A Restricted Latent Class Hidden Markov Model for Polytomous Responses, Polytomous Attributes, and Covariates: Identifiability and Application

We introduce a restricted latent class exploratory model for longitudinal data with ordinal attributes and respondent-specific covariates. Responses follow a time inhomogeneous hidden Markov model where the probability of a particular latent state at a time point is conditional on values at the previous time point of the respondent's covariates and latent state. We prove that the model is identifiable, state a Bayesian formulation, and demonstrate its efficacy in a variety of scenarios through two simulation studies. We apply the model to response data from a mathematics examination, comparing the results to a previously published confirmatory analysis, and also apply it to emotional state response data which was measured over a several-day period.