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Stable maximum likelihood estimation (MLE) of item parameters in 3PLM with a modest sample size remains a challenge. The current study presents a mixture-modeling approach to 3PLM based on which a feasible Expectation-Maximization-Maximization (EMM) MLE algorithm is proposed. The simulation study indicates that EMM is comparable to the Bayesian EM in terms of bias and RMSE. EMM also produces smaller standard errors (SEs) than MMLE/EM. In order to further demonstrate the feasibility, the method has also been applied to two real-world data sets. The point estimates in EMM are close to those from the commercial programs, BILOG-MG and flexMIRT, but the SEs are smaller.
Change-point analysis (CPA) is a method for detecting abrupt changes in parameter(s) underlying a sequence of random variables. It has been applied to detect examinees’ aberrant test-taking behavior by identifying abrupt test performance change. Previous studies utilized maximum likelihood estimations of ability parameters, focusing on detecting one change point for each examinee. This article proposes a Bayesian CPA procedure using response times (RTs) to detect abrupt changes in examinee speed, which may be related to aberrant responding behaviors. The lognormal RT model is used to derive a procedure for detecting aberrant RT patterns. The method takes the numbers and locations of the change points as parameters in the model to detect multiple change points or multiple aberrant behaviors. Given the change points, the corresponding speed of each segment in the test can be estimated, which enables more accurate inferences about aberrant behaviors. Simulation study results indicate that the proposed procedure can effectively detect simulated aberrant behaviors and estimate change points accurately. The method is applied to data from a high-stakes computerized adaptive test, where its applicability is demonstrated.
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