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

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  • Steven Andrew Culpepper

    (University of Illinois at Urbana-Champaign)

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.

Suggested Citation

  • Steven Andrew Culpepper, 2019. "An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 921-940, December.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:4:d:10.1007_s11336-019-09683-4
    DOI: 10.1007/s11336-019-09683-4
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    References listed on IDEAS

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    Cited by:

    1. Steven Andrew Culpepper, 2023. "A Note on Weaker Conditions for Identifying Restricted Latent Class Models for Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 158-174, March.
    2. Yuqi Gu, 2023. "Generic Identifiability of the DINA Model and Blessing of Latent Dependence," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 117-131, March.
    3. Motonori Oka & Kensuke Okada, 2023. "Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 302-331, March.
    4. Jing Ouyang & Gongjun Xu, 2022. "Identifiability of Latent Class Models with Covariates," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1343-1360, December.
    5. Xuliang Gao & Wenchao Ma & Daxun Wang & Yan Cai & Dongbo Tu, 2021. "A Class of Cognitive Diagnosis Models for Polytomous Data," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 297-322, June.
    6. James Joseph Balamuta & Steven Andrew Culpepper, 2022. "Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA–GAMMA Data Augmentation," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 903-945, September.
    7. Yinghan Chen & Ying Liu & Steven Andrew Culpepper & Yuguo Chen, 2021. "Inferring the Number of Attributes for the Exploratory DINA Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 30-64, March.
    8. Chen-Wei Liu & Björn Andersson & Anders Skrondal, 2020. "A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 322-357, June.
    9. Kazuhiro Yamaguchi & Jonathan Templin, 2022. "Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1390-1421, December.

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