| Abstract: | Cross‐level invariance in a multilevel item response model can be investigated by testing whether the within‐level item discriminations are equal to the between‐level item discriminations. Testing the cross‐level invariance assumption is important to understand constructs in multilevel data. However, in most multilevel item response model applications, the cross‐level invariance is assumed without testing of the cross‐level invariance assumption. In this study, the detection methods of differential item discrimination (DID) over levels and the consequences of ignoring DID are illustrated and discussed with the use of multilevel item response models. Simulation results showed that the likelihood ratio test (LRT) performed well in detecting global DID at the test level when some portion of the items exhibited DID. At the item level, the Akaike information criterion (AIC), the sample‐size adjusted Bayesian information criterion (saBIC), LRT, and Wald test showed a satisfactory rejection rate (>.8) when some portion of the items exhibited DID and the items had lower intraclass correlations (or higher DID magnitudes). When DID was ignored, the accuracy of the item discrimination estimates and standard errors was mainly problematic. Implications of the findings and limitations are discussed. |
