A copula formulation for multivariate latent Markov models

We specify a general formulation for multivariate latent Markov models for panel data, where outcomes are possibly of mixed-type (categorical, discrete, continuous). Conditionally on a time-varying discrete latent variable and covariates, the joint distribution of outcomes simultaneously observed is expressed through a parametric copula. We therefore do not make any conditional independence assumption. The observed likelihood is maximized by means of an expectation–maximization algorithm. In a simulation study, we argue how modeling the residual contemporary dependence might be crucial in order to avoid bias in the parameter estimates. We illustrate through an original application to assessment of poverty through direct and indirect indicators in a cohort of Italian households.