Evaluation of global testing procedures for item fit to the Rasch model

Two types of global testing procedures for item fit to the Rasch model were evaluated using simulation studies. The first type incorporates three tests based on first-order statistics: van den Wollenberg's Q(1) test, Glas's R-1 test, and Andersen's LR test. The second type incorporates three tests based on second-order statistics: van den Wollenberg's Q(2) test, Glas's R-2 test, and a non-parametric test proposed by Ponocny. The Type I error rates and the power against the violation of parallel item response curves, unidimensionality and local independence were analysed in relation to sample size and test length. In general, the outcomes indicate a satisfactory performance of all tests, except the Q(2) test which exhibits an inflated Type I error rate. Further, it was found that both types of tests have power against all three types of model violation. A possible explanation is the interdependencies among the assumptions underlying the model.