Improved Wald Statistics for Item-Level Model Comparison in Diagnostic Classification Models

Diagnostic classification models (DCMs) have been widely used in education, psychology, and many other disciplines. To select the most appropriate DCM for each item, the Wald test has been recommended. However, prior research has revealed that this test provides inflated Type I error rates. To address this problem, the authors propose to replace the asymptotic covariance matrix from the original version of the Wald statistic with a matrix obtained from improved computation methods. In this study, the Wald test based on the observed information matrix and the Wald test based on the sandwich-type matrix are proposed for item-level model comparisons and a simulation study is conducted to investigate their empirical behavior. Simulation results indicate that when the sample size is reasonably large (N ≥ 1 , 000), the Type I error rates of the Wald test based on the sandwich-type matrix are accurate with adequate or excellent power under most of the simulation conditions.