The Use of Theory of Linear Mixed-Effects Models to Detect Fraudulent Erasuresat an Aggregate Level

Oct 15, 2026

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Wollack and colleagues proposed an erasure detection index (EDI) to identify fraudulent erasures for individual examinees, later extended to three aggregate- or group-level EDIs. Building on that work, the article introduces a new aggregate-level EDI that incorporates the empirical best linear unbiased predictor from the linear mixed-effects model literature. A simulation study shows higher power than existing indices while maintaining satisfactory Type I error rates. A real-data application is also provided.

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Abstract

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Method

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The Use of Theory of Linear Mixed-Effects Models to Detect Fraudulent Erasuresat an Aggregate Level Luyao Peng 1,2 and Sandip Sinharay3 Educational and Psychological Measurement 2022, Vol. 82(1) 177–200 􀀂 The Author(s) 2021 Article reuse guidelines: [sagepub.com/journals-permissions](sagepub.com/journals-permissions)[ ](sagepub.com/journals-permissions)[DOI: 10.1177/0013164421994893](DOI: 10.1177/0013164421994893)[ ](DOI: 10.1177/0013164421994893)[journals.sagepub.com/home/epm](journals.sagepub.com/home/epm) Abstract Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs for detecting fraudulent erasures at the aggregate or group level. This article follows up on the research of Wollack and Eckerly (2017) and Sinharay (2018) and suggests a new aggregate-level EDI by incorporating the empirical best linear unbiased predictor from the literature of linear mixed-effects models (e.g., McCulloch et al., 2008). A simulation study shows that the new EDI has larger power than the indices of Wollack and Eckerly (2017) and Sinharay (2018). In addition, the new index has satisfactory Type I error rates. A real data example is also included. Keywords data forensics, erasure analysis, linear mixed-effects model, empirical best linear unbiased predictor, test fraud Test administrators are increasingly concerned about fraudulent erasures or ‘‘test tampering,’’ which is a major type of test fraud (e.g., Wollack & Schoenig, 2018) . 1 Beijing Language and Culture University, Beijing, China 2ByteDance, Beijing, China 3Educational Testing Service, Princeton, NJ, USA Corresponding Author: Luyao Peng, Center for the Cognitive Science of Language, Beijing Language and Culture University, Beijing, China. Email: [luyaopeng@blcu.edu.cn](luyaopeng@blcu.edu.cn) The educator cheating scandal in Atlanta public schools in 2009 (e.g., Maynes, 2013; Wollack et al., 2015) demonstrated the severity of teacher/administrator tampering and sent a signal that the U.S. states should actively detect test tampering. Consequently, the Standard 8.11 of the Standards for Educational and Psychological Testing (American Educational Research Association, American Psychological Association, & National Council for Measurement in Education, 2014) includes the recommendation that testing programs may use technologies such as computer analyses of erasure patterns in the answer sheets to detect possible irregularities. Erasure analysis is regularly performed for several state tests (e.g., McClintock, 2015)—the analysis mostly involves the flagging of schools with an unexpectedly large number of erasures. Wollack et al. (2015) suggested the erasure detection index (EDI) for detecting fraudulent erasures for individual examinees. Wollack and Eckerly (2017) and Sinharay (2018) extended the index of Wollack et al. (2015) to suggest three EDIs that can be used to perform erasure analysis at an aggregate or group level, where the groups could refer to the classes, schools, or districts that the examinees belong to. The main goal of this article is to continue the research of Wollack and Eckerly (2017) and Sinharay (2018) and to propose a new EDI for performing erasure analysis at an aggregate level using the theory of linear mixed-effects models (LMMs; e.g., McCulloch et al., 2008) . It is demonstrated that the new EDI has larger power than the indices ofWollack and Eckerly (2017) and Sinharay (2018) . In addition, the new EDI is shown to have satisfactory Type I error rates in all simulation conditions. The next section includes reviews of the EDIs that were suggested by Wollack et al. (2015), Wollack and Eckerly (2017), and Sinharay (2018) to detect fraudulent erasures. The new EDI, which is based on the theory of LMMs, is introduced in the Method section. In the Simu

FAQs

What is the paper’s main objective?

To propose a new aggregate-level erasure detection index using linear mixed-effects model theory, extending prior aggregate/group EDIs.

How does the new EDI differ from earlier indices?

It incorporates the empirical best linear unbiased predictor from the linear mixed-effects models literature to detect fraudulent erasures at the aggregate level.

What do simulation results indicate about the new EDI?

The new EDI has larger power than the earlier indices and shows satisfactory Type I error rates across simulation conditions.

Oct 15, 2026

Uploaded by acoobca