Abstract
Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parametersθ=(θ 1, …,θ n ) and item parametersβ=(β 1, …,β k ), whereβ j may be vector valued. Withθ considered a random sample from a prior distribution with parameterφ, the estimation of (θ, β) is studied under the theory of the EM algorithm. An example and computational details are presented for the Rasch model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Andersen, E. B. Asymptotic properties of conditional maximum-likelihood estimators.Journal of the Royal Statistical Society, B, 1970,32, 283–301.
Andersen, E. & Madsen, M. Estimating the parameters of the latent population distribution.Psychometrika, 1977,42, 357–374.
Birnbaum, A. Some latent trait models. In F. M. Lord, & M. R. Novick (Eds.),Statistical theories of mental test scores. Reading: Addison-Wesley, 1968.
Bock, R. D. & Aitkin, M. Marginal maximum likelihood estimation of item parameters: an application of an EM algorithm.Psychometrika, 1981,46, 443–459.
Conte, S. D. & de Boor, C.Elementary numerical analysis: an algorithmic approach. New York: McGraw-Hill, 1972.
Dempster, A. P., Laird, N. M. & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm.Journal of the Royal Statistical Society, Series B, 1977,39, 1–22.
Dempster, A. P., Rubin, D. B. & Tsutakawa, R. K. Estimation in covariance components models.Journal of the American Statistical Association, 1981,76, 341–353.
Finney, D. J.Probit analysis (3rd ed.). New York: Cambridge University Press, 1971.
Lord, F. M. & Novick, M. R.Statistical theories of mental test scores. Reading: Addison-Wesley, 1968.
Mosteller, F. & Wallace, D. L.Inference and disputed authorship: The Federalist. Reading: Addison-Wesley, 1964.
Rasch, G.Probabilistic models for some intelligence and attainment tests. Copenhagen: Paedogogiske Institut., 1960.
Sanathanan, L. & Blumenthal, S. The logistic model and estimation of latent structure.Journal of the American Statistical Association, 1978,73, 794–799.
Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis.Educational and Psychological Measurement, 1969,29, 23–48.
Author information
Authors and Affiliations
Additional information
This work was supported by Contract No. N00014-81-K-0265, Modification No. P00002, from Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research. The authors wish to thank an anonymous reviewer for