Nonparametric Item Response Curve Estimation With Correction for Measurement Error

Nonparametric or kernel regression estimation of item response curves (IRCs) is often used in item analysis in testing programs. These estimates are biased when the observed scores are used as the regressor because the observed scores are contaminated by measurement error. Accuracy of this estimation is a concern theoretically and operationally. This study investigates the deconvolution kernel estimation of IRCs, which corrects for the measurement error in the regressor variable. A comparison of the traditional kernel estimation and the deconvolution estimation of IRCs is carried out using both simulated and operational data. It is found that, in item analysis, the traditional kernel estimation is comparable to the deconvolution kernel estimation in capturing important features of the IRC.