A Family of Generalized Diagnostic Classification Models for Multiple Choice Option-Based Scoring

This article proposes a new family of diagnostic classification models (DCM) called the Generalized Diagnostic Classification Models for Multiple Choice Option-Based Scoring (GDCM-MC). The GDCM-MC is created for multiple choice assessments with response options designed to attract particular kinds of student thinking and understanding, both desired (correct) thinking and problematic (incorrect or partially correct) thinking. Key features that combine to distinguish GDCM-MC are: (a) an expanded latent space that can include both desirable and problematic facets of thinking, (b) an expanded Q matrix that includes a row for each response option and that uses a three-valued coding scheme to specify which latent states are strongly attracted to that option, (c) a guessing component that responds to the forced choice aspect of multiple choice questions, and (d) a general modeling framework that can incorporate the diagnostic modeling functionality of almost any dichotomous DCM, such as deterministic input, noisy ``and'' gate (DINA), reparameterized unified model (RUM), loglinear cognitive diagnosis model (LCDM), or general diagnostic model (GDM). The article discusses these four components and presents the GDCM-MC model equation as a mixture of cognitive and guessing components. Two identifiability theorems are presented. A Bayesian Markov Chain Monte Carlo (MCMC) model estimation algorithm is discussed, and real and simulated data studies are reported.