Are All Item Response Functions Monotonically Increasing?

Abstract

Item response functions of the parametric logistic IRT models follow the logistic form which is monotonically increasing. However, item response functions of some real items are nonmonotonic which might lead to examinees with lower proficiency levels receiving higher scores. This study compared three nonparametric IRF estimation methods--the nonparametric smooth regression method, the item-ability regression method, and the B-spline nonparametric IRF method--to determine whether they could detect the nonmonotonic IRF accurately using simulated data. In addition, these methods were used to identify items with nonmonotonic IRFs on real assessments. Results present that three nonparametric methods can detect the nonmonotonic IRF equally and each real assessment has some items with nonmonotonic IRFs. Investigations on the reasons for and the consequences of the nonmonotonicity were conducted for several items and indicate that the nonmonotonicity can affect the fairness and comparability of the test score. Thus, the nonmonotonicity should be checked before applying the parametric logistic models.