Detection of two-way outliers in multivariate data and application to cheating detection in educational tests
Yunxiao Chen, Yan Lu, Irini Moustaki
The Annals of Applied Statistics · 2022 · Volume 16 · Issue 3
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.
Keywords
Bayesian hierarchical model, compound decision, False discovery rate, item response theory, latent class analysis, outlier detection, test fairness
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