LogisticCopula:A Copula Based Extension of Logistic Regression

An implementation of a method of extending a logistic regression model beyond linear effects of the co-variates. The extension in is constructed by first equating the logistic regression model to a naive Bayes model where all the margins are specified to follow natural exponential distributions conditional on Y, that is, a model for Y given X that is specified through the distribution of X given Y, where the columns of X are assumed to be mutually independent conditional on Y. Subsequently, the model is expanded by adding vine - copulas to relax the assumption of mutual independence, where pair-copulas are added in a stage-wise, forward selection manner. Some heuristics are employed during the process of selecting edges, as well as the families of pair-copula models. After each component is added, the parameters are updated by a (smaller) number of gradient steps to maximise the likelihood. When the algorithm has stopped adding edges, based the criterion that a new edge should improve the likelihood more than k times the number new parameters, the parameters are updated with a larger number of gradient steps, or until convergence.