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Normalization rules for item response models: Simulation results

ABSTRACT This research examines the statistical methodology that is used to estimate the parameters in item response models. An integral part of an item response model is the normalization rule that is used to identify the distributional parameters. The main result shown here is that only Verhelst–Glas normalizations that arbitrarily set one difficulty and one dispersion parameter to unity are consistent with the basic assumptions underlying the two-parameter logistic model. Failure to employ this type of normalization will lead to scores that depend on the item composition of the test and differential item difficulty (DIF) will compromise the validity of the estimated ability scores when different groups are being compared. It is also shown that some of the tests for DIF fail when the data are generated by an IRT model with a random effect. Most of the results are based on simulations of a four item model. Because the data generation mechanism is known, it is possible to determine the effect on ability scores and parameter estimates when different normalizations or different distribution parameter values are used.