Detecting Differential Item Functioning among Multiple Groups Using IRT Residual DIF Framework

Abstract

This study presents a generalized version of the residual differential item functioning (RDIF) detection framework in item response theory, named GRDIF, to analyze differential item functioning (DIF) in multiple groups. The GRDIF framework retains the advantages of the original RDIF framework, such as computational efficiency and ease of implementation. The performance of GRDIF was assessed through a simulation study and compared with existing DIF detection methods, including the generalized Mantel-Haenszel, Lasso-DIF, and alignment methods. Results showed that the GRDIF framework demonstrated well-controlled Type I error rates close to the nominal level of .05 and satisfactory power in detecting uniform, nonuniform, and mixed DIF across different simulated conditions. Each of the three GRDIF statistics, $GRDI{F}_R$, $GRDI{F}_S$, and $GRDI{F}_{RS}$, effectively detected the specific type of DIF for which it was designed, with $GRDI{F}_{RS}$ exhibiting the most robust performance across all types of DIF. The GRDIF framework outperformed other DIF detection methods under various conditions, suggesting its potential for practical applications, particularly in large-scale assessments involving multiple groups. Additionally, an empirical study demonstrated the efficacy and utility of the GRDIF framework in conducting DIF analysis with a high-stakes assessment data set.