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The Impact of Markov Chain Convergence on Estimation of Mixture IRT Model Parameters
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Jang, Yoonsun; Cohen, Allan S. – Educational and Psychological Measurement, 2020
A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the…
Descriptors: Markov Processes, Item Response Theory, Accuracy, Inferences
Differential Item Functioning Analysis Using a Mixture 3-Parameter Logistic Model with a Covariate on the TIMSS 2007 Mathematics Test
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Choi, Youn-Jeng; Alexeev, Natalia; Cohen, Allan S. – International Journal of Testing, 2015
The purpose of this study was to explore what may be contributing to differences in performance in mathematics on the Trends in International Mathematics and Science Study 2007. This was done by using a mixture item response theory modeling approach to first detect latent classes in the data and then to examine differences in performance on items…
Descriptors: Test Bias, Mathematics Achievement, Mathematics Tests, Item Response Theory
Recovery of Item Parameters in the Nominal Response Model: A Comparison of Marginal Maximum Likelihood Estimation and Markov Chain Monte Carlo Estimation.
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Wollack, James A.; Bolt, Daniel M.; Cohen, Allan S.; Lee, Young-Sun – Applied Psychological Measurement, 2002
Compared the quality of item parameter estimates for marginal maximum likelihood (MML) and Markov Chain Monte Carlo (MCMC) with the nominal response model using simulation. The quality of item parameter recovery was nearly identical for MML and MCMC, and both methods tended to produce good estimates. (SLD)
Descriptors: Estimation (Mathematics), Markov Processes, Monte Carlo Methods, Simulation
Accuracy of Parameter Estimation in Gibbs Sampling under the Two-Parameter Logistic Model.
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Kim, Seock-Ho; Cohen, Allan S. – 1999
The accuracy of Gibbs sampling, a Markov chain Monte Carlo procedure, was considered for estimation of item and ability parameters under the two-parameter logistic model. Memory test data were analyzed to illustrate the Gibbs sampling procedure. Simulated data sets were analyzed using Gibbs sampling and the marginal Bayesian method. The marginal…
Descriptors: Bayesian Statistics, Estimation (Mathematics), Item Response Theory, Markov Processes
An Evaluation of a Markov Chain Monte Carlo Method for the Two-Parameter Logistic Model.
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Kim, Seock-Ho; Cohen, Allan S. – 1998
The accuracy of the Markov Chain Monte Carlo (MCMC) procedure Gibbs sampling was considered for estimation of item parameters of the two-parameter logistic model. Data for the Law School Admission Test (LSAT) Section 6 were analyzed to illustrate the MCMC procedure. In addition, simulated data sets were analyzed using the MCMC, marginal Bayesian…
Descriptors: Bayesian Statistics, Estimation (Mathematics), Higher Education, Markov Processes