Abstract
The examination of measurement invariance in polytomous items is complicated by the possibility that the magnitude and sign of lack of invariance may vary across the steps underlying the set of polytomous response options, a concept referred to as differential step functioning (DSF). This article describes three classes of nonparametric DSF effect estimators that are based on the models specified by the graded response model (GRM), the continuation ratio model, and the generalized partial credit model. A simulation study was conducted to compare the statistical properties of the three DSF effect estimators under a variety of conditions. The results of the simulation study indicate that the DSF effect estimator based on the GRM yielded the highest level of stability while maintaining the lowest overall level of bias.
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