usage

## S3 method for class 'lqs'
predict(object, newdata, na.action = na.pass, ...)
## S3 method for class 'lqs'
predict(object, newdata, na.action = na.pass, ...)

Arguments

`object`	object inheriting from class `"lqs"`
`newdata`	matrix or data frame of cases to be predicted or, if `object` has a formula, a data frame with columns of the same names as the variables used. A vector will be interpreted as a row vector. If `newdata` is missing, an attempt will be made to retrieve the data used to fit the `lqs` object.
`na.action`	function determining what should be done with missing values in `newdata`. The default is to predict `NA`.
`...`	arguments to be passed from or to other methods.

Details

This function is a method for the generic function predict() for class lqs. It can be invoked by calling predict(x) for an object x of the appropriate class, or directly by calling predict.lqs(x) regardless of the class of the object.

Missing values in newdata are handled by returning NA if the linear fit cannot be evaluated. If newdata is omitted and the na.action of the fit omitted cases, these will be omitted on the prediction.

Value

A vector of predictions.

Author(s)

B.D. Ripley

Examples

set.seed(123)
fm <- lqs(stack.loss ~ ., data = stackloss, method = "S", nsamp = "exact")
predict(fm, stackloss)
set.seed(123)
fm <- lqs(stack.loss ~ ., data = stackloss, method = "S", nsamp = "exact")
predict(fm, stackloss)

Predict Method for Class 'mca'

Description

Used to compute coordinates for additional rows or additional factors in a multiple correspondence analysis.

Usage

## S3 method for class 'mca'
predict(object, newdata, type = c("row", "factor"), ...)
## S3 method for class 'mca'
predict(object, newdata, type = c("row", "factor"), ...)

Arguments

`object`	An object of class `"mca"`, usually the result of a call to `mca`.
`newdata`	A data frame containing either additional rows of the factors used to fit `object` or additional factors for the cases used in the original fit.
`type`	Are predictions required for further rows or for new factors?
`...`	Additional arguments from `predict`: unused.

Value

If type = "row", the coordinates for the additional rows.

If type = "factor", the coordinates of the column vertices for the levels of the new factors.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Classify from Quadratic Discriminant Analysis

Description

Classify multivariate observations in conjunction with qda

Usage

## S3 method for class 'qda'
predict(object, newdata, prior = object$prior,
        method = c("plug-in", "predictive", "debiased", "looCV"), ...)
## S3 method for class 'qda'
predict(object, newdata, prior = object$prior,
        method = c("plug-in", "predictive", "debiased", "looCV"), ...)

Arguments

`object`	object of class `"qda"`
`newdata`	data frame of cases to be classified or, if `object` has a formula, a data frame with columns of the same names as the variables used. A vector will be interpreted as a row vector. If newdata is missing, an attempt will be made to retrieve the data used to fit the `qda` object.
`prior`	The prior probabilities of the classes, by default the proportions in the training set or what was set in the call to `qda`.
`method`	This determines how the parameter estimation is handled. With `"plug-in"` (the default) the usual unbiased parameter estimates are used and assumed to be correct. With `"debiased"` an unbiased estimator of the log posterior probabilities is used, and with `"predictive"` the parameter estimates are integrated out using a vague prior. With `"looCV"` the leave-one-out cross-validation fits to the original dataset are computed and returned.
`...`	arguments based from or to other methods

Details

This function is a method for the generic function predict() for class "qda". It can be invoked by calling predict(x) for an object x of the appropriate class, or directly by calling predict.qda(x) regardless of the class of the object.

Missing values in newdata are handled by returning NA if the quadratic discriminants cannot be evaluated. If newdata is omitted and the na.action of the fit omitted cases, these will be omitted on the prediction.

Value

a list with components

`class`	The MAP classification (a factor)
`posterior`	posterior probabilities for the classes

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
zq <- qda(train, cl)
predict(zq, test)$class
tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
zq <- qda(train, cl)
predict(zq, test)$class

Method for Profiling glm Objects

Description

Investigates the profile log-likelihood function for a fitted model of class "glm".

As from R 4.4.0 was migrated to package stats with additional functionality.

Quadratic Discriminant Analysis

Description

Quadratic discriminant analysis.

Usage

qda(x, ...)

## S3 method for class 'formula'
qda(formula, data, ..., subset, na.action)

## Default S3 method:
qda(x, grouping, prior = proportions,
    method, CV = FALSE, nu, ...)

## S3 method for class 'data.frame'
qda(x, ...)

## S3 method for class 'matrix'
qda(x, grouping, ..., subset, na.action)
qda(x, ...)

## S3 method for class 'formula'
qda(formula, data, ..., subset, na.action)

## Default S3 method:
qda(x, grouping, prior = proportions,
    method, CV = FALSE, nu, ...)

## S3 method for class 'data.frame'
qda(x, ...)

## S3 method for class 'matrix'
qda(x, grouping, ..., subset, na.action)

Arguments

`formula`	A formula of the form `groups ~ x1 + x2 + ...` That is, the response is the grouping factor and the right hand side specifies the (non-factor) discriminators.
`data`	An optional data frame, list or environment from which variables specified in `formula` are preferentially to be taken.
`x`	(required if no formula is given as the principal argument.) a matrix or data frame or Matrix containing the explanatory variables.
`grouping`	(required if no formula principal argument is given.) a factor specifying the class for each observation.
`prior`	the prior probabilities of class membership. If unspecified, the class proportions for the training set are used. If specified, the probabilities should be specified in the order of the factor levels.
`subset`	An index vector specifying the cases to be used in the training sample. (NOTE: If given, this argument must be named.)
`na.action`	A function to specify the action to be taken if `NA`s are found. The default action is for the procedure to fail. An alternative is na.omit, which leads to rejection of cases with missing values on any required variable. (NOTE: If given, this argument must be named.)
`method`	`"moment"` for standard estimators of the mean and variance, `"mle"` for MLEs, `"mve"` to use `cov.mve`, or `"t"` for robust estimates based on a t distribution.
`CV`	If true, returns results (classes and posterior probabilities) for leave-out-out cross-validation. Note that if the prior is estimated, the proportions in the whole dataset are used.
`nu`	degrees of freedom for `method = "t"`.
`...`	arguments passed to or from other methods.

Details

Uses a QR decomposition which will give an error message if the within-group variance is singular for any group.

Value

an object of class "qda" containing the following components:

`prior`	the prior probabilities used.
`means`	the group means.
`scaling`	for each group `i`, `scaling[,,i]` is an array which transforms observations so that within-groups covariance matrix is spherical.
`ldet`	a vector of half log determinants of the dispersion matrix.
`lev`	the levels of the grouping factor.
`terms`	(if formula is a formula) an object of mode expression and class term summarizing the formula.
`call`	the (matched) function call.

unless CV=TRUE, when the return value is a list with components:

`class`	The MAP classification (a factor)
`posterior`	posterior probabilities for the classes

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Examples

tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
z <- qda(train, cl)
predict(z,test)$class
tr <- sample(1:50, 25)
train <- rbind(iris3[tr,,1], iris3[tr,,2], iris3[tr,,3])
test <- rbind(iris3[-tr,,1], iris3[-tr,,2], iris3[-tr,,3])
cl <- factor(c(rep("s",25), rep("c",25), rep("v",25)))
z <- qda(train, cl)
predict(z,test)$class

Absenteeism from School in Rural New South Wales

Description

The quine data frame has 146 rows and 5 columns. Children from Walgett, New South Wales, Australia, were classified by Culture, Age, Sex and Learner status and the number of days absent from school in a particular school year was recorded.

Usage

quine
quine

Format

This data frame contains the following columns:

Eth: ethnic background: Aboriginal or Not, ("A" or "N").
Sex: sex: factor with levels ("F" or "M").
Age: age group: Primary ("F0"), or forms "F1," "F2" or "F3".
Lrn: learner status: factor with levels Average or Slow learner, ("AL" or "SL").
Days: days absent from school in the year.

