Journal
ANNALS OF APPLIED STATISTICS
Volume 16, Issue 3, Pages 1718-1746Publisher
INST MATHEMATICAL STATISTICS-IMS
DOI: 10.1214/21-AOAS1564
Keywords
Bayesian hierarchical model; outlier detection; false discovery rate; compound decision; test fairness; item response theory; latent class analysis
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The paper introduces a new latent variable model for simultaneous detection of outlying individuals and items in item-response-type data. A statistical decision framework is developed to control false discovery rates of outlier detection, with statistical inference carried out under a Bayesian framework using a Markov Chain Monte Carlo algorithm. The proposed method is evaluated through a case study and simulation studies for detecting cheating in educational tests.
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.
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