A Two-Stage Approach to Differentiating Normal and Aberrant Behavior in Computer Based Testing

Statistical methods for identifying aberrances on psychological and educational tests are pivotal to detect flaws in the design of a test or irregular behavior of test takers. Two approaches have been taken in the past to address the challenge of aberrant behavior detection, which are (1) modeling aberrant behavior via mixture modeling methods, and (2) flagging aberrant behavior via residual based outlier detection methods. In this paper, we propose a two-stage method that is conceived of as a combination of both approaches. In the first stage, a mixture hierarchical model is fitted to the response and response time data to distinguish normal and aberrant behaviors using Markov chain Monte Carlo (MCMC) algorithm. In the second stage, a further distinction between rapid guessing and cheating behavior is made at a person level using a Bayesian residual index. Simulation results show that the two-stage method yields accurate item and person parameter estimates, as well as high true detection rate and low false detection rate, under different manipulated conditions mimicking NAEP parameters. A real data example is given in the end to illustrate the potential application of the proposed method.