TY - JOUR
T1 - Asymptotically Normally Distributed Person Fit Indices for Detecting Spuriously High Scores on Difficult Items
AU - Xia, Yan
AU - Zheng, Yi
N1 - Publisher Copyright:
© 2017, The Author(s) 2017.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Snijders developed a family of person fit indices that asymptotically follow the standard normal distribution, when the ability parameter is estimated. So far, l*z, U*, W*, ECI2*z, and ECI4*z from this family have been proposed in previous literature. One common property shared by l*z, U*, and W* (also ECI2*z, and ECI4*z 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 l*z, U*, W*, ECI2*z, and ECI4*z. 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.
AB - Snijders developed a family of person fit indices that asymptotically follow the standard normal distribution, when the ability parameter is estimated. So far, l*z, U*, W*, ECI2*z, and ECI4*z from this family have been proposed in previous literature. One common property shared by l*z, U*, and W* (also ECI2*z, and ECI4*z 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 l*z, U*, W*, ECI2*z, and ECI4*z. 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.
KW - asymptotically standard normal distribution
KW - item response theory
KW - person fit statistic
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U2 - 10.1177/0146621617730391
DO - 10.1177/0146621617730391
M3 - Article
AN - SCOPUS:85041912445
VL - 42
SP - 343
EP - 358
JO - Applied Psychological Measurement
JF - Applied Psychological Measurement
SN - 0146-6216
IS - 5
ER -