TY - JOUR
T1 - An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes
T2 - Identifiability and Estimation
AU - Culpepper, Steven Andrew
N1 - Publisher Copyright:
© 2019, The Psychometric Society.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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.
AB - 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.
KW - Bayesian
KW - cognitive diagnosis
KW - latent class
KW - multivariate ordinal data
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U2 - 10.1007/s11336-019-09683-4
DO - 10.1007/s11336-019-09683-4
M3 - Article
C2 - 31432312
AN - SCOPUS:85071250831
SN - 0033-3123
VL - 84
SP - 921
EP - 940
JO - Psychometrika
JF - Psychometrika
IS - 4
ER -