Restricted latent class models for polytomous attributes
Wayman, Eric Alan
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Permalink
https://hdl.handle.net/2142/130018
Description
Title
Restricted latent class models for polytomous attributes
Author(s)
Wayman, Eric Alan
Issue Date
2025-07-02
Director of Research (if dissertation) or Advisor (if thesis)
Culpepper, Steven
Doctoral Committee Chair(s)
Douglas, Jeffrey
Committee Member(s)
Chen, Yuguo
Park, Trevor
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Abstract
Chapter 1: We present an exploratory restricted latent class model where response data is for a single time point, polytomous, and differing across items, and where latent classes reflect a multi-attribute state where each attribute is ordinal. Our model extends previous work to allow for correlation of the attributes through a multivariate probit specification and to allow for respondent-specific covariates. We demonstrate that the model recovers parameters well in a variety of realistic scenarios, and apply the model to the analysis of a particular dataset designed to diagnose depression. The application demonstrates the utility of the model in identifying the latent structure of depression beyond single-factor approaches which have been used in the past.
Chapter 2: We introduce a restricted latent class exploratory model for longitudinal data with ordinal attributes and respondent-specific covariates. Responses follow a 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 a simulation study. As a real-world demonstration, we apply the model to response data from a mathematics examination, and compare the results to a previously published confirmatory analysis.
Chapter 3: This chapter extends the longitudinal model of Chapter 2 to handle the case where in the longitudinal data some respondents have missing response vectors at one or more time points. We assume that the data is missing completely at random, and treat the missing response vectors as parameters following the same conditional independence and dependence assumptions as the observed response vectors. We demonstrate the performance of this model via simulation studies with increasing percentages of missing data, and apply the model to a dataset where some respondents had missing response vectors.
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