An Explicit Form With Continuous Attribute Profile of the Partial Mastery DINA Model

Abstract

Cognitive diagnosis models (CDMs) are the statistical framework for cognitive diagnostic assessment in education and psychology. They generally assume that subjects’ latent attributes are dichotomous—mastery or nonmastery, which seems quite deterministic. As an alternative to dichotomous attribute mastery, attention is drawn to the use of a continuous attribute mastery format in recent literature. To obtain subjects’ finer-grained attribute mastery for more precise diagnosis and guidance, an equivalent but more explicit form of the partial-mastery-deterministic inputs, noisy “and” gate (DINA) model (termed continuous attribute profile [CAP]-DINA form) is proposed in this article. Its parameters estimation algorithm based on this form using Bayesian techniques with Markov chain Monte Carlo algorithm is also presented. Two simulation studies are conducted then to explore its parameter recovery and model misspecification, and the results demonstrate that the CAP-DINA form performs robustly with satisfactory efficiency in these two aspects. A real data study of the English test also indicates it has a better model fit than DINA.