A Model Fit Statistic for Generalized Partial Credit Model

Investigating the fit of a parametric model is an important part of the measurement process when implementing item response theory (IRT), but research examining it is limited. A general nonparametric approach for detecting model misfit, introduced by J. Douglas and A. S. Cohen (2001), has exhibited promising results for the two-parameter logistic model and Samejima s graded response model. This study extends this approach to test the fit of generalized partial credit model (GPCM). The empirical Type I error rate and power of the proposed method are assessed for various test lengths, sample sizes, and type of assessment. Overall, the proposed fit statistic performed well under the studied conditions in that the Type I error rate was not inflated and the power was acceptable, especially for moderate to large sample sizes. A further advantage of the nonparametric approach is that it provides a convenient graphical display of possible misfit.