mixmcm: A community-contributed command for fitting mixtures of Markov chain models using maximum likelihood and the EM algorithm

Abstract

Markov chain models and finite mixture models have been widely applied in various strands of the academic literature. Several studies analyzing dynamic processes have combined both modeling approaches to account for unobserved heterogeneity within a population. In this article, we describe mixmcm, a community-contributed command that fits the general class of mixed Markov chain models, accounting for the possibility of both entries into and exits from the population. To account for the possibility of incomplete information within the data (that is, unobserved heterogeneity), the model is fit with maximum likelihood using the expectation-maximization algorithm. mixmcm enables users to fit the mixed Markov chain models parametrically or semiparametrically, depending on the specifications chosen for the transition probabilities and the mixing distribution. mixmcm also allows for endogenous identification of the optimal number of homogeneous chains, that is, unobserved types or “components”. We illustrate mixmcm‘s usefulness through three examples analyzing farm dynamics using an unbalanced panel of commercial French farms.