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An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation

Published online by Cambridge University Press:  01 January 2025

Steven Andrew Culpepper Open the ORCID record for Steven Andrew Culpepper [Opens in a new window]
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, 725 South Wright Street, Champaign, IL61820, USA. Email:[email protected]
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Abstract

Diagnostic models (DMs) provide researchers and practitioners with tools to classify respondents into substantively relevant classes. DMs are widely applied to binary response data; however, binary response models are not applicable to the wealth of ordinal data collected by educational, psychological, and behavioral researchers. Prior research developed confirmatory ordinal DMs that require expert knowledge to specify the underlying structure. This paper introduces an exploratory DM for ordinal data. In particular, we present an exploratory ordinal DM, which uses a cumulative probit link along with Bayesian variable selection techniques to uncover the latent structure. Furthermore, we discuss new identifiability conditions for structured multinomial mixture models with binary attributes. We provide evidence of accurate parameter recovery in a Monte Carlo simulation study across moderate to large sample sizes. We apply the model to twelve items from the public-use, Early Childhood Longitudinal Study, Kindergarten Class of 1998–1999 approaches to learning and self-description questionnaire and report evidence to support a three-attribute solution with eight classes to describe the latent structure underlying the teacher and parent ratings. In short, the developed methodology contributes to the development of ordinal DMs and broadens their applicability to address theoretical and substantive issues more generally across the social sciences.

Keywords

multivariate ordinal datacognitive diagnosislatent classBayesian
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 4 , December 2019 , pp. 921 - 940
Copyright
Copyright © 2019 The Psychometric Society

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