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

Abstract

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 respondent's latent state at the current time point is conditional on the respondent's latent state at the previous time point as well as the respondent's covariates at the current time point. 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.

60 pages, 3 figures, 34 tables. Edited language for clarity, removed one table, and fixed typos. Published in the Journal of Educational and Behavioral Statistics

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• Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
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• A Restricted Latent Class Model with Polytomous Attributes and Respondent-Level Covariates