Evaluating Model-Data Fit by Comparing Parametric and Nonparametric Item Response Functions: Application of a Tukey-Hann Procedure.

This study describes an approach for examining model-data fit for the dichotomous Rasch model using Tukey-Hann item response functions (TH-IRFs). The procedure proposed in this paper is based on an iterative version of a smoothing technique proposed by Tukey (1977) for estimating nonparametric item response functions (IRFs). A root integrated squared error (RISE) statistic (Douglas and Cohen, 2001) is used to compare the TH-IRFs to the Rasch IRFs. Data from undergraduate students at a large university are used to demonstrate this iterative smoothing technique. The RISE statistic is used for comparing the item response functions to assess model-data fit. A comparison between the residual based Infit and Outfit statistics and RISE statistics are also examined. The results suggest that the RISE statistic and TH-IRFs provide a useful analytical and graphical approach for evaluating item fit. Implications for research, theory and practice related to model-data fit are discussed.