Restricted latent class models for polytomous attributes

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois Urbana-Champaign

Year dc:date

2025

Author dc:creator

• Wayman, Eric Alan

Contributors dc:contributor

• Culpepper, Steven
• Douglas, Jeffrey
• Chen, Yuguo
• Park, Trevor

• Statistics

Statement dc:rights

• Copyright 2025 Eric Alan Wayman

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/130018

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F130018