Source

S. Quine, quoted in Aitkin, M. (1978) The analysis of unbalanced cross classifications (with discussion). Journal of the Royal Statistical Society series A 141, 195–223.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Blood Pressure in Rabbits

Description

Five rabbits were studied on two occasions, after treatment with saline (control) and after treatment with the $5-HT_3$ antagonist MDL 72222. After each treatment ascending doses of phenylbiguanide were injected intravenously at 10 minute intervals and the responses of mean blood pressure measured. The goal was to test whether the cardiogenic chemoreflex elicited by phenylbiguanide depends on the activation of $5-HT_3$ receptors.

Usage

Rabbit
Rabbit

Format

This data frame contains 60 rows and the following variables:

BPchange: change in blood pressure relative to the start of the experiment.
Dose: dose of Phenylbiguanide in micrograms.
Run: label of run ("C1" to "C5", then "M1" to "M5").
Treatment: placebo or the $5-HT_3$ antagonist MDL 72222.
Animal: label of animal used ("R1" to "R5").

Source

J. Ludbrook (1994) Repeated measurements and multiple comparisons in cardiovascular research. Cardiovascular Research 28, 303–311.
[The numerical data are not in the paper but were supplied by Professor Ludbrook]

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Rational Approximation

Description

Find rational approximations to the components of a real numeric object using a standard continued fraction method.

Usage

rational(x, cycles = 10, max.denominator = 2000, ...)
rational(x, cycles = 10, max.denominator = 2000, ...)

Arguments

`x`	Any object of mode numeric. Missing values are now allowed.
`cycles`	The maximum number of steps to be used in the continued fraction approximation process.
`max.denominator`	An early termination criterion. If any partial denominator exceeds `max.denominator` the continued fraction stops at that point.
`...`	arguments passed to or from other methods.

Details

Each component is first expanded in a continued fraction of the form

x = floor(x) + 1/(p1 + 1/(p2 + ...)))

Value

A numeric object with the same attributes as x but with entries rational approximations to the values. This effectively rounds relative to the size of the object and replaces very small entries by zero.

Examples

X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
rational(solve(X, X/5))
X <- matrix(runif(25), 5, 5)
zapsmall(solve(X, X/5)) # print near-zeroes as zero
rational(solve(X, X/5))

Convert a Formula Transformed by 'denumerate'

Description

denumerate converts a formula written using the conventions of loglm into one that terms is able to process. renumerate converts it back again to a form like the original.

Usage

renumerate(x)
renumerate(x)

Arguments

`x`	A formula, normally as modified by `denumerate`.

Details

This is an inverse function to denumerate. It is only needed since terms returns an expanded form of the original formula where the non-marginal terms are exposed. This expanded form is mapped back into a form corresponding to the one that the user originally supplied.

Value

A formula where all variables with names of the form .vn, where n is an integer, converted to numbers, n, as allowed by the formula conventions of loglm.

Examples

denumerate(~(1+2+3)^3 + a/b)
## ~ (.v1 + .v2 + .v3)^3 + a/b
renumerate(.Last.value)
## ~ (1 + 2 + 3)^3 + a/b
denumerate(~(1+2+3)^3 + a/b)
## ~ (.v1 + .v2 + .v3)^3 + a/b
renumerate(.Last.value)
## ~ (1 + 2 + 3)^3 + a/b

Robust Fitting of Linear Models

Description

Fit a linear model by robust regression using an M estimator.

Usage

rlm(x, ...)

## S3 method for class 'formula'
rlm(formula, data, weights, ..., subset, na.action,
    method = c("M", "MM", "model.frame"),
    wt.method = c("inv.var", "case"),
    model = TRUE, x.ret = TRUE, y.ret = FALSE, contrasts = NULL)

## Default S3 method:
rlm(x, y, weights, ..., w = rep(1, nrow(x)),
    init = "ls", psi = psi.huber,
    scale.est = c("MAD", "Huber", "proposal 2"), k2 = 1.345,
    method = c("M", "MM"), wt.method = c("inv.var", "case"),
    maxit = 20, acc = 1e-4, test.vec = "resid", lqs.control = NULL)

psi.huber(u, k = 1.345, deriv = 0)
psi.hampel(u, a = 2, b = 4, c = 8, deriv = 0)
psi.bisquare(u, c = 4.685, deriv = 0)
rlm(x, ...)

## S3 method for class 'formula'
rlm(formula, data, weights, ..., subset, na.action,
    method = c("M", "MM", "model.frame"),
    wt.method = c("inv.var", "case"),
    model = TRUE, x.ret = TRUE, y.ret = FALSE, contrasts = NULL)

## Default S3 method:
rlm(x, y, weights, ..., w = rep(1, nrow(x)),
    init = "ls", psi = psi.huber,
    scale.est = c("MAD", "Huber", "proposal 2"), k2 = 1.345,
    method = c("M", "MM"), wt.method = c("inv.var", "case"),
    maxit = 20, acc = 1e-4, test.vec = "resid", lqs.control = NULL)

psi.huber(u, k = 1.345, deriv = 0)
psi.hampel(u, a = 2, b = 4, c = 8, deriv = 0)
psi.bisquare(u, c = 4.685, deriv = 0)

Arguments

`formula`	a formula of the form `y ~ x1 + x2 + ...`.
`data`	an optional data frame, list or environment from which variables specified in `formula` are preferentially to be taken.
`weights`	a vector of prior weights for each case.
`subset`	An index vector specifying the cases to be used in fitting.
`na.action`	A function to specify the action to be taken if `NA`s are found. The ‘factory-fresh’ default action in R is `na.omit`, and can be changed by `options(na.action=)`.
`x`	a matrix or data frame containing the explanatory variables.
`y`	the response: a vector of length the number of rows of `x`.
`method`	currently either M-estimation or MM-estimation or (for the `formula` method only) find the model frame. MM-estimation is M-estimation with Tukey's biweight initialized by a specific S-estimator. See the ‘Details’ section.
`wt.method`	are the weights case weights (giving the relative importance of case, so a weight of 2 means there are two of these) or the inverse of the variances, so a weight of two means this error is half as variable?
`model`	should the model frame be returned in the object?
`x.ret`	should the model matrix be returned in the object?
`y.ret`	should the response be returned in the object?
`contrasts`	optional contrast specifications: see `lm`.
`w`	(optional) initial down-weighting for each case.
`init`	(optional) initial values for the coefficients OR a method to find initial values OR the result of a fit with a `coef` component. Known methods are `"ls"` (the default) for an initial least-squares fit using weights `w*weights`, and `"lts"` for an unweighted least-trimmed squares fit with 200 samples.
`psi`	the psi function is specified by this argument. It must give (possibly by name) a function `g(x, ..., deriv)` that for `deriv=0` returns psi(x)/x and for `deriv=1` returns psi'(x). Tuning constants will be passed in via `...`.
`scale.est`	method of scale estimation: re-scaled MAD of the residuals (default) or Huber's proposal 2 (which can be selected by either `"Huber"` or `"proposal 2"`).
`k2`	tuning constant used for Huber proposal 2 scale estimation.
`maxit`	the limit on the number of IWLS iterations.
`acc`	the accuracy for the stopping criterion.
`test.vec`	the stopping criterion is based on changes in this vector.
`...`	additional arguments to be passed to `rlm.default` or to the `psi` function.
`lqs.control`	An optional list of control values for `lqs`.
`u`	numeric vector of evaluation points.
`k`, `a`, `b`, `c`	tuning constants.
`deriv`	`0` or `1`: compute values of the psi function or of its first derivative.

Details

Fitting is done by iterated re-weighted least squares (IWLS).

Psi functions are supplied for the Huber, Hampel and Tukey bisquare proposals as psi.huber, psi.hampel and psi.bisquare. Huber's corresponds to a convex optimization problem and gives a unique solution (up to collinearity). The other two will have multiple local minima, and a good starting point is desirable.

Selecting method = "MM" selects a specific set of options which ensures that the estimator has a high breakdown point. The initial set of coefficients and the final scale are selected by an S-estimator with k0 = 1.548; this gives (for $n \gg p$ ) breakdown point 0.5. The final estimator is an M-estimator with Tukey's biweight and fixed scale that will inherit this breakdown point provided c > k0; this is true for the default value of c that corresponds to 95% relative efficiency at the normal. Case weights are not supported for method = "MM".

