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|.
Highlights
Item response theory (IRT) is a statistical method based on an examinee’s response to explain his/her ability
Aberrant responses often occurred in educational measurement
This paper followed the idea of Lord (1981) and provided a generalized formula of statistical bias in the maximum likelihood estimation with or without aberrant responses, which presented the relationship between bias and the probability of aberrant response
Summary
Reviewed by: Daniel Bolt, University of Wisconsin-Madison, United States Seongah Im, University of Hawaii at Manoa, United States. 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|
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