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For the analysis of multivariate categorical longitudinal data, we propose an extension of the dynamic logit model. The resulting model is based on a marginal parameterization of the conditional distribution of each vector of response variables given the covariates, the lagged response variables, and a set of subject-specific parameters for the unobserved heterogeneity. The latter ones are assumed to follow a first-order Markov chain. For the maximum likelihood estimation of the model parameters, we outline an EM algorithm. The data analysis approach based on the proposed model is illustrated by a simulation study and an application to a dataset, which derives from the Panel Study on Income Dynamics and concerns fertility and female participation to the labor market.
Bartolucci et al. (Tue,) studied this question.