Multivariate Logistic Models

Abstract

SUMMARY When data composed of several categorical responses together with categorical or continuous predictors are observed, the multivariate logistic transform introduced by McCullagh and Nelder can be used to define a class of regression models that is, in many applications, particularly suitable for relating the joint distribution of the responses to predictors. In this paper we give a general definition of this class of models and study their properties. A computational scheme for performing maximum likelihood estimation for data sets of moderate size is described and a system of model formulae that succinctly define particular models is introduced. Applications of these models to longitudinal problems are illustrated by numerical examples.