Value

An object of class "rlm" inheriting from "lm". Note that the df.residual component is deliberately set to NA to avoid inappropriate estimation of the residual scale from the residual mean square by "lm" methods.

The additional components not in an lm object are

`s`	the robust scale estimate used
`w`	the weights used in the IWLS process
`psi`	the psi function with parameters substituted
`conv`	the convergence criteria at each iteration
`converged`	did the IWLS converge?
`wresid`	a working residual, weighted for `"inv.var"` weights only.

Note

Prior to version 7.3-52, offset terms in formula were omitted from fitted and predicted values.

References

P. J. Huber (1981) Robust Statistics. Wiley.

F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw and W. A. Stahel (1986) Robust Statistics: The Approach based on Influence Functions. Wiley.

A. Marazzi (1993) Algorithms, Routines and S Functions for Robust Statistics. Wadsworth & Brooks/Cole.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

summary(rlm(stack.loss ~ ., stackloss))
rlm(stack.loss ~ ., stackloss, psi = psi.hampel, init = "lts")
rlm(stack.loss ~ ., stackloss, psi = psi.bisquare)
summary(rlm(stack.loss ~ ., stackloss))
rlm(stack.loss ~ ., stackloss, psi = psi.hampel, init = "lts")
rlm(stack.loss ~ ., stackloss, psi = psi.bisquare)

Relative Curvature Measures for Non-Linear Regression

Description

Calculates the root mean square parameter effects and intrinsic relative curvatures, $c^\theta$ and $c^\iota$ , for a fitted nonlinear regression, as defined in Bates & Watts, section 7.3, p. 253ff

Usage

rms.curv(obj)
rms.curv(obj)

Arguments

obj

Fitted model object of class "nls". The model must be fitted using the default algorithm.

Details

The method of section 7.3.1 of Bates & Watts is implemented. The function deriv3 should be used generate a model function with first derivative (gradient) matrix and second derivative (Hessian) array attributes. This function should then be used to fit the nonlinear regression model.

A print method, print.rms.curv, prints the pc and ic components only, suitably annotated.

If either pc or ic exceeds some threshold (0.3 has been suggested) the curvature is unacceptably high for the planar assumption.

Value

A list of class rms.curv with components pc and ic for parameter effects and intrinsic relative curvatures multiplied by sqrt(F), ct and ci for $c^\theta$ and $c^\iota$ (unmultiplied), and C the C-array as used in section 7.3.1 of Bates & Watts.

References

Bates, D. M, and Watts, D. G. (1988) Nonlinear Regression Analysis and its Applications. Wiley, New York.

Examples

# The treated sample from the Puromycin data
mmcurve <- deriv3(~ Vm * conc/(K + conc), c("Vm", "K"),
                  function(Vm, K, conc) NULL)
Treated <- Puromycin[Puromycin$state == "treated", ]
(Purfit1 <- nls(rate ~ mmcurve(Vm, K, conc), data = Treated,
                start = list(Vm=200, K=0.1)))
rms.curv(Purfit1)
##Parameter effects: c^theta x sqrt(F) = 0.2121
##        Intrinsic: c^iota  x sqrt(F) = 0.092
# The treated sample from the Puromycin data
mmcurve <- deriv3(~ Vm * conc/(K + conc), c("Vm", "K"),
                  function(Vm, K, conc) NULL)
Treated <- Puromycin[Puromycin$state == "treated", ]
(Purfit1 <- nls(rate ~ mmcurve(Vm, K, conc), data = Treated,
                start = list(Vm=200, K=0.1)))
rms.curv(Purfit1)
##Parameter effects: c^theta x sqrt(F) = 0.2121
##        Intrinsic: c^iota  x sqrt(F) = 0.092

Simulate Negative Binomial Variates

Description

Function to generate random outcomes from a Negative Binomial distribution, with mean mu and variance mu + mu^2/theta.

Usage

rnegbin(n, mu = n, theta = stop("'theta' must be specified"))
rnegbin(n, mu = n, theta = stop("'theta' must be specified"))

Arguments

`n`	If a scalar, the number of sample values required. If a vector, `length(n)` is the number required and `n` is used as the mean vector if `mu` is not specified.
`mu`	The vector of means. Short vectors are recycled.
`theta`	Vector of values of the `theta` parameter. Short vectors are recycled.

Details

The function uses the representation of the Negative Binomial distribution as a continuous mixture of Poisson distributions with Gamma distributed means. Unlike rnbinom the index can be arbitrary.

Value

Vector of random Negative Binomial variate values.

Side Effects

Changes .Random.seed in the usual way.

Examples

# Negative Binomials with means fitted(fm) and theta = 4.5
fm <- glm.nb(Days ~ ., data = quine)
dummy <- rnegbin(fitted(fm), theta = 4.5)
# Negative Binomials with means fitted(fm) and theta = 4.5
fm <- glm.nb(Days ~ ., data = quine)
dummy <- rnegbin(fitted(fm), theta = 4.5)

Road Accident Deaths in US States

Description

A data frame with the annual deaths in road accidents for half the US states.

Usage

road
road

Format

Columns are:

state: name.
deaths: number of deaths.
drivers: number of drivers (in 10,000s).
popden: population density in people per square mile.
rural: length of rural roads, in 1000s of miles.
temp: average daily maximum temperature in January.
fuel: fuel consumption in 10,000,000 US gallons per year.

Source

Imperial College, London M.Sc. exercise

Numbers of Rotifers by Fluid Density

Description

The data give the numbers of rotifers falling out of suspension for different fluid densities. There are two species, pm Polyartha major and kc, Keratella cochlearis and for each species the number falling out and the total number are given.

Usage

rotifer
rotifer

Format

density: specific density of fluid.
pm.y: number falling out for P. major.
pm.total: total number of P. major.
kc.y: number falling out for K. cochlearis.
kc.tot: total number of K. cochlearis.

Source

D. Collett (1991) Modelling Binary Data. Chapman & Hall. p. 217

Accelerated Testing of Tyre Rubber

Description

Data frame from accelerated testing of tyre rubber.

Usage

Rubber
Rubber

Format

loss: the abrasion loss in gm/hr.
hard: the hardness in Shore units.
tens: tensile strength in kg/sq m.

Source

O.L. Davies (1947) Statistical Methods in Research and Production. Oliver and Boyd, Table 6.1 p. 119.

O.L. Davies and P.L. Goldsmith (1972) Statistical Methods in Research and Production. 4th edition, Longmans, Table 8.1 p. 239.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Sammon's Non-Linear Mapping

Description

One form of non-metric multidimensional scaling.

Usage

sammon(d, y = cmdscale(d, k), k = 2, niter = 100, trace = TRUE,
       magic = 0.2, tol = 1e-4)
sammon(d, y = cmdscale(d, k), k = 2, niter = 100, trace = TRUE,
       magic = 0.2, tol = 1e-4)

Arguments

`d`	distance structure of the form returned by `dist`, or a full, symmetric matrix. Data are assumed to be dissimilarities or relative distances, but must be positive except for self-distance. This can contain missing values.
`y`	An initial configuration. If none is supplied, `cmdscale` is used to provide the classical solution. (If there are missing values in `d`, an initial configuration must be provided.) This must not have duplicates.
`k`	The dimension of the configuration.
`niter`	The maximum number of iterations.
`trace`	Logical for tracing optimization. Default `TRUE`.
`magic`	initial value of the step size constant in diagonal Newton method.
`tol`	Tolerance for stopping, in units of stress.

Details

This chooses a two-dimensional configuration to minimize the stress, the sum of squared differences between the input distances and those of the configuration, weighted by the distances, the whole sum being divided by the sum of input distances to make the stress scale-free.

An iterative algorithm is used, which will usually converge in around 50 iterations. As this is necessarily an $O(n^2)$ calculation, it is slow for large datasets. Further, since the configuration is only determined up to rotations and reflections (by convention the centroid is at the origin), the result can vary considerably from machine to machine. In this release the algorithm has been modified by adding a step-length search (magic) to ensure that it always goes downhill.

Value

Two components:

`points`	A two-column vector of the fitted configuration.
`stress`	The final stress achieved.

