A Class of Logistic Regression Models for Multivariate Binary Time Series

A logistic model for multivariate binary time series is proposed. First, we establish the equivalence between a log-linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others. The logistic formulation is used to describe a Markov chain for each series, which implies a Markov model for the vector of time series. A pseudolikelihood estimation procedure is presented. The methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health-maintenance plan.