Item Characteristic Curve Asymmetry: A Better Way to Accommodate Slips and Guesses Than a Four-Parameter Model?

Abstract

Four-parameter models have received increasing psychometric attention in recent years, as a reduced upper asymptote for item characteristic curves can be appealing for measurement applications such as adaptive testing and person-fit assessment. However, applications can be challenging due to the large number of parameters in the model. In this article, we demonstrate in the context of mathematics assessments how the slip and guess parameters of a four-parameter model may often be empirically related. This observation also has a psychological explanation to the extent that both asymptote parameters may be manifestations of a single item complexity characteristic. The relationship between lower and upper asymptotes motivates the consideration of an asymmetric item response theory model as a three-parameter alternative to the four-parameter model. Using actual response data from mathematics multiple-choice tests, we demonstrate the empirical superiority of a three-parameter asymmetric model in several standardized tests of mathematics. To the extent that a model of asymmetry ultimately portrays slips and guesses not as purely random but rather as proficiency-related phenomena, we argue that the asymmetric approach may also have greater psychological plausibility.