Side Effects

If trace is true, the initial stress and the current stress are printed out every 10 iterations.

References

Sammon, J. W. (1969) A non-linear mapping for data structure analysis. IEEE Trans. Comput., C-18 401–409.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge University Press.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

swiss.x <- as.matrix(swiss[, -1])
swiss.sam <- sammon(dist(swiss.x))
plot(swiss.sam$points, type = "n")
text(swiss.sam$points, labels = as.character(1:nrow(swiss.x)))
swiss.x <- as.matrix(swiss[, -1])
swiss.sam <- sammon(dist(swiss.x))
plot(swiss.sam$points, type = "n")
text(swiss.sam$points, labels = as.character(1:nrow(swiss.x)))

Ships Damage Data

Description

Data frame giving the number of damage incidents and aggregate months of service by ship type, year of construction, and period of operation.

Usage

ships
ships

Format

type: type: "A" to "E".
year: year of construction: 1960–64, 65–69, 70–74, 75–79 (coded as "60", "65", "70", "75").
period: period of operation : 1960–74, 75–79.
service: aggregate months of service.
incidents: number of damage incidents.

Source

P. McCullagh and J. A. Nelder, (1983), Generalized Linear Models. Chapman & Hall, section 6.3.2, page 137

Shoe wear data of Box, Hunter and Hunter

Description

A list of two vectors, giving the wear of shoes of materials A and B for one foot each of ten boys.

Usage

shoes
shoes

Source

G. E. P. Box, W. G. Hunter and J. S. Hunter (1978) Statistics for Experimenters. Wiley, p. 100

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Percentage of Shrimp in Shrimp Cocktail

Description

A numeric vector with 18 determinations by different laboratories of the amount (percentage of the declared total weight) of shrimp in shrimp cocktail.

Usage

shrimp
shrimp

Source

F. J. King and J. J. Ryan (1976) Collaborative study of the determination of the amount of shrimp in shrimp cocktail. J. Off. Anal. Chem. 59, 644–649.

R. G. Staudte and S. J. Sheather (1990) Robust Estimation and Testing. Wiley.

Space Shuttle Autolander Problem

Description

The shuttle data frame has 256 rows and 7 columns. The first six columns are categorical variables giving example conditions; the seventh is the decision. The first 253 rows are the training set, the last 3 the test conditions.

Usage

shuttle
shuttle

Format

This data frame contains the following factor columns:

stability: stable positioning or not (stab / xstab).
error: size of error (MM / SS / LX / XL).
sign: sign of error, positive or negative (pp / nn).
wind: wind sign (head / tail).
magn: wind strength (Light / Medium / Strong / Out of Range).
vis: visibility (yes / no).
use: use the autolander or not. (auto / noauto.)

Source

D. Michie (1989) Problems of computer-aided concept formation. In Applications of Expert Systems 2, ed. J. R. Quinlan, Turing Institute Press / Addison-Wesley, pp. 310–333.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Growth Curves for Sitka Spruce Trees in 1988

Description

The Sitka data frame has 395 rows and 4 columns. It gives repeated measurements on the log-size of 79 Sitka spruce trees, 54 of which were grown in ozone-enriched chambers and 25 were controls. The size was measured five times in 1988, at roughly monthly intervals.

Usage

Sitka
Sitka

Format

This data frame contains the following columns:

size: measured size (height times diameter squared) of tree, on log scale.
Time: time of measurement in days since 1 January 1988.
tree: number of tree.
treat: either "ozone" for an ozone-enriched chamber or "control".

Source

P. J. Diggle, K.-Y. Liang and S. L. Zeger (1994) Analysis of Longitudinal Data. Clarendon Press, Oxford

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Growth Curves for Sitka Spruce Trees in 1989

Description

The Sitka89 data frame has 632 rows and 4 columns. It gives repeated measurements on the log-size of 79 Sitka spruce trees, 54 of which were grown in ozone-enriched chambers and 25 were controls. The size was measured eight times in 1989, at roughly monthly intervals.

Usage

Sitka89
Sitka89

Format

This data frame contains the following columns:

size: measured size (height times diameter squared) of tree, on log scale.
Time: time of measurement in days since 1 January 1988.
tree: number of tree.
treat: either "ozone" for an ozone-enriched chamber or "control".

Source

P. J. Diggle, K.-Y. Liang and S. L. Zeger (1994) Analysis of Longitudinal Data. Clarendon Press, Oxford

AFM Compositions of Aphyric Skye Lavas

Description

The Skye data frame has 23 rows and 3 columns.

Usage

Skye
Skye

Format

This data frame contains the following columns:

A: Percentage of sodium and potassium oxides.
F: Percentage of iron oxide.
M: Percentage of magnesium oxide.

Source

R. N. Thompson, J. Esson and A. C. Duncan (1972) Major element chemical variation in the Eocene lavas of the Isle of Skye. J. Petrology, 13, 219–253.

References

J. Aitchison (1986) The Statistical Analysis of Compositional Data. Chapman and Hall, p.360.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

# ternary() is from the on-line answers.
ternary <- function(X, pch = par("pch"), lcex = 1,
                    add = FALSE, ord = 1:3, ...)
{
  X <- as.matrix(X)
  if(any(X < 0)) stop("X must be non-negative")
  s <- drop(X %*% rep(1, ncol(X)))
  if(any(s<=0)) stop("each row of X must have a positive sum")
  if(max(abs(s-1)) > 1e-6) {
    warning("row(s) of X will be rescaled")
    X <- X / s
  }
  X <- X[, ord]
  s3 <- sqrt(1/3)
  if(!add)
  {
    oldpty <- par("pty")
    on.exit(par(pty=oldpty))
    par(pty="s")
    plot(c(-s3, s3), c(0.5-s3, 0.5+s3), type="n", axes=FALSE,
         xlab="", ylab="")
    polygon(c(0, -s3, s3), c(1, 0, 0), density=0)
    lab <- NULL
    if(!is.null(dn <- dimnames(X))) lab <- dn[[2]]
    if(length(lab) < 3) lab <- as.character(1:3)
    eps <- 0.05 * lcex
    text(c(0, s3+eps*0.7, -s3-eps*0.7),
         c(1+eps, -0.1*eps, -0.1*eps), lab, cex=lcex)
  }
  points((X[,2] - X[,3])*s3, X[,1], ...)
}

ternary(Skye/100, ord=c(1,3,2))
# ternary() is from the on-line answers.
ternary <- function(X, pch = par("pch"), lcex = 1,
                    add = FALSE, ord = 1:3, ...)
{
  X <- as.matrix(X)
  if(any(X < 0)) stop("X must be non-negative")
  s <- drop(X %*% rep(1, ncol(X)))
  if(any(s<=0)) stop("each row of X must have a positive sum")
  if(max(abs(s-1)) > 1e-6) {
    warning("row(s) of X will be rescaled")
    X <- X / s
  }
  X <- X[, ord]
  s3 <- sqrt(1/3)
  if(!add)
  {
    oldpty <- par("pty")
    on.exit(par(pty=oldpty))
    par(pty="s")
    plot(c(-s3, s3), c(0.5-s3, 0.5+s3), type="n", axes=FALSE,
         xlab="", ylab="")
    polygon(c(0, -s3, s3), c(1, 0, 0), density=0)
    lab <- NULL
    if(!is.null(dn <- dimnames(X))) lab <- dn[[2]]
    if(length(lab) < 3) lab <- as.character(1:3)
    eps <- 0.05 * lcex
    text(c(0, s3+eps*0.7, -s3-eps*0.7),
         c(1+eps, -0.1*eps, -0.1*eps), lab, cex=lcex)
  }
  points((X[,2] - X[,3])*s3, X[,1], ...)
}

ternary(Skye/100, ord=c(1,3,2))

Snail Mortality Data

Description

Groups of 20 snails were held for periods of 1, 2, 3 or 4 weeks in carefully controlled conditions of temperature and relative humidity. There were two species of snail, A and B, and the experiment was designed as a 4 by 3 by 4 by 2 completely randomized design. At the end of the exposure time the snails were tested to see if they had survived; the process itself is fatal for the animals. The object of the exercise was to model the probability of survival in terms of the stimulus variables, and in particular to test for differences between species.

