A class of regression models for multivariate categorical responses

Abstract

When data composed of several categorical responses together with categorical or continuous predictors are observed, it is often useful to relate the response probabilities to the predictors via a generalised linear model with a composite link function. This paper discusses a class of link functions that lie between the two extremes of the multivariate logistic transform of McCullagh & Nelder (1989) and the log-linear decomposition of contingency table analysis. The models derived from these link functions are shown to inherit various desirable properties of both the multivariate logistic regression models and the log-linear regression models. A computational scheme for implementing these models is derived and they are demonstrated to be computationally more tractable than the multivariate logistic regression models. Their application is illustrated in a numerical example.