Centering, Scale Indeterminacy, and Differential Item Functioning Detection in Hierarchical Generalized Linear and Generalized Linear Mixed Models

Abstract

In this article, we discuss and illustrate two centering and anchoring options available in differential item functioning (DIF) detection studies based on the hierarchical generalized linear and generalized linear mixed modeling frameworks. We compared and contrasted the assumptions of the two options, and examined the properties of their DIF estimates with a simulation study. For reference purposes, the results were compared to those obtained from using the Mantel-Haenszel procedure as well. Finally, we discuss some implications regarding the choice of model parameterizations for DIF detection using these frameworks.

Notes

¹All the models in these analyses were analyzed using the software program HLM6 (Raudenbush, Bryk, Cheong, Congdon, & Du Toit, 2004).

²Whereas the simulation study assumed conditions with a short test (6 items), our findings were expected to be generalizable to any length of a test with similar simulation conditions except the number of items. The results of another simulation study with 18-item tests with six comparable conditions confirmed our expectations. Due to limited space, we did not include the results here. They could be requested from the corresponding author.