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Asymptotically Normally Distributed Person Fit Indices for Detecting Spuriously High Scores on Difficult Items

Asymptotically Normally Distributed Person Fit Indices for Detecting Spuriously High Scores on... Snijders developed a family of person fit indices that asymptotically follow the standard normal distribution, when the ability parameter is estimated. So far, lz*, U*, W*, ECI2z*, and ECI4z* from this family have been proposed in previous literature. One common property shared by lz*, U*, and W* (also ECI2z* and ECI4z* in some specific conditions) is that they employ symmetric weight functions and thus identify spurious scores on both easy and difficult items in the same manner. However, when the purpose is to detect only the spuriously high scores on difficult items, such as cheating, guessing, and having item preknowledge, using symmetric weight functions may jeopardize the detection rates of the target aberrant response patterns. By specifying two types of asymmetric weight functions, this study proposes SHa(λ)* (λ = 1/2 or 1) and SHb(β)* (β = 2 or 3) based on Snijders’s framework to specifically detect spuriously high scores on difficult items. Two simulation studies were carried out to investigate the Type I error rates and empirical power of SHa(λ)* and SHb(β)*, compared with lz*, U*, W*, ECI2z*, and ECI4z*. The empirical results demonstrated satisfactory performance of the proposed indices. Recommendations were also made on the choice of different person fit indices based on specific purposes. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Psychological Measurement SAGE

Asymptotically Normally Distributed Person Fit Indices for Detecting Spuriously High Scores on Difficult Items

Xia, Yan; Zheng, Yi
Applied Psychological Measurement , Volume 42 (5): 16 – Jul 1, 2018
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Publisher
SAGE
Copyright
© The Author(s) 2017
ISSN
0146-6216
eISSN
1552-3497
DOI
10.1177/0146621617730391
Publisher site
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Abstract

Snijders developed a family of person fit indices that asymptotically follow the standard normal distribution, when the ability parameter is estimated. So far, lz*, U*, W*, ECI2z*, and ECI4z* from this family have been proposed in previous literature. One common property shared by lz*, U*, and W* (also ECI2z* and ECI4z* in some specific conditions) is that they employ symmetric weight functions and thus identify spurious scores on both easy and difficult items in the same manner. However, when the purpose is to detect only the spuriously high scores on difficult items, such as cheating, guessing, and having item preknowledge, using symmetric weight functions may jeopardize the detection rates of the target aberrant response patterns. By specifying two types of asymmetric weight functions, this study proposes SHa(λ)* (λ = 1/2 or 1) and SHb(β)* (β = 2 or 3) based on Snijders’s framework to specifically detect spuriously high scores on difficult items. Two simulation studies were carried out to investigate the Type I error rates and empirical power of SHa(λ)* and SHb(β)*, compared with lz*, U*, W*, ECI2z*, and ECI4z*. The empirical results demonstrated satisfactory performance of the proposed indices. Recommendations were also made on the choice of different person fit indices based on specific purposes.

Journal

Applied Psychological Measurement – SAGE

Published: Jul 1, 2018

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