The data are unusual in that in most cases fatalities during the experiment were fairly small.

Usage

snails
snails

Format

The data frame contains the following components:

Species: snail species A (1) or B (2).
Exposure: exposure in weeks.
Rel.Hum: relative humidity (4 levels).
Temp: temperature, in degrees Celsius (3 levels).
Deaths: number of deaths.
N: number of snails exposed.

Source

Zoology Department, The University of Adelaide.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Returns of the Standard and Poors 500

Description

Returns of the Standard and Poors 500 Index in the 1990's

Usage

SP500
SP500

Format

A vector of returns of the Standard and Poors 500 index for all the trading days in 1990, 1991, ..., 1999.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Extract Standardized Residuals from a Linear Model

Description

The standardized residuals. These are normalized to unit variance, fitted including the current data point.

Usage

stdres(object)
stdres(object)

Arguments

object

any object representing a linear model.

Value

The vector of appropriately transformed residuals.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

The Saturated Steam Pressure Data

Description

Temperature and pressure in a saturated steam driven experimental device.

Usage

steam
steam

Format

The data frame contains the following components:

Temp: temperature, in degrees Celsius.
Press: pressure, in Pascals.

Source

N.R. Draper and H. Smith (1981) Applied Regression Analysis. Wiley, pp. 518–9.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Choose a model by AIC in a Stepwise Algorithm

Description

Performs stepwise model selection by AIC.

Usage

stepAIC(object, scope, scale = 0,
        direction = c("both", "backward", "forward"),
        trace = 1, keep = NULL, steps = 1000, use.start = FALSE,
        k = 2, ...)
stepAIC(object, scope, scale = 0,
        direction = c("both", "backward", "forward"),
        trace = 1, keep = NULL, steps = 1000, use.start = FALSE,
        k = 2, ...)

Arguments

`object`	an object representing a model of an appropriate class. This is used as the initial model in the stepwise search.
`scope`	defines the range of models examined in the stepwise search. This should be either a single formula, or a list containing components `upper` and `lower`, both formulae. See the details for how to specify the formulae and how they are used.
`scale`	used in the definition of the AIC statistic for selecting the models, currently only for `lm` and `aov` models (see `extractAIC` for details).
`direction`	the mode of stepwise search, can be one of `"both"`, `"backward"`, or `"forward"`, with a default of `"both"`. If the `scope` argument is missing the default for `direction` is `"backward"`.
`trace`	if positive, information is printed during the running of `stepAIC`. Larger values may give more information on the fitting process.
`keep`	a filter function whose input is a fitted model object and the associated `AIC` statistic, and whose output is arbitrary. Typically `keep` will select a subset of the components of the object and return them. The default is not to keep anything.
`steps`	the maximum number of steps to be considered. The default is 1000 (essentially as many as required). It is typically used to stop the process early.
`use.start`	if true the updated fits are done starting at the linear predictor for the currently selected model. This may speed up the iterative calculations for `glm` (and other fits), but it can also slow them down. Not used in R.
`k`	the multiple of the number of degrees of freedom used for the penalty. Only `k = 2` gives the genuine AIC: `k = log(n)` is sometimes referred to as BIC or SBC.
`...`	any additional arguments to `extractAIC`. (None are currently used.)

Details

The set of models searched is determined by the scope argument. The right-hand-side of its lower component is always included in the model, and right-hand-side of the model is included in the upper component. If scope is a single formula, it specifies the upper component, and the lower model is empty. If scope is missing, the initial model is used as the upper model.

Models specified by scope can be templates to update object as used by update.formula.

There is a potential problem in using glm fits with a variable scale, as in that case the deviance is not simply related to the maximized log-likelihood. The glm method for extractAIC makes the appropriate adjustment for a gaussian family, but may need to be amended for other cases. (The binomial and poisson families have fixed scale by default and do not correspond to a particular maximum-likelihood problem for variable scale.)

Where a conventional deviance exists (e.g. for lm, aov and glm fits) this is quoted in the analysis of variance table: it is the unscaled deviance.

Value

the stepwise-selected model is returned, with up to two additional components. There is an "anova" component corresponding to the steps taken in the search, as well as a "keep" component if the keep= argument was supplied in the call. The "Resid. Dev" column of the analysis of deviance table refers to a constant minus twice the maximized log likelihood: it will be a deviance only in cases where a saturated model is well-defined (thus excluding lm, aov and survreg fits, for example).

Note

The model fitting must apply the models to the same dataset. This may be a problem if there are missing values and an na.action other than na.fail is used (as is the default in R). We suggest you remove the missing values first.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
quine.stp <- stepAIC(quine.nxt,
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1),
    trace = FALSE)
quine.stp$anova

cpus1 <- cpus
for(v in names(cpus)[2:7])
  cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])),
                    include.lowest = TRUE)
cpus0 <- cpus1[, 2:8]  # excludes names, authors' predictions
cpus.samp <- sample(1:209, 100)
cpus.lm <- lm(log10(perf) ~ ., data = cpus1[cpus.samp,2:8])
cpus.lm2 <- stepAIC(cpus.lm, trace = FALSE)
cpus.lm2$anova

example(birthwt)
birthwt.glm <- glm(low ~ ., family = binomial, data = bwt)
birthwt.step <- stepAIC(birthwt.glm, trace = FALSE)
birthwt.step$anova
birthwt.step2 <- stepAIC(birthwt.glm, ~ .^2 + I(scale(age)^2)
    + I(scale(lwt)^2), trace = FALSE)
birthwt.step2$anova

quine.nb <- glm.nb(Days ~ .^4, data = quine)
quine.nb2 <- stepAIC(quine.nb)
quine.nb2$anova
quine.hi <- aov(log(Days + 2.5) ~ .^4, quine)
quine.nxt <- update(quine.hi, . ~ . - Eth:Sex:Age:Lrn)
quine.stp <- stepAIC(quine.nxt,
    scope = list(upper = ~Eth*Sex*Age*Lrn, lower = ~1),
    trace = FALSE)
quine.stp$anova

cpus1 <- cpus
for(v in names(cpus)[2:7])
  cpus1[[v]] <- cut(cpus[[v]], unique(quantile(cpus[[v]])),
                    include.lowest = TRUE)
cpus0 <- cpus1[, 2:8]  # excludes names, authors' predictions
cpus.samp <- sample(1:209, 100)
cpus.lm <- lm(log10(perf) ~ ., data = cpus1[cpus.samp,2:8])
cpus.lm2 <- stepAIC(cpus.lm, trace = FALSE)
cpus.lm2$anova

example(birthwt)
birthwt.glm <- glm(low ~ ., family = binomial, data = bwt)
birthwt.step <- stepAIC(birthwt.glm, trace = FALSE)
birthwt.step$anova
birthwt.step2 <- stepAIC(birthwt.glm, ~ .^2 + I(scale(age)^2)
    + I(scale(lwt)^2), trace = FALSE)
birthwt.step2$anova

quine.nb <- glm.nb(Days ~ .^4, data = quine)
quine.nb2 <- stepAIC(quine.nb)
quine.nb2$anova

The Stormer Viscometer Data

Description

The stormer viscometer measures the viscosity of a fluid by measuring the time taken for an inner cylinder in the mechanism to perform a fixed number of revolutions in response to an actuating weight. The viscometer is calibrated by measuring the time taken with varying weights while the mechanism is suspended in fluids of accurately known viscosity. The data comes from such a calibration, and theoretical considerations suggest a nonlinear relationship between time, weight and viscosity, of the form Time = (B1*Viscosity)/(Weight - B2) + E where B1 and B2 are unknown parameters to be estimated, and E is error.

Usage

stormer
stormer

Format

The data frame contains the following components:

Viscosity: viscosity of fluid.
Wt: actuating weight.
Time: time taken.

Source

E. J. Williams (1959) Regression Analysis. Wiley.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Extract Studentized Residuals from a Linear Model

Description

The Studentized residuals. Like standardized residuals, these are normalized to unit variance, but the Studentized version is fitted ignoring the current data point. (They are sometimes called jackknifed residuals).

Usage

studres(object)
studres(object)

Arguments

object

any object representing a linear model.

