SIMULTANEOUSLY MODELING JOINT AND MARGINAL DISTRIBUTIONS OF MULTIVARIATE CATEGORICAL RESPONSES

We discuss model-fitting methods for analyzing simultaneously the join t and marginal distributions of multivariate categorical responses. Th e models are members of a broad class of generalized logit and logline ar models. We fit them by improving a maximum likelihood algorithm tha t uses Lagrange's method of undetermined multipliers and a Newton-Raph son iterative scheme. We also discuss goodness-of-fit tests and adjust ed residuals, and give asymptotic distributions of model parameter est imators. For this class of models, inferences are equivalent for Poiss on and multinomial sampling assumptions. Simultaneous models for joint and marginal distributions may be useful in a variety of applications , including studies dealing with longitudinal data, multiple indicator s in opinion research, cross-over designs, social mobility, and inter- rater agreement. The models are illustrated for one such application, using data from a recent General Social Survey regarding opinions abou t various types of government spending.