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Detection of two-way outliers in multivariate data and application to cheating detection in educational tests

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  • Chen, Yunxiao
  • Lu, Yan
  • Moustaki, Irini

Abstract

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.

Suggested Citation

  • Chen, Yunxiao & Lu, Yan & Moustaki, Irini, 2022. "Detection of two-way outliers in multivariate data and application to cheating detection in educational tests," LSE Research Online Documents on Economics 112499, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:112499
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    File URL: http://eprints.lse.ac.uk/112499/
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    References listed on IDEAS

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    More about this item

    Keywords

    Bayesian hierarchical model; outlier detection; false discovery rate; compound decision; test fairness; item response theory; latent class analysis;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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