A CLASS OF REGRESSION-MODELS FOR MULTIVARIATE CATEGORICAL RESPONSES

When data composed of several categorical responses together with cate gorical or continuous predictors are observed, it is often useful to r elate the response probabilities to the predictors via a generalised l inear model with a composite link function. This paper discusses a cla ss of link functions that lie between the two extremes of the multivar iate logistic transform of McCullagh & Nelder (1989) and the log-linea r decomposition of contingency table analysis. The models derived from these link functions are shown to inherit various desirable propertie s of both the multivariate logistic regression models and the log-line ar regression models. A computational scheme for implementing these mo dels is derived and they are demonstrated to be computationally more t ractable than the multivariate logistic regression models. Their appli cation is illustrated in a numerical example.