Discrete Latent Markov Models for Normally Distributed Response Data

Van de Pol and Langeheine (1990) presented a general framework for Markov modeling of repeatedly measured discrete data. We discuss analogical single indicator models for normally distributed responses. In contrast to discrete models, which have been studied extensively, analogical continuous response models have hardly been considered. These models are formulated as highly constrained multinormal finite mixture models (McLachlan & Peel, 2000). The assumption of conditional independence, which is often postulated in the discrete models, may be relaxed in the normal-based models. In these models, the observed correlation between two variables may thus be due to the presence of two or more latent classes and the presence of within-class dependence. The latter may be subjected to structural equation modeling. In addition to presenting various normal-based Markov models, we demonstrate how these models, formulated as multinormal finite mixtures, may be fitted using the freely available program Mx (Neale, Boker, Xie, & Maes, 2002). To illustrate the application of some of the models, we report the analysis of data relating to the understanding of the conservation of continuous quantity (i.e., a Piagetian construct).