Nonparametric Methods in Cognitively Diagnostic Assessment

Parametric estimation is the prevailing method for fitting diagnostic classification models. In the early days of cognitively diagnostic modeling, publicly available implementations of parametric estimation methods were scarce and often encountered technical difficulties in practice. In response to these difficulties, a number of researchers explored the potential of methods that do not rely on a parametric statistical model—nonparametric methods for short—as alternatives to, for example, MLE for assigning examinees to proficiency classes. Of particular interest were clustering methods because efficient implementations were readily available in the major statistical software packages. This article provides a review of nonparametric concepts and methods, as they have been developed and adopted for cognitive diagnosis: clustering methods and the Asymptotic Classification Theory of Cognitive Diagnosis (ACTCD), the Nonparametric Classification (NPC) method, and its generalization, the General NPC method. Also included in this review are two methods that employ the NPC method as a computational device: joint MLE for cognitive diagnosis and the nonparametric Q-matrix refinement and reconstruction method.