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Restricted Latent Class Models for Nominal Response Data: Identifiability and Estimation

Published online by Cambridge University Press:  27 December 2024

Ying Liu  and
Steven Andrew Culpepper Open the ORCID record for Steven Andrew Culpepper [Opens in a new window]
Ying Liu
Affiliation:
University of Illinois at Urbana-Champaign
Steven Andrew Culpepper*
Affiliation:
University of Illinois at Urbana-Champaign
*
Correspondence should be made to Steven Andrew Culpepper, Department of Statistics, University of Illinois at Urbana-Champaign, Computing Applications Building, Room 152, 605 E. Springfield Ave., Champaign, IL61820, USA. Email: [email protected]
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Abstract

Restricted latent class models (RLCMs) provide an important framework for diagnosing and classifying respondents on a collection of multivariate binary responses. Recent research made significant advances in theory for establishing identifiability conditions for RLCMs with binary and polytomous response data. Multiclass data, which are unordered nominal response data, are also widely collected in the social sciences and psychometrics via forced-choice inventories and multiple choice tests. We establish new identifiability conditions for parameters of RLCMs for multiclass data and discuss the implications for substantive applications. The new identifiability conditions are applicable to a wealth of RLCMs for polytomous and nominal response data. We propose a Bayesian framework for inferring model parameters, assess parameter recovery in a Monte Carlo simulation study, and present an application of the model to a real dataset.

Keywords

restricted latent class modelsnominal response datacognitive diagnosis modelidentifiabilityBayesian
Type
Theory and Methods
Information
Psychometrika , Volume 89 , Issue 2 , June 2024 , pp. 592 - 625
Copyright
Copyright © 2023 The Author(s), under exclusive licence to The Psychometric Society

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