Nonparametric item response function estimation for assessing parametric model fit

Methods are developed that investigate the fit of parametric item response models by comparing them to models fitted under nonparametric assumptions. The approach is primarily graphical, but is made inferential through resampling from an estimated parametric model. The identifiability and estimation consistency of item response theory models are discussed and shown to be vital to the interpretation of differences between two fitted item response theory models. Simulation studies and real-data examples illustrate these techniques.