A Unifying Framework for Markov Modeling in Discrete Space and Discrete Time

The focus of this article is on Markov models for the analysis of panel data and, more specifically, on data obtained from repeated measurements of one categorical variable at several consecutive points in time. We first review developments in the field that attack the two main problems of the simple Markov model. The Mixed Markov model extends the simple model by allowing for population heterogeneity; the Latent Markov model incorporates measurement error and latent change into the simple model. Second, we present the more general Latent Mixed Markov model and show how both the Mixed Markov model and the Latent Markov model, as well as several more specific models, relate to this more general model. Finally, we reanalyze the Los Angeles panel data on depression with a focus on stability and change.