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September 2022 Detection of two-way outliers in multivariate data and application to cheating detection in educational tests
Yunxiao Chen, Yan Lu, Irini Moustaki
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Ann. Appl. Stat. 16(3): 1718-1746 (September 2022). DOI: 10.1214/21-AOAS1564


The paper proposes a new latent variable model for the simultaneous (two-way) detection of outlying individuals and items for item-response-type data. The proposed model is a synergy between a factor model for binary responses and continuous response times that captures normal item response behaviour and a latent class model that captures the outlying individuals and items. A statistical decision framework is developed under the proposed model that provides compound decision rules for controlling local false discovery/nondiscovery rates of outlier detection. Statistical inference is carried out under a Bayesian framework for which a Markov chain Monte Carlo algorithm is developed. The proposed method is applied to the detection of cheating in educational tests, due to item leakage, using a case study of a computer-based nonadaptive licensure assessment. The performance of the proposed method is evaluated by simulation studies.


We thank the Editor, Associate Editor, and three referees for their helpful comments.


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Yunxiao Chen. Yan Lu. Irini Moustaki. "Detection of two-way outliers in multivariate data and application to cheating detection in educational tests." Ann. Appl. Stat. 16 (3) 1718 - 1746, September 2022.


Received: 1 December 2020; Revised: 1 October 2021; Published: September 2022
First available in Project Euclid: 19 July 2022

Digital Object Identifier: 10.1214/21-AOAS1564

Keywords: Bayesian hierarchical model , compound decision , False discovery rate , item response theory , latent class analysis , outlier detection , test fairness

Rights: Copyright © 2022 Institute of Mathematical Statistics


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Vol.16 • No. 3 • September 2022
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