Structural Parameter Standard Error Estimation Method in Diagnostic Classification Models: Estimation and Application

Abstract

The information matrix or its inverse variance–covariance matrix for the maximum likelihood estimates of model parameters in diagnostic classification models plays a key role in statistical inference. Although both the item and structural parameters should be contained in the calculation of the information matrix simultaneously, previous studies have mainly focused on performance of the item parameter standard error (SE), no study has investigated the structural parameter SE estimation methods systematically. In this study, we propose a class of structural parameter SE estimation methods based on the empirical cross-product matrix, the observed information matrix, and the sandwich-type covariance matrix. A simulation study was conducted under different attribute hierarchy structures, the findings suggest that the proposed methods are useful for empirical researchers and practitioners in evaluating the variability of structural parameter estimators. We illustrate the application of the structural parameter SE estimation methods for exploring the presence of an attribute hierarchy using real data.