Complex Versus Simple Modeling for DIF Detection: When the Intraclass Correlation Coefficient (ρ) of the Studied Item Is Less Than the ρ of the Total Score

Abstract

Previous research has demonstrated that differential item functioning (DIF) methods that do not account for multilevel data structure could result in too frequent rejection of the null hypothesis (i.e., no DIF) when the intraclass correlation coefficient (ρ) of the studied item was the same as the ρ of the total score. The current study extended previous research by comparing the performance of DIF methods when ρ of the studied item was less than ρ of the total score, a condition that may be observed with considerable frequency in practice. The performance of two simple and frequently used DIF methods that do not account for multilevel data structure, the Mantel-Haenszel test (MH) and logistic regression (LR), was compared with the performance of a complex and less frequently used DIF method that does account for multilevel data structure, hierarchical logistic regression (HLR). Simulation indicated that HLR and LR performed equivalently in terms of significance tests under most conditions, and MH was conservative across most of the conditions. Effect size estimate of HLR was equally accurate and consistent as effect size estimates of LR and MH under the Rasch model and was more accurate and consistent than LR and MH effect size estimates under the two-parameter item response theory model. The results of the current study provide evidence to help researchers further understand the comparative performance between complex and simple modeling for DIF detection under multilevel data structure. © The Author(s) 2013.