A closer look at the measurement of change: Integrating latent state-trait models into the general framework of latent mixed Markov modeling

It is shown how two extensions of the latent Markov model that have been developed by Rolf Langeheine and his colleagues (latent mixed Markov models, latent state-trait models) can be integrated into a common general frame of reference. In particular, it is demonstrated that latent state-trait models are a special subgroup of latent mixed Markov models. The different chains of a latent mixed Markov models are equivalent to the trait values of a latent state-trait model. Moreover, it is described in detail how the response probabilities of a latent mixed Markov models must be restricted to get a latent state-trait model. Based on this integration of latent state-trait models into the general framework of latent mixed Markov modeling, new extensions of the classical latent state-trait model were formulated to consider individual differences in the distributions of latent state variables as well as individual differences in the process of change. Moreover, it is shown how latent state-trait theory can guide the selection of the number of chains in latent Markov models as well as in latent mixed Markov models.