Two-step likelihood ratio test for item-level model comparison in cognitive diagnosis models

Abstract

There has been an increase of interest in psychometric models referred to as cognitive diagnosis models (CDMs). A critical concern is in selecting the most appropriate model at the item level. Several tests for model comparison have been employed, which include the likelihood ratio (LR) and the Wald (W) tests. Although the LR test is relatively more robust than the W test, the current implementation of the LR test is very time consuming, given that it requires calibrating many different models and comparing them to the general model. In this article, we introduce the two-step LR test (2LR), an approximation to the LR test based on a two-step estimation procedure under the generalized deterministic inputs, noisy, "and" gate (G-DINA) model framework, the two-step LR test (2LR). The 2LR test is shown to have similar performance as the LR test. This approximation only requires calibration of the more general model, so that this statistic may be easily applied in empirical research.