On Kernel Smoothing in Polytomous IRT: A New Minimum Distance Estimator

In Item Response Theory (IRT), the Item Category Response Function (ICRF), deÞning the relation between ability and probability of choosing a particular option for a test item, and the Item Response Function (IRF), describing the relation between ability and probability of obtaining a particular score for an item, are both of crucial importance. In analogy with the standard statistical methodology, these functions may be estimated by using both parametric and nonparametric approaches. Here, the performance of the well-known nonparametric kernel estimator is investigated in the polytomous case giving a description of the cross-validation approach to estimate the smoothing parameter, and providing pointwise conÞdence intervals for IRFs. Moreover, based on the consistency of this approach, a kernel-based minimum distance estimator of parametric IRT functions is proposed and evaluated by a Monte Carlo simulation study.