An Assessment of the Nonparametric Approach for Evaluating the Fit of Item Response Models

As item response theory has been more widely applied, investigating the fit of a parametric model becomes an important part of the measurement process. There is a lack of promising solutions to the detection of model misfit in IRT. Douglas and Cohen introduced a general nonparametric approach, RISE (Root Integrated Squared Error), for detecting model misfit. The purposes of this study were to extend the use of RISE to more general and comprehensive applications by manipulating a variety of factors (e.g., test length, sample size, IRT models, ability distribution). The results from the simulation study demonstrated that RISE outperformed G² and S‐X² in that it controlled Type I error rates and provided adequate power under the studied conditions. In the empirical study, RISE detected reasonable numbers of misfitting items compared to G² and S‐X², and RISE gave a much clearer picture of the location and magnitude of misfit for each misfitting item. In addition, there was no practical consequence to classification before and after replacement of misfitting items detected by three fit statistics.