Modeling Structure and Chance in Transitions: Mixed Latent Partial Markov-Chain Models

A family of finite mixture distribution models is presented which allows specification of basically different developmental processes in distinct latent subpopulations. In particular, random fluctuation between states for one latent subpopulation can be modeled together with stability or coherent developmental trajectories for others. Formally, these models are introduced within the framework of mixed latent Markov chains with multiple indicators per occasion. Identifiability conditions which become necessary because of the random fluctuation assumption for a part of the population are discussed. Model specification and interpretation are illustrated by an application to empirical data on therapeutic interventions in infancy and early childhood.