Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimator of item parameters: An application of an EM algorithm.Psychometrika, 46, 443–459.
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.
Leonard, T. (1975). Bayesian estimation methods for two-way contingency tables.Journal of the Royal Statistical Society, 37(B), 23–37.
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.
Lord, F. M. (1980).Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters.Journal for the Society of Applied Mathematics, 11, 431–441.
Mislevy, R. J., & Bock, R. D. (1981).BILOG—Maximum Likelihood item analysis and test scoring: LOGISTIC model. Chicago: International Educational Services.
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.
O'Hagan, A. (1976). On posterior joint and marginal modes.Biometrika, 63, 329–333.
Raiffa, H., & Schlaifer, R. (1961).Applied statistical decision theory. Boston: Harvard University, Division of Research, Graduate School of Business Administration.
Rigdon, S. E., & Tsutakawa, R. K. (1983). Estimation in latent trait models.Psychometrika, 48, 567–574.
Swaminathan, H. (1981). Bayesian estimation in the two-parameter logistic model (Research Report LR-12). Boston: University of Massachusetts, School of Education.
Swaminathan, H., & Gifford, J. A. (1982). Bayesian estimation in the Rasch model.Journal of Educational Statistics, 7, 175–191.
Tsutakawa, R. K. (1984). Estimation of two-parameter logistic item response curves.Journal of Educational Statistics, 9, 263–276.
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.
Wingersky, M. S., Barton, M. A., & Lord, F. M. (1982).LOGIST user's guide. Princeton, NJ: Educational Testing Services.
Author information
Authors and Affiliations
Additional information
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.
Rights and permissions
About this article
Cite this article
Tsutakawa, R.K., Lin, H.Y. Bayesian estimation of item response curves. Psychometrika 51, 251–267 (1986). https://doi.org/10.1007/BF02293983
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293983