Abstract
A Bayes estimation procedure is introduced that allows the nature and strength of prior beliefs to be easily specified and modal posterior estimates to be obtained as easily as maximum likelihood estimates. The procedure is based on constructing posterior distributions that are formally identical to likelihoods, but are based on sampled data as well as artificial data reflecting prior information. Improvements in performance of modal Bayes procedures relative to maximum likelihood estimation are illustrated for Rasch-type models. Improvements range from modest to dramatic, depending on the model and the number of items being considered.
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References
Anderson, E. B. (1980).Discrete statistical models with social science applications. Amsterdam: North Holland.
Bickel, P., & Doksum, K. (1977).Mathematical statistics: Basic ideas and selected topics. SAn Francisco: Holden-Day.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete datavia the EM algorithm.Nournal of the Royal Statistical Society, Series B,39, 1–38.
Hambleton, R. K., & Swaminathan, H. (1984).Item response theory: Principles and applications. The Hague: Nihoff/Kluwer.
Jannarone, R. J. (1987).Locally depdent models of reflecting learning abilities (Tech. Rep. #87-67). Columbia, SC: University of South Carolina, Center for Machine Intelligence.
Jannarone, R. J., Yu, Kai, F., & Takefuji, Y. (1988). “Conjunctoids”: Probabilistic learning models for binary events.Neural Networks, 1, 355–337.
Mislevy, R. J. (1986). Bayes modal estimation in item response models.Psychometrika, 51, 177–195.
Novick, M. R., & Jackson, P. H. (1974).Statistical methods for educational and psychological research. New York: McGraw-Hill.
Swaminathan, H., & Gifford, J. A. (1981, June).Bayesian estimation for the three-parameter logistic model. Paper presented at the annual Psychometric Society meetings, Chapel Hill, NC.
Swaminathan, H., & Gifford, J. A. (1982). Bayesian estimation in the Rasch model.Journal of Educational Statistics, 7, 175–197.
Swaminathan, H., & Gifford, J. A. (1985). Bayesian estimation for the one-parameter logistic model.Psychometrika, 47, 349–364.
Tanner, M., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation.Journal of the American Stastistical Association, 82, 528–540.
Tsutakawa, R. K., & Lin, H. Y. (1986). Bayesian estimation of item response curves.Psychometrika, 51, 251–267.
Wright, B. (1986).Bayes' answer to perfection. Unpublished Manuscript. University of Chicago.
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This research was supported by ORN Contact #00014-86-K0087. We wish to thank Sheng-Hui Chu and Dzung-Ji Lii for providing intelligent and energetic programming support for this article. We also thank one of the reviewers for pointing out several interesting and useful perspectives.
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Jannarone, R.J., Yu, K.F. & Laughlin, J.E. Easy bayes estimation for rasch-type models. Psychometrika 55, 449–460 (1990). https://doi.org/10.1007/BF02294760
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DOI: https://doi.org/10.1007/BF02294760