A Model for Repeated Measurements of a Multivariate Binary Response

This article presents a logit model for a vector of binary variables observed for each subject under multiple conditions. The model contains a vector of random effects to account for correlations among the repeated measurements. A nonparametric treatment of the random effects implies a multivariate log-linear model having quasi-symmetric structure for the cross-classification of responses at the various conditions. The fit yields estimates of within-subject effects comparing the conditions for each variable. The estimates are identical to conditional maximum likelihood estimates for a fixed-effects version of the logit model. Extensions incorporate independent groups or allow variables to have multiple response categories.