In this study, the authors extend the standard item response model with internal restrictions on item difficulty (MIRID) to fit polytomous items using cumulative logits and adjacent-category logits. Moreover, the new model incorporates discrimination parameters and is rooted in a multilevel framework. It is a nonlinear mixed model so that existing…

Recent research examining racial differences on standardized cognitive tests has focused on the impact of test item difficulty. Studies using data from the SAT and GRE have reported a correlation between item difficulty and differential item functioning (DIF) such that minority test takers are less likely than majority test takers to respond…