Value

The vector of appropriately transformed residuals.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Summary Method Function for Objects of Class 'loglm'

Description

Returns a summary list for log-linear models fitted by iterative proportional scaling using loglm.

Usage

## S3 method for class 'loglm'
summary(object, fitted = FALSE, ...)
## S3 method for class 'loglm'
summary(object, fitted = FALSE, ...)

Arguments

`object`	a fitted loglm model object.
`fitted`	if `TRUE` return observed and expected frequencies in the result. Using `fitted = TRUE` may necessitate re-fitting the object.
`...`	arguments to be passed to or from other methods.

Details

This function is a method for the generic function summary() for class "loglm". It can be invoked by calling summary(x) for an object x of the appropriate class, or directly by calling summary.loglm(x) regardless of the class of the object.

Value

a list is returned for use by print.summary.loglm. This has components

`formula`	the formula used to produce `object`
`tests`	the table of test statistics (likelihood ratio, Pearson) for the fit.
`oe`	if `fitted = TRUE`, an array of the observed and expected frequencies, otherwise `NULL`.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Summary Method Function for Objects of Class 'negbin'

Description

Identical to summary.glm, but with three lines of additional output: the ML estimate of theta, its standard error, and twice the log-likelihood function.

Usage

## S3 method for class 'negbin'
summary(object, dispersion = 1, correlation = FALSE, ...)
## S3 method for class 'negbin'
summary(object, dispersion = 1, correlation = FALSE, ...)

Arguments

`object`	fitted model object of class `negbin` inheriting from `glm` and `lm`. Typically the output of `glm.nb`.
`dispersion`	as for `summary.glm`, with a default of 1.
`correlation`	as for `summary.glm`.
`...`	arguments passed to or from other methods.

Details

summary.glm is used to produce the majority of the output and supply the result. This function is a method for the generic function summary() for class "negbin". It can be invoked by calling summary(x) for an object x of the appropriate class, or directly by calling summary.negbin(x) regardless of the class of the object.

Value

As for summary.glm; the additional lines of output are not included in the resultant object.

Side Effects

A summary table is produced as for summary.glm, with the additional information described above.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

## IGNORE_RDIFF_BEGIN
summary(glm.nb(Days ~ Eth*Age*Lrn*Sex, quine, link = log))
## IGNORE_RDIFF_END
## IGNORE_RDIFF_BEGIN
summary(glm.nb(Days ~ Eth*Age*Lrn*Sex, quine, link = log))
## IGNORE_RDIFF_END

Summary Method for Robust Linear Models

Description

summary method for objects of class "rlm"

Usage

## S3 method for class 'rlm'
summary(object, method = c("XtX", "XtWX"), correlation = FALSE, ...)
## S3 method for class 'rlm'
summary(object, method = c("XtX", "XtWX"), correlation = FALSE, ...)

Arguments

`object`	the fitted model. This is assumed to be the result of some fit that produces an object inheriting from the class `rlm`, in the sense that the components returned by the `rlm` function will be available.
`method`	Should the weighted (by the IWLS weights) or unweighted cross-products matrix be used?
`correlation`	logical. Should correlations be computed (and printed)?
`...`	arguments passed to or from other methods.

Details

This function is a method for the generic function summary() for class "rlm". It can be invoked by calling summary(x) for an object x of the appropriate class, or directly by calling summary.rlm(x) regardless of the class of the object.

Value

If printing takes place, only a null value is returned. Otherwise, a list is returned with the following components. Printing always takes place if this function is invoked automatically as a method for the summary function.

`correlation`	The computed correlation coefficient matrix for the coefficients in the model.
`cov.unscaled`	The unscaled covariance matrix; i.e, a matrix such that multiplying it by an estimate of the error variance produces an estimated covariance matrix for the coefficients.
`sigma`	The scale estimate.
`stddev`	A scale estimate used for the standard errors.
`df`	The number of degrees of freedom for the model and for residuals.
`coefficients`	A matrix with three columns, containing the coefficients, their standard errors and the corresponding t statistic.
`terms`	The terms object used in fitting this model.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

summary(rlm(calls ~ year, data = phones, maxit = 50))
summary(rlm(calls ~ year, data = phones, maxit = 50))

Student Survey Data

Description

This data frame contains the responses of 237 Statistics I students at the University of Adelaide to a number of questions.

Usage

survey
survey

Format

The components of the data frame are:

Sex: The sex of the student. (Factor with levels "Male" and "Female".)
Wr.Hnd: span (distance from tip of thumb to tip of little finger of spread hand) of writing hand, in centimetres.
NW.Hnd: span of non-writing hand.
W.Hnd: writing hand of student. (Factor, with levels "Left" and "Right".)
Fold: “Fold your arms! Which is on top” (Factor, with levels "R on L", "L on R", "Neither".)
Pulse: pulse rate of student (beats per minute).
Clap: ‘Clap your hands! Which hand is on top?’ (Factor, with levels "Right", "Left", "Neither".)
Exer: how often the student exercises. (Factor, with levels "Freq" (frequently), "Some", "None".)
Smoke: how much the student smokes. (Factor, levels "Heavy", "Regul" (regularly), "Occas" (occasionally), "Never".)
Height: height of the student in centimetres.
M.I: whether the student expressed height in imperial (feet/inches) or metric (centimetres/metres) units. (Factor, levels "Metric", "Imperial".)
Age: age of the student in years.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Synthetic Classification Problem

Description

The synth.tr data frame has 250 rows and 3 columns. The synth.te data frame has 100 rows and 3 columns. It is intended that synth.tr be used from training and synth.te for testing.

Usage

synth.tr
synth.te
synth.tr
synth.te

Format

These data frames contains the following columns:

xs: x-coordinate
ys: y-coordinate
yc: class, coded as 0 or 1.

Source

Ripley, B.D. (1994) Neural networks and related methods for classification (with discussion). Journal of the Royal Statistical Society series B 56, 409–456.

Ripley, B.D. (1996) Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press.

Estimate theta of the Negative Binomial

Description

Given the estimated mean vector, estimate theta of the Negative Binomial Distribution.

Usage

theta.md(y, mu, dfr, weights, limit = 20, eps = .Machine$double.eps^0.25)

theta.ml(y, mu, n, weights, limit = 10, eps = .Machine$double.eps^0.25,
         trace = FALSE)

theta.mm(y, mu, dfr, weights, limit = 10, eps = .Machine$double.eps^0.25)
theta.md(y, mu, dfr, weights, limit = 20, eps = .Machine$double.eps^0.25)

theta.ml(y, mu, n, weights, limit = 10, eps = .Machine$double.eps^0.25,
         trace = FALSE)

theta.mm(y, mu, dfr, weights, limit = 10, eps = .Machine$double.eps^0.25)

Arguments

`y`	Vector of observed values from the Negative Binomial.
`mu`	Estimated mean vector.
`n`	Number of data points (defaults to the sum of `weights`)
`dfr`	Residual degrees of freedom (assuming `theta` known). For a weighted fit this is the sum of the weights minus the number of fitted parameters.
`weights`	Case weights. If missing, taken as 1.
`limit`	Limit on the number of iterations.
`eps`	Tolerance to determine convergence.
`trace`	logical: should iteration progress be printed?

Details

theta.md estimates by equating the deviance to the residual degrees of freedom, an analogue of a moment estimator.

theta.ml uses maximum likelihood.

theta.mm calculates the moment estimator of theta by equating the Pearson chi-square $\sum (y-\mu)^2/(\mu+\mu^2/\theta)$ to the residual degrees of freedom.

Value

The required estimate of theta, as a scalar. For theta.ml, the standard error is given as attribute "SE".

