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.