Abstract
In this paper, the marginal posterior distributions for both of item parameters and their hyperparameters of the item response model were derived numerically using the Gibbs Sampler. In order to make use of the Gibbs Sampler, the latent variables were introduced and generated by pseudo random numbers. Simulaton study showed that the proposed method provided more precise estimation of item parameters.
Then, this method was extended to the case where the items or the subjects are clasiified into several groups and therefore the item parameters or the ability parameters are partially exchangeable. The application of this method to the real data resulted in reasonable estimates.
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Requests for the computer program employed in this work should be sent to Tomoyasu Nakamura, Research and Development Division, National Institute of Multimedia Education, 2–12 Wakaba-ku, Chiba-shi, 261 Japan.
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Shigemasu, K., Nakamura, T. A Bayesian Marginal Inference in Estimating item Parameters Using the Gibbs Sampler. Behaviormetrika 23, 97–110 (1996). https://doi.org/10.2333/bhmk.23.97
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DOI: https://doi.org/10.2333/bhmk.23.97