Examples

quine.nb <- glm.nb(Days ~ .^2, data = quine)
theta.md(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))
theta.ml(quine$Days, fitted(quine.nb))
theta.mm(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))

## weighted example
yeast <- data.frame(cbind(numbers = 0:5, fr = c(213, 128, 37, 18, 3, 1)))
fit <- glm.nb(numbers ~ 1, weights = fr, data = yeast)
## IGNORE_RDIFF_BEGIN
summary(fit)
## IGNORE_RDIFF_END
mu <- fitted(fit)
theta.md(yeast$numbers, mu, dfr = 399, weights = yeast$fr)
theta.ml(yeast$numbers, mu, limit = 15, weights = yeast$fr)
theta.mm(yeast$numbers, mu, dfr = 399, weights = yeast$fr)
quine.nb <- glm.nb(Days ~ .^2, data = quine)
theta.md(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))
theta.ml(quine$Days, fitted(quine.nb))
theta.mm(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))

## weighted example
yeast <- data.frame(cbind(numbers = 0:5, fr = c(213, 128, 37, 18, 3, 1)))
fit <- glm.nb(numbers ~ 1, weights = fr, data = yeast)
## IGNORE_RDIFF_BEGIN
summary(fit)
## IGNORE_RDIFF_END
mu <- fitted(fit)
theta.md(yeast$numbers, mu, dfr = 399, weights = yeast$fr)
theta.ml(yeast$numbers, mu, limit = 15, weights = yeast$fr)
theta.mm(yeast$numbers, mu, dfr = 399, weights = yeast$fr)

Spatial Topographic Data

Description

The topo data frame has 52 rows and 3 columns, of topographic heights within a 310 feet square.

Usage

topo
topo

Format

This data frame contains the following columns:

x: x coordinates (units of 50 feet)
y: y coordinates (units of 50 feet)
z: heights (feet)

Source

Davis, J.C. (1973) Statistics and Data Analysis in Geology. Wiley.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Effect of Swedish Speed Limits on Accidents

Description

An experiment was performed in Sweden in 1961–2 to assess the effect of a speed limit on the motorway accident rate. The experiment was conducted on 92 days in each year, matched so that day j in 1962 was comparable to day j in 1961. On some days the speed limit was in effect and enforced, while on other days there was no speed limit and cars tended to be driven faster. The speed limit days tended to be in contiguous blocks.

Usage

Traffic
Traffic

Format

This data frame contains the following columns:

year: 1961 or 1962.
day: of year.
limit: was there a speed limit?
y: traffic accident count for that day.

Source

Svensson, A. (1981) On the goodness-of-fit test for the multiplicative Poisson model. Annals of Statistics, 9, 697–704.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Plot a Histogram

Description

Creates a histogram on the current graphics device.

Usage

truehist(data, nbins = "Scott", h, x0 = -h/1000,
         breaks, prob = TRUE, xlim = range(breaks),
         ymax = max(est), col = "cyan",
         xlab = deparse(substitute(data)), bty = "n", ...)
truehist(data, nbins = "Scott", h, x0 = -h/1000,
         breaks, prob = TRUE, xlim = range(breaks),
         ymax = max(est), col = "cyan",
         xlab = deparse(substitute(data)), bty = "n", ...)

Arguments

`data`	numeric vector of data for histogram. Missing values (`NA`s) are allowed and omitted.
`nbins`	The suggested number of bins. Either a positive integer, or a character string naming a rule: `"Scott"` or `"Freedman-Diaconis"` or `"FD"`. (Case is ignored.)
`h`	The bin width, a strictly positive number (takes precedence over `nbins`).
`x0`	Shift for the bins - the breaks are at `x0 + h * (..., -1, 0, 1, ...)`
`breaks`	The set of breakpoints to be used. (Usually omitted, takes precedence over `h` and `nbins`).
`prob`	If true (the default) plot a true histogram. The vertical axis has a relative frequency density scale, so the product of the dimensions of any panel gives the relative frequency. Hence the total area under the histogram is 1 and it is directly comparable with most other estimates of the probability density function. If false plot the counts in the bins.
`xlim`	The limits for the x-axis.
`ymax`	The upper limit for the y-axis.
`col`	The colour for the bar fill: the default is colour 5 in the default R palette.
`xlab`	label for the plot x-axis. By default, this will be the name of `data`.
`bty`	The box type for the plot - defaults to none.
`...`	additional arguments to `rect` or `plot`.

Details

This plots a true histogram, a density estimate of total area 1. If breaks is specified, those breakpoints are used. Otherwise if h is specified, a regular grid of bins is used with width h. If neither breaks nor h is specified, nbins is used to select a suitable h.

Side Effects

A histogram is plotted on the current device.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Unbiased Cross-Validation for Bandwidth Selection

Description

Uses unbiased cross-validation to select the bandwidth of a Gaussian kernel density estimator.

Usage

ucv(x, nb = 1000, lower, upper)
ucv(x, nb = 1000, lower, upper)

Arguments

`x`	a numeric vector
`nb`	number of bins to use.
`lower`, `upper`	Range over which to minimize. The default is almost always satisfactory.

Value

a bandwidth.

References

Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

ucv(geyser$duration)
ucv(geyser$duration)

Nutritional and Marketing Information on US Cereals

Description

The UScereal data frame has 65 rows and 11 columns. The data come from the 1993 ASA Statistical Graphics Exposition, and are taken from the mandatory F&DA food label. The data have been normalized here to a portion of one American cup.

Usage

UScereal
UScereal

Format

This data frame contains the following columns:

mfr: Manufacturer, represented by its first initial: G=General Mills, K=Kelloggs, N=Nabisco, P=Post, Q=Quaker Oats, R=Ralston Purina.
calories: number of calories in one portion.
protein: grams of protein in one portion.
fat: grams of fat in one portion.
sodium: milligrams of sodium in one portion.
fibre: grams of dietary fibre in one portion.
carbo: grams of complex carbohydrates in one portion.
sugars: grams of sugars in one portion.
shelf: display shelf (1, 2, or 3, counting from the floor).
potassium: grams of potassium.
vitamins: vitamins and minerals (none, enriched, or 100%).

Source

The original data are available at https://lib.stat.cmu.edu/datasets/1993.expo/.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

The Effect of Punishment Regimes on Crime Rates

Description

Criminologists are interested in the effect of punishment regimes on crime rates. This has been studied using aggregate data on 47 states of the USA for 1960 given in this data frame. The variables seem to have been re-scaled to convenient numbers.

Usage

UScrime
UScrime

Format

This data frame contains the following columns:

M: percentage of males aged 14–24.
So: indicator variable for a Southern state.
Ed: mean years of schooling.
Po1: police expenditure in 1960.
Po2: police expenditure in 1959.
LF: labour force participation rate.
M.F: number of males per 1000 females.
Pop: state population.
NW: number of non-whites per 1000 people.
U1: unemployment rate of urban males 14–24.
U2: unemployment rate of urban males 35–39.
GDP: gross domestic product per head.
Ineq: income inequality.
Prob: probability of imprisonment.
Time: average time served in state prisons.
y: rate of crimes in a particular category per head of population.

Source

Ehrlich, I. (1973) Participation in illegitimate activities: a theoretical and empirical investigation. Journal of Political Economy, 81, 521–565.

Vandaele, W. (1978) Participation in illegitimate activities: Ehrlich revisited. In Deterrence and Incapacitation, eds A. Blumstein, J. Cohen and D. Nagin, pp. 270–335. US National Academy of Sciences.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Veteran's Administration Lung Cancer Trial

Description

Veteran's Administration lung cancer trial from Kalbfleisch & Prentice.

Usage

VA
VA

Format

A data frame with columns:

stime: survival or follow-up time in days.
status: dead or censored.
treat: treatment: standard or test.
age: patient's age in years.
Karn: Karnofsky score of patient's performance on a scale of 0 to 100.
diag.time: times since diagnosis in months at entry to trial.
cell: one of four cell types.
prior: prior therapy?

Source

Kalbfleisch, J.D. and Prentice R.L. (1980) The Statistical Analysis of Failure Time Data. Wiley.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Counts of Waders at 15 Sites in South Africa

Description

The waders data frame has 15 rows and 19 columns. The entries are counts of waders in summer.

