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.