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Inferring Latent Structure in Polytomous Data with a Higher-Order Diagnostic Model.

Steven Andrew Culpepper1, James J Balamuta2

  • 1Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, IL.

Multivariate Behavioral Research
|October 26, 2021
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Summary

This study introduces a new Bayesian method for diagnostic models (DMs) to classify individuals using polytomous data. The approach enhances latent structure inference in social and behavioral sciences research.

Keywords:
BayesianPolytomous response datacognitive diagnosislatent classlatent structure models

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Area of Science:

  • Social and Behavioral Sciences
  • Psychometrics
  • Statistical Modeling

Background:

  • Diagnostic models (DMs) classify respondents into latent classes based on attributes.
  • Current DMs face challenges in exploratory analysis of polytomous data and higher-order structures.

Purpose of the Study:

  • To propose a novel method for inferring latent structure in polytomous response data.
  • To advance exploratory diagnostic models using a higher-order factor model.

Main Methods:

  • A novel Bayesian formulation incorporating variable selection techniques.
  • Utilizing a higher-order factor model to describe dependence among discrete latent attributes.
  • Monte Carlo simulation for parameter recovery assessment.

Main Results:

  • The proposed method accurately recovers parameters in simulation studies.
  • Demonstrated application to the 2012 Programme for International Student Assessment (PISA) problem-solving data.

Conclusions:

  • The new Bayesian approach effectively infers latent structure for polytomous data.
  • This method advances diagnostic modeling in social and behavioral research.