A Polytomous Model of Cognitive Diagnostic Assessment for Graded Data

Abstract

Pursuing the line of the difference models in IRT (Thissen & Steinberg, 1986), this article proposed a new cognitive diagnostic model for graded/polytomous data based on the deterministic input, noisy, and gate (Haertel, 1989; Junker & Sijtsma, 2001), which is named the DINA model for graded data (DINA-GD). We investigated the performance of a full Bayesian estimation of the proposed model. In the simulation, the classification accuracy and item recovery for the DINA-GD model were investigated. The results indicated that the proposed model had acceptable examinees' correct attribute classification rate and item parameter recovery. In addition, a real-data example was used to illustrate the application of this new model with the graded data or polytomously scored items.