On the Use of Nonparametric Item Characteristic Curve Estimation Techniques for Checking Parametric Model Fit

Abstract

The purpose of this study was to assess the model fit of a 2PL through comparison with the nonparametric item characteristic curve (ICC) estimation procedures. Results indicate that three nonparametric procedures implemented produced ICCs that are similar to that of the 2PL for items simulated to fit the 2PL. However for misfitting items, especially nonmonotone items, the greatest difference is between the 2PL and kernel smoothing procedures. In general, the differences between ICCs from the nonparametric procedures and the 2PL are reduced as both sample size and test length increase. The false positive rate of the test for model fit is promising for nonparametric ICC estimation methods. Power to detect misfitting items simulated with 4PL is low. Power to detect nonmonotone items is generally much higher. Power is best for kernel smoothing but also good for isotonic regression in the medium to large sample sizes and longer test length conditions. Power for the smoothed isotonic regression is uniformly low.