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

Eric Alan Wayman, Steven Andrew Culpepper, Jeff Douglas, Jesse Bowers

Abstract

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.

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

Abstract

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.
Paper Structure (26 sections, 82 equations, 1 figure, 15 tables)

This paper contains 26 sections, 82 equations, 1 figure, 15 tables.

Table of Contents

  1. Introduction
  2. Overall approach
  3. Measurement model
  4. Monotonicity condition
  5. Structural model
  6. Bayesian model
  7. Likelihood and prior related to observed data
  8. Priors related to coefficients for measurement model
  9. Priors for structural model
  10. Integrating out the variance parameter
  11. Parameter expansion
  12. Algorithm
  13. Augmented data and measurement thresholds
  14. Beta and delta
  15. Latent states and related auxiliary variables
  16. ...and 11 more sections

Figures (1)

  • Figure 1: Directed graphical model (for alt text, see Supplementary Material D)