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Abstract
The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of an item response theory (IRT) model and a diagnostic classification model (DCM). Common modeling and testing procedures utilize unidimensional IRT to provide an estimate of a students overall ability. Recent advances in psychometrics have focused on measuring multiple dimensions to provide more detailed feedback for students, teachers, and other stakeholders. DCMs provide multidimensional feedback by using multiple categorical variables that represent skills underlying a test that students may or may not have mastered. The SICM model combines an IRT model with a DCM model that uses categorical variables that represent misconceptions instead of skills. In addition to the type of information common testing procedures provide about an examinee an overall continuous ability, the SICM model also is able to provide multidimensional, diagnostic feedback in the form of statistical estimates of misconceptions. This additional feedback can be used by stakeholders to tailor instruction for students needs. Results of a simulation study demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions. Results of an empirical data analysis highlight the need to address statistical considerations of the model from the onset of the assessment development process.