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

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)921-940
Number of pages20
JournalPsychometrika
Volume84
Issue number4
DOIs
StateAccepted/In press - Jan 1 2019

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Model Diagnostics
Identifiability
Attribute
Research Personnel
Binary
Social Sciences
Sample Size
Longitudinal Studies
Ordinal Data
Learning
Psychology
Binary Response Model
Research
Bayesian Variable Selection
Multinomial Model
Probit
Binary Response
Longitudinal Study
Mixture Model
Questionnaire

Keywords

  • Bayesian
  • cognitive diagnosis
  • latent class
  • multivariate ordinal data

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics

Cite this

An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes : Identifiability and Estimation. / Culpepper, Steven Andrew.

In: Psychometrika, Vol. 84, No. 4, 01.12.2019, p. 921-940.

Research output: Contribution to journalArticle

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