Modeling repeated ordered categorical data using copulas

A parametric model for longitudinal ordered categorical data is proposed. The marginal distributions are modeled using standard regression models and the association between pairs of successive margins is characterized by a set of bivariate copula distributions under a first order Markov hypothesis. Several bivariate copula families, including Frank’s, Plackett’s, Clayton’s, Joe’s and Mardia’s are used to model the association between successive responses. The corresponding log-likelihood is written in terms of the initial margin and of the transition probabilities.Parameters from the marginal regression model and from the pairwise association copula are estimated by direct likelihood maximization. The method is illustrated by analyzing data from a trial on acute migraine.