A Residual‐Based Differential Item Functioning Detection Framework in Item Response Theory

Differential item functioning (DIF) of test items should be evaluated using practical methods that can produce accurate and useful results. Among a plethora of DIF detection techniques, we introduce the new Residual DIF (RDIF) framework, which stands out for its accessibility without sacrificing efficacy. This framework consists of three item response theory (IRT) residual statistics: RDIFR$RDI{F_R}$, RDIFS$RDI{F_S}$, and RDIFRS$RDI{F_{RS}}$. We conducted a simulation study with a 40‐item test to assess the performance of RDIF in comparison with the Mantel‐Haenszel, logistic regression, and IRT‐based likelihood ratio test methods. Even when analyzing small sample sizes, the results revealed RDIFRS$RDI{F_{RS}}$ to be the most robust DIF detection statistic with strict control of Type I error across all simulated conditions when paired with the purification procedure. Also, RDIFR$RDI{F_R}$ and RDIFS$RDI{F_S}$ proved to be powerful indicators of uniform and nonuniform DIF, respectively. Therefore, RDIFRS$RDI{F_{RS}}$ should serve as the primary flagging criterion, whereas RDIFR$RDI{F_R}$ and RDIFS$RDI{F_S}$ best serve as indicators of DIF type. An empirical DIF study also showed that the RDIF framework could perform satisfactorily with real data from a large‐scale assessment. Overall, the RDIF framework demonstrated its potential as a new standard for IRT‐based DIF detection methodology.