Association models for a multivariate binary response

Models for a multivariate binary response are parameterized by univariate m arginal probabilities and dependence ratios of all orders. The w-order depe ndence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence. This parameterizat ion supports likelihood-based inference for both regression parameters, rel ating marginal probabilities to explanatory variables, and association mode l parameters, relating dependence ratios to simple and meaningful mechanism s. Five types of association models are proposed, where responses are (1) i ndependent given a necessary factor for the possibility of a success, (2) i ndependent given a latent binary factor, (3) independent given a latent bet a distributed variable, (4) follow a Markov chain, and (5) follow one of tw o first-order Markov chains depending on the realization of a binary latent factor. These models are illustrated by reanalyzing three data sets, forem ost a set of binary time series on auranofin therapy against arthritis. Lik elihood-based approaches are contrasted with approaches based on generalize d estimating equations. Association models specified by dependence ratios a re contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients.