Using Two-Level Factor Analysis to Test for Cluster Bias in Ordinal Data

The test for cluster bias is a test of measurement invariance across clusters in 2-level data. This article examines the true positive rates (empirical power) and false positive rates of the test for cluster bias using the likelihood ratio test (LRT) and the Wald test with ordinal data. A simulation study indicates that the scaled version of the LRT that accounts for nonnormality of the data gives untrustworthy results, whereas the unscaled LRT and the Wald test have acceptable false positive rates and perform well in terms of empirical power rate if the amount of cluster bias is large. The test for cluster bias is illustrated with data from research on teacher-student relations.