Illustrating the Use of Nonparametric Regression to Assess Differential Item and Bundle Functioning Among Multiple Groups

Abstract

The purpose of this article is to illustrate the use of nonparametric regression with kernel smoothing (Ramsay, 1991), as implemented with the computer program TESTGRAF (Ramsay, 2000), to investigate differential item or bundle functioning among multiple groups. Nonparametric regression is a flexible procedure used to estimate and display the relation between the probability that examinees with a given proficiency level will choose different options to multiple-choice items. The unit of analysis can be an item or a bundle of items. It can also be used to detect differential performance across two or more groups of examinees matched on overall proficiency. We present three examples to illustrate how nonparametric regression can be applied to multilingual, multicultural data to study group differences.