arXiv subjects

Jesse Bowers

Publications and source records attributed to Jesse Bowers.

4 recordsLinked to original sources

arXiv2025

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 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.

stat.ME↗

arXiv2024

A Restricted Latent Class Model with Polytomous Attributes and Respondent-Level Covariates

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.

stat.ME↗

arXiv2024

Equivalence Set Restricted Latent Class Models (ESRLCM)

Latent Class Models (LCMs) are used to cluster multivariate categorical data, commonly used to interpret survey responses. We propose a novel Bayesian model called the Equivalence Set Restricted Latent Class Model (ESRLCM). This model identifies clusters who have common item response probabilities, and does so more generically than traditional restricted latent attribute models. We verify the identifiability of ESRLCMs, and demonstrate the effectiveness in both simulations and real-world applications.

stat.ML↗

arXiv2022

Dependent Latent Class Models

Latent Class Models (LCMs) are used to cluster multivariate categorical data (e.g. group participants based on survey responses). Traditional LCMs assume a property called conditional independence. This assumption can be restrictive, leading to model misspecification and overparameterization. To combat this problem, we developed a novel Bayesian model called a Dependent Latent Class Model (DLCM), which permits conditional dependence. We verify identifiability of DLCMs. We also demonstrate the effectiveness of DLCMs in both simulations and real-world applications. Compared to traditional LCMs, DLCMs are effective in applications with time series, overlapping items, and structural zeroes.

stat.ML↗