A Bi-Factor Generalized Cognitive Diagnosis Model Framework

Cognitive diagnosis models (CDMs) are often applied to constructs that are largely unidimensional in nature (e.g., mathematics, reading, mental health status) where a set of discrete attributes coexists with a dominant general proficiency dimension. This article presents the bi-factor CDM model (BF-CDM), which partitions item responses into a direct effect of continuous general proficiency and a discrete attribute-mastery tier, allowing mastery classifications to be made beyond what is attributable to general ability. By modeling both tiers explicitly, the BF-CDM makes it possible to evaluate the contribution of the discrete tier itself. Specifically, it can show whether the hypothesized attributes carry diagnostic information beyond general proficiency, both through model comparison with the nested unidimensional model and through the reliability of the attribute-specific component. A simulation study manipulating sample size, test length, number of attributes, and attribute-tier discrimination shows accurate recovery of item and person parameters, and of the model-implied response functions. An application to reading comprehension data from PISA illustrates the practical value of the model: reliability of attribute-mastery classifications drops substantially once variance attributable to general proficiency is partialled out, indicating that much of the apparent diagnostic precision obtained under a saturated attribute structure reflects a single dominant general factor.