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Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing Misconceptions

Published online by Cambridge University Press:  01 January 2025

Laine Bradshaw  and
Jonathan Templin
Laine Bradshaw*
Affiliation:
Department of Educational Psychology, The University of Georgia
Jonathan Templin
Affiliation:
Department of Educational Psychology, The University of Georgia
*
Requests for reprints should be sent to Laine Bradshaw, Department of Educational Psychology, The University of Georgia, 323 Aderhold Hall, Athens, GA 30602, USA. E-mail: laineb@uga.edu
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Abstract

Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student’s overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for students, teachers, and other stakeholders. Diagnostic classification models (DCMs) provide multidimensional feedback by using categorical latent variables that represent distinct skills underlying a test that students may or may not have mastered. The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of a unidimensional IRT model and a DCM where the categorical latent variables represent misconceptions instead of skills. In addition to an estimate of ability along a latent continuum, the SICM model provides multidimensional, diagnostic feedback in the form of statistical estimates of probabilities that students have certain misconceptions. Through an empirical data analysis, we show how this additional feedback can be used by stakeholders to tailor instruction for students’ needs. We also provide results from a simulation study that demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions.

Keywords

diagnostic classification modelsitem response theorydiagnosing student misconceptionsmultidimensional measurement modelnominal response

Information

Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 3 , July 2014 , pp. 403 - 425
Copyright
Copyright © 2013 The Psychometric Society

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Footnotes

Electronic Supplementary Material The online version of this article (doi:10.1007/s11336-013-9350-4) contains supplementary material, which is available to authorized users.

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