Linear MixedEffects Models
Description
This generic function fits a linear mixedeffects model in the
formulation described in Laird and Ware (1982) but allowing for nested
random effects. The withingroup errors are allowed to be correlated
and/or have unequal variances.
This page describes the formula method;
the methods lme.lmList
and lme.groupedData
are documented separately.
Usage
lme(fixed, data, random, correlation, weights, subset, method,
na.action, control, contrasts = NULL, keep.data = TRUE)
lme(fixed, data, random, correlation, weights, subset, method,
na.action, control, contrasts = NULL, keep.data = TRUE)
update(object, fixed., ..., evaluate = TRUE)
Arguments
object 
an object inheriting from class lme , representing
a fitted linear mixedeffects model.

fixed 
a twosided linear formula object describing the
fixedeffects part of the model, with the response on the left of a
~ operator and the terms, separated by + operators, on
the right, an "lmList" object, or a
"groupedData" object.
There is limited support for formulae such as resp ~ 1 and
resp ~ 0 , and less prior to version ‘3.1112’.

fixed. 
Changes to the fixedeffects formula – see
update.formula for details.

data 
an optional data frame containing the variables named in
fixed , random , correlation , weights , and
subset . By default the variables are taken from the
environment from which lme is called.

random 
optionally, any of the following: (i) a onesided formula
of the form ~ x1 + ... + xn  g1/.../gm , with x1 + ... + xn
specifying the model for the random effects and g1/.../gm the
grouping structure (m may be equal to 1, in which case no
/ is required). The random effects formula will be repeated
for all levels of grouping, in the case of multiple levels of
grouping; (ii) a list of onesided formulas of the form
~ x1 + ... + xn  g , with possibly different random effects models
for each grouping level. The order of nesting will be assumed the
same as the order of the elements in the list; (iii) a onesided
formula of the form ~ x1 + ... + xn , or a pdMat object with
a formula (i.e. a nonNULL value for formula(object) ),
or a list of such formulas or pdMat objects. In this case, the
grouping structure formula will be derived from the data used to
fit the linear mixedeffects model, which should inherit from class
"groupedData" ; (iv) a named list of formulas or pdMat
objects as in (iii), with the grouping factors as names. The order of
nesting will be assumed the same as the order of the order of the
elements in the list; (v) an reStruct object. See the
documentation on pdClasses for a description of the available
pdMat classes. Defaults to a formula consisting of the right
hand side of fixed .

correlation 
an optional corStruct object describing the
withingroup correlation structure. See the documentation of
corClasses for a description of the available corStruct
classes. Defaults to NULL ,
corresponding to no withingroup correlations.

weights 
an optional varFunc object or onesided formula
describing the withingroup heteroscedasticity structure. If given as
a formula, it is used as the argument to varFixed ,
corresponding to fixed variance weights. See the documentation on
varClasses for a description of the available varFunc
classes. Defaults to NULL , corresponding to homoscedastic
withingroup errors.

subset 
an optional expression indicating the subset of the rows of
data that should be used in the fit. This can be a logical
vector, or a numeric vector indicating which observation numbers are
to be included, or a character vector of the row names to be
included. All observations are included by default.

method 
a character string. If "REML" the model is fit by
maximizing the restricted loglikelihood. If "ML" the
loglikelihood is maximized. Defaults to "REML" .

na.action 
a function that indicates what should happen when the
data contain NA s. The default action (na.fail ) causes
lme to print an error message and terminate if there are any
incomplete observations.

control 
a list of control values for the estimation algorithm to
replace the default values returned by the function lmeControl .
Defaults to an empty list.

contrasts 
an optional list. See the contrasts.arg
of model.matrix.default .

keep.data 
logical: should the data argument (if supplied
and a data frame) be saved as part of the model object?

... 
some methods for this generic require additional
arguments. None are used in this method.

evaluate 
If TRUE evaluate the new call else return the call.

Details
offset
terms in fixed
are an error since 3.1157
(202203): previously they were silently ignored.
Value
An object of class "lme"
representing the linear mixedeffects
model fit. Generic functions such as print
, plot
and
summary
have methods to show the results of the fit. See
lmeObject
for the components of the fit. The functions
resid
, coef
, fitted
,
fixed.effects
, and
random.effects
can be used to extract some of its components.
Note
The function does not do any scaling internally: the optimization will
work best when the response is scaled so its variance is of the order
of one.
Author(s)
José Pinheiro and Douglas Bates [email protected]
References
The computational methods follow the general framework of Lindstrom
and Bates (1988). The model formulation is described in Laird and Ware
(1982). The variancecovariance parametrizations are described in
Pinheiro and Bates (1996). The different correlation structures
available for the correlation
argument are described in Box,
Jenkins and Reinsel (1994), Littell et al (1996), and Venables and
Ripley (2002). The use of variance functions for linear and nonlinear
mixed effects models is presented in detail in Davidian and Giltinan
(1995).
Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994).
Time Series Analysis: Forecasting and Control, 3rd Edition, Holden–Day.
Davidian, M. and Giltinan, D.M. (1995).
Nonlinear Mixed Effects Models for Repeated Measurement Data, Chapman and Hall.
doi:10.1201/9780203745502.
Laird, N.M. and Ware, J.H. (1982).
RandomEffects Models for Longitudinal Data.
Biometrics 38, 963–974.
doi:10.2307/2529876.
Lindstrom, M.J. and Bates, D.M. (1988).
NewtonRaphson and EM Algorithms for Linear MixedEffects Models for RepeatedMeasures Data.
Journal of the American Statistical Association 83, 1014–1022.
doi:10.2307/2290128.
Littell, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D. (1996).
SAS Systems for Mixed Models, SAS Institute.
Pinheiro, J.C. and Bates., D.M. (1996).
Unconstrained Parametrizations for VarianceCovariance Matrices.
Statistics and Computing 6, 289–296.
doi:10.1007/BF00140873.
Pinheiro, J.C., and Bates, D.M. (2000).
MixedEffects Models in S and SPLUS, Springer.
doi:10.1007/b98882.
Venables, W.N. and Ripley, B.D. (2002).
Modern Applied Statistics with S, 4th Edition, SpringerVerlag.
doi:10.1007/9780387217062.
See Also
corClasses
,
lme.lmList
,
lme.groupedData
,
lmeControl
,
lmeObject
,
lmeStruct
,
lmList
,
pdClasses
,
plot.lme
,
predict.lme
,
qqnorm.lme
,
residuals.lme
,
reStruct
,
simulate.lme
,
summary.lme
,
varClasses
,
varFunc
Examples
fm1 < lme(distance ~ age, data = Orthodont)
fm2 < lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
summary(fm1)
summary(fm2)