On the power of the test for cluster bias.

Cluster bias refers to measurement bias with respect to the clustering variable in multilevel data. The absence of cluster bias implies absence of bias with respect to any cluster-level (level 2) variable. The variables that possibly cause the bias do not have to be measured to test for cluster bias. Therefore, the test for cluster bias serves as a global test of measurement bias with respect to any level 2 variable. However, the validity of the global test depends on the Type I and Type II error rates of the test. We compare the performance of the test for cluster bias with the restricted factor analysis (RFA) test, which can be used if the variable that leads to measurement bias is measured. It appeared that the RFA test has considerably more power than the test for cluster bias. However, the false positive rates of the test for cluster bias were generally around the expected values, while the RFA test showed unacceptably high false positive rates in some conditions. We conclude that if no significant cluster bias is found, still significant bias with respect to a level 2 violator can be detected with an RFA model. Although the test for cluster bias is less powerful, an advantage of the test is that the cause of the bias does not need to be measured, or even known.