## Abstract

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.Weconclude 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.

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.Weconclude 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.

Original language | English |
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Journal | British Journal of Mathematical and Statistical Psychology |

Early online date | 16 Mar 2015 |

DOIs | |

Publication status | Published - 2015 |