, Volume 79, Issue 3, pp 403–425 | Cite as

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

  • Laine Bradshaw
  • Jonathan Templin


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.

Key words

diagnostic classification models item response theory diagnosing student misconceptions multidimensional measurement model nominal response 



This research was supported by the National Science Foundation grants DRL-0822064; SES-0750859; and SES-1030337. The opinions expressed are those of the authors and do not necessarily reflect the views of NSF.

Supplementary material

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Copyright information

© The Psychometric Society 2013

Authors and Affiliations

  1. 1.Department of Educational PsychologyThe University of GeorgiaAthensUSA

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