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This article demonstrates that the Rasch model cannot reveal systematic differential item functioning (DIF) in single tests. The person total score is the sufficient statistic for the person parameter estimate, eliminating the possibility for residuals at the test level. An alternative approach is to use  subset DIF analysis  to search for DIF in item subsets that form the components of the broader latent trait .  In this methodology, person parameter estimates are initially calculated using all test items. Then, in separate analyses, these person estimates are compared to the observed means in each subset, and the residuals assessed. As such, this methodology tests the assumption that the person locations in each factor group are invariant across subsets. The first objective is to demonstrate that in single tests differences in factor groups will appear as differences in the mean person estimates and the distributions of these estimates. The second objective is to demonstrate how subset DIF analysis reveals differences between person estimates and the observed means in subsets. Implications for practitioners are discussed.

The Rasch Model Cannot Reveal Systematic Differential Item Functioning in Single Tests: Subset DIF Analysis as an Alternative Methodology