Usage

waders
waders

Format

This data frame contains the following columns (species)

S1: Oystercatcher
S2: White-fronted Plover
S3: Kitt Lutz's Plover
S4: Three-banded Plover
S5: Grey Plover
S6: Ringed Plover
S7: Bar-tailed Godwit
S8: Whimbrel
S9: Marsh Sandpiper
S10: Greenshank
S11: Common Sandpiper
S12: Turnstone
S13: Knot
S14: Sanderling
S15: Little Stint
S16: Curlew Sandpiper
S17: Ruff
S18: Avocet
S19: Black-winged Stilt

The rows are the sites:

A = Namibia North coast
B = Namibia North wetland
C = Namibia South coast
D = Namibia South wetland
E = Cape North coast
F = Cape North wetland
G = Cape West coast
H = Cape West wetland
I = Cape South coast
J= Cape South wetland
K = Cape East coast
L = Cape East wetland
M = Transkei coast
N = Natal coast
O = Natal wetland

Source

J.C. Gower and D.J. Hand (1996) Biplots Chapman & Hall Table 9.1. Quoted as from:

R.W. Summers, L.G. Underhill, D.J. Pearson and D.A. Scott (1987) Wader migration systems in south and eastern Africa and western Asia. Wader Study Group Bulletin 49 Supplement, 15–34.

Examples

plot(corresp(waders, nf=2))
plot(corresp(waders, nf=2))

House Insulation: Whiteside's Data

Description

Mr Derek Whiteside of the UK Building Research Station recorded the weekly gas consumption and average external temperature at his own house in south-east England for two heating seasons, one of 26 weeks before, and one of 30 weeks after cavity-wall insulation was installed. The object of the exercise was to assess the effect of the insulation on gas consumption.

Usage

whiteside
whiteside

Format

The whiteside data frame has 56 rows and 3 columns.:

Insul: A factor, before or after insulation.
Temp: Purportedly the average outside temperature in degrees Celsius. (These values is far too low for any 56-week period in the 1960s in South-East England. It might be the weekly average of daily minima.)
Gas: The weekly gas consumption in 1000s of cubic feet.

Source

A data set collected in the 1960s by Mr Derek Whiteside of the UK Building Research Station. Reported by

Hand, D. J., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. eds (1993) A Handbook of Small Data Sets. Chapman & Hall, p. 69.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

require(lattice)
xyplot(Gas ~ Temp | Insul, whiteside, panel =
  function(x, y, ...) {
    panel.xyplot(x, y, ...)
    panel.lmline(x, y, ...)
  }, xlab = "Average external temperature (deg. C)",
  ylab = "Gas consumption  (1000 cubic feet)", aspect = "xy",
  strip = function(...) strip.default(..., style = 1))

gasB <- lm(Gas ~ Temp, whiteside, subset = Insul=="Before")
gasA <- update(gasB, subset = Insul=="After")
summary(gasB)
summary(gasA)
gasBA <- lm(Gas ~ Insul/Temp - 1, whiteside)
summary(gasBA)

gasQ <- lm(Gas ~ Insul/(Temp + I(Temp^2)) - 1, whiteside)
coef(summary(gasQ))

gasPR <- lm(Gas ~ Insul + Temp, whiteside)
anova(gasPR, gasBA)
options(contrasts = c("contr.treatment", "contr.poly"))
gasBA1 <- lm(Gas ~ Insul*Temp, whiteside)
coef(summary(gasBA1))
require(lattice)
xyplot(Gas ~ Temp | Insul, whiteside, panel =
  function(x, y, ...) {
    panel.xyplot(x, y, ...)
    panel.lmline(x, y, ...)
  }, xlab = "Average external temperature (deg. C)",
  ylab = "Gas consumption  (1000 cubic feet)", aspect = "xy",
  strip = function(...) strip.default(..., style = 1))

gasB <- lm(Gas ~ Temp, whiteside, subset = Insul=="Before")
gasA <- update(gasB, subset = Insul=="After")
summary(gasB)
summary(gasA)
gasBA <- lm(Gas ~ Insul/Temp - 1, whiteside)
summary(gasBA)

gasQ <- lm(Gas ~ Insul/(Temp + I(Temp^2)) - 1, whiteside)
coef(summary(gasQ))

gasPR <- lm(Gas ~ Insul + Temp, whiteside)
anova(gasPR, gasBA)
options(contrasts = c("contr.treatment", "contr.poly"))
gasBA1 <- lm(Gas ~ Insul*Temp, whiteside)
coef(summary(gasBA1))

Bandwidth Selection by Pilot Estimation of Derivatives

Description

Uses the method of Sheather & Jones (1991) to select the bandwidth of a Gaussian kernel density estimator.

Usage

width.SJ(x, nb = 1000, lower, upper, method = c("ste", "dpi"))
width.SJ(x, nb = 1000, lower, upper, method = c("ste", "dpi"))

Arguments

`x`	a numeric vector
`nb`	number of bins to use.
`upper`, `lower`	range over which to search for solution if `method = "ste"`.
`method`	Either `"ste"` ("solve-the-equation") or `"dpi"` ("direct plug-in").

Value

a bandwidth.

Note

A faster version for large n (thousands) is available in R $\ge$ 3.4.0 as part of bw.SJ: quadruple its value for comparability with this version.

References

Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B 53, 683–690.

Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization. Wiley.

Wand, M. P. and Jones, M. C. (1995) Kernel Smoothing. Chapman & Hall.

Examples

width.SJ(geyser$duration, method = "dpi")
width.SJ(geyser$duration)

width.SJ(galaxies, method = "dpi")
width.SJ(galaxies)
width.SJ(geyser$duration, method = "dpi")
width.SJ(geyser$duration)

width.SJ(galaxies, method = "dpi")
width.SJ(galaxies)

Write a Matrix or Data Frame

Description

Writes a matrix or data frame to a file or the console, using column labels and a layout respecting columns.

Usage

write.matrix(x, file = "", sep = " ", blocksize)
write.matrix(x, file = "", sep = " ", blocksize)

Arguments

`x`	matrix or data frame.
`file`	name of output file. The default (`""`) is the console.
`sep`	The separator between columns.
`blocksize`	If supplied and positive, the output is written in blocks of `blocksize` rows. Choose as large as possible consistent with the amount of memory available.

Details

If x is a matrix, supplying blocksize is more memory-efficient and enables larger matrices to be written, but each block of rows might be formatted slightly differently.

If x is a data frame, the conversion to a matrix may negate the memory saving.

Side Effects

A formatted file is produced, with column headings (if x has them) and columns of data.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Weight Loss Data from an Obese Patient

Description

The data frame gives the weight, in kilograms, of an obese patient at 52 time points over an 8 month period of a weight rehabilitation programme.

Usage

wtloss
wtloss

Format

This data frame contains the following columns:

Days: time in days since the start of the programme.
Weight: weight in kilograms of the patient.

Source

Dr T. Davies, Adelaide.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

Examples

## IGNORE_RDIFF_BEGIN
wtloss.fm <- nls(Weight ~ b0 + b1*2^(-Days/th),
    data = wtloss, start = list(b0=90, b1=95, th=120))
wtloss.fm
## IGNORE_RDIFF_END
plot(wtloss)
with(wtloss, lines(Days, fitted(wtloss.fm)))
## IGNORE_RDIFF_BEGIN
wtloss.fm <- nls(Weight ~ b0 + b1*2^(-Days/th),
    data = wtloss, start = list(b0=90, b1=95, th=120))
wtloss.fm
## IGNORE_RDIFF_END
plot(wtloss)
with(wtloss, lines(Days, fitted(wtloss.fm)))

Package 'MASS'

Help Index

Determinations of Nickel Content

Description

Usage

Source

References

Accidental Deaths in the US 1973-1978

Description

Usage

Details

Source

References

Try All One-Term Additions to a Model

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Australian AIDS Survival Data

Description

Usage

Format

Note

Source

References

Brain and Body Weights for 28 Species

Description

Usage

Format

Note

Source

References

Anorexia Data on Weight Change

Description

Usage

Format

Source

References

Likelihood Ratio Tests for Negative Binomial GLMs

Description

Usage

Arguments

Details

Note

References

See Also

Examples

Adaptive Numerical Integration

Description

Usage

Arguments

Details

Value

References

Examples

Presence of Bacteria after Drug Treatments

Description

Usage

Format

Details

Source

References

Examples

Bandwidth for density() via Normal Reference Distribution

Description

Usage

Arguments

Value

References

Examples

Biased Cross-Validation for Bandwidth Selection

Description

Usage

Arguments

Value

References