The Restricted DINA Model: A Comprehensive Cognitive Diagnostic Model for Classroom-Level Assessments

The nonparametric classification (NPC) method has been proven to be a suitable procedure for cognitive diagnostic assessments at a classroom level. However, its nonparametric nature impedes the obtention of a model likelihood, hindering the exploration of crucial psychometric aspects, such as model fit or reliability. Reporting the reliability and validity of scores is imperative in any applied context. The present study proposes the restricted deterministic input, noisy "and" gate (R-DINA) model, a parametric cognitive diagnosis model based on the NPC method that provides the same attribute profile classifications as the nonparametric method while allowing to derive a model likelihood and, subsequently, to compute fit and reliability indices. The suitability of the new proposal is examined by means of an exhaustive simulation study and a real data illustration. The results show that the R-DINA model properly recovers the posterior probabilities of attribute mastery, thus becoming a suitable alternative for comprehensive small-scale diagnostic assessments.