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Bayesian estimation of item response curves

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Item response curves for a set of binary responses are studied from a Bayesian viewpoint of estimating the item parameters. For the two-parameter logistic model with normally distributed ability, restricted bivariate beta priors are used to illustrate the computation of the posterior mode via the EM algorithm. The procedure is illustrated by data from a mathematics test.

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  • Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimator of item parameters: An application of an EM algorithm.Psychometrika, 46, 443–459.

    Google Scholar 

  • Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion).Journal of the Royal Statistical Society, 39(B), 1–38.

    Google Scholar 

  • Leonard, T. (1975). Bayesian estimation methods for two-way contingency tables.Journal of the Royal Statistical Society, 37(B), 23–37.

    Google Scholar 

  • Lindley, D. V., & Smith, A. F. M. (1972). Bayes estimates for the linear model (with discussion).Journal of the Royal Statistical Society, 34(B), 1–41.

    Google Scholar 

  • Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters.Journal for the Society of Applied Mathematics, 11, 431–441.

    Google Scholar 

  • Mislevy, R. J., & Bock, R. D. (1981).BILOG—Maximum Likelihood item analysis and test scoring: LOGISTIC model. Chicago: International Educational Services.

    Google Scholar 

  • Novick, M. R., Jackson, P. H., Thayer, D. T., & Cole, N. S. (1972). Estimating multiple regressions inm groups: A cross-validation study.British Journal of Mathematical & Statistical Psychology, 25, 33–50.

    Google Scholar 

  • O'Hagan, A. (1976). On posterior joint and marginal modes.Biometrika, 63, 329–333.

    Google Scholar 

  • Raiffa, H., & Schlaifer, R. (1961).Applied statistical decision theory. Boston: Harvard University, Division of Research, Graduate School of Business Administration.

    Google Scholar 

  • Rigdon, S. E., & Tsutakawa, R. K. (1983). Estimation in latent trait models.Psychometrika, 48, 567–574.

    Google Scholar 

  • Swaminathan, H. (1981). Bayesian estimation in the two-parameter logistic model (Research Report LR-12). Boston: University of Massachusetts, School of Education.

    Google Scholar 

  • Swaminathan, H., & Gifford, J. A. (1982). Bayesian estimation in the Rasch model.Journal of Educational Statistics, 7, 175–191.

    Google Scholar 

  • Tsutakawa, R. K. (1984). Estimation of two-parameter logistic item response curves.Journal of Educational Statistics, 9, 263–276.

    Google Scholar 

  • Tsutakawa, R. K. (1985). Estimation of item parameters and theGEM algorithm. In D. J. Weiss (Ed.),Proceedings of the 1982 Item Response Theory and Computerized Adaptive Testing Conference (pp. 180–188). Minneapolis: University of Minnesota, Department of Psychology.

    Google Scholar 

  • Wingersky, M. S., Barton, M. A., & Lord, F. M. (1982).LOGIST user's guide. Princeton, NJ: Educational Testing Services.

    Google Scholar 

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This work was supported under Contract No. N00014-85-K-0113, NR 150-535, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank Mark D. Reckase for providing the ACT data used in the illustration and Michael J. Soltys for computational assistance. They also wish to thank the editor and four anonymous reviewers for many valuable suggestions.

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Tsutakawa, R.K., Lin, H.Y. Bayesian estimation of item response curves. Psychometrika 51, 251–267 (1986).

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