Evaluating the Impact of Multidimensionality on Type I and Type II Error Rates using the Q-Index Item Fit Statistic for the Rasch Model.

Abstract

To understand the role of fit statistics in Rasch measurement is simple: applied researchers can only benefit from the desirable properties of the Rasch model when the data fit the model. The purpose of the current study was to assess the Q-Index robustness (Ostini and Nering, 2006), and its performance was compared to the current popular fit statistics known as MSQ Infit, MSQ Outfit, and standardized Infit and Outfit (ZSTDs) under varying conditions of test length, sample size, item difficulty (normal and uniform), and dimensionality utilizing a Monte Carlo simulation. The Type I and Type II error rates are also examined across fit indices. This study provides applied researchers guidelines the robustness and appropriateness of the use of the Q-Index, which is an alternative to the currently available item fit statistics. The Q-Index was slightly more sensitive to the levels of multidimensionality set in the study while MSQ Infit, Outfit, and standardized Infit and Outfit (ZSTDs) failed to identify the multidimensional conditions. The Type I error rate of the Q-Index was lower than the rest of the fit indices; however, the Type II error rate was higher than the anticipated beta = .20 across all fit indices.