A short note on aberrant responses bias in item response theory

Abstract

Item response models often cannot calculate true individual response probabilities because of the existence of response disturbances (such as guessing and cheating). Many studies on aberrant responses under item response theory (IRT) framework had been conducted. Some of them focused on how to reduce the effect of aberrant responses, and others focused on how to detect aberrant examinees, such as person fit analysis. The purpose of this research was to derive a generalized formula of bias with/without aberrant responses, that showed the effect of both non-aberrant and aberrant response data on the bias of capability estimation mathematically. A new evaluation criterion, named aberrant absolute bias (|ABIAS|), was proposed to detect aberrant examinees. Simulation studies and application to a real dataset were conducted to demonstrate the efficiency and the utility of |ABIAS|.