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A Note on the Odds Ratio DIF Index

Recently, Jin et al. (2018) proposed using the log of the odds ratio (OR) as a differential item functioning (DIF) index for item responses that follow the Rasch model. The OR is relatively simple to calculate and does not require grouping examinees by ability. This index was more robust to unbalanced DIF than the Mantel–Haenszel (MH) or logistic regression (LR) procedures and had only slightly lower power when the DIF was balanced. Unbalanced DIF occurs when the average magnitude of DIF favors one group instead of balancing across items. Unbalanced DIF can become confounded with true group mean differences, so indices robust to unbalanced DIF are useful. However, in the last paragraph the authors noted: ‘‘It was suspected that the OR method will not perform well when data follow the twoor three-parameter logistic model’’ (p. 628). This brief commentary explains one problem with using the OR method with 2PL or 3PL item responses: If the response functions are identical for both groups, when the group mean difference is large, the log of the OR will vary with the value of the item parameters.