  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.
