Modeling effects of differential item functioning in polytomous items.

Conventional two-group DIF analysis for dichotomous items is extended to factorial DIF analysis for polytomous items where multiple grouping factors with multiple groups in each are jointly analyzed. By adopting the formulation of general linear models, item parameters across all possible groups are treated as a dependent variable and the grouping factors as independent variables. These item parameters are then reparameterized as a set of grand item parameters and sets of DIF parameters representing main and interaction effects of the factors on the items. Results of simulation studies show that the parameters of the proposed modeling could be satisfactorily recovered. A real data set of 10 polytomous items and 1924 subjects was analyzed. Applications and implications of the proposed modeling are addressed.