Wald Test Formulations in DIF Detection of CDM Data with the Proportional Reasoning Test

Abstract

This study aims to conduct differential item functioning analyses in the context of cognitive diagnosis assessments using various formulations of the Wald test. In implementing the Wald test, two scenarios are considered: one where the underlying reduced model can be assumed; and another where a saturated CDM is used. Illustration of the different Wald test to detect DIF in CDM data was based on the items’ performance of the Proportional Reasoning test among low- and high-performing school students. A benchmark simulation study was included to compare the performance of the Wald test in each scenario. The agreement of the latent attribute classification based on different cognitive diagnosis models was also discussed.