Nonparametric Cognitive Diagnosis When Attributes Are Polytomous

Cognitive diagnosis models provide diagnostic information on whether examinees have mastered the skills, called “attributes,” that characterize a given knowledge domain. Based on attribute mastery, distinct proficiency classes are defined to which examinees are assigned based on their item responses. Attributes are typically perceived as binary. However, polytomous attributes may yield higher precision in the assessment of examinees’ attribute mastery. Karelitz (2004) introduced the ordered-category attribute coding framework (OCAC) to accommodate polytomous attributes. Other approaches to handle polytomous attributes in cognitive diagnosis have been proposed in the literature. However, the heavy parameterization of these models often created difficulties in fitting these models. In this article, a nonparametric method for cognitive diagnosis is proposed for use with polytomous attributes, called the nonparametric polytomous attributes diagnostic classification (NPADC) method, that relies on an adaptation of the OCAC framework. The new NPADC method proposed here can be used with various cognitive diagnosis models. It does not require large sample sizes; it is computationally efficient and highly effective as is evidenced by the recovery rates of the proficiency classes observed in large-scale simulation studies. The NPADC method is also used with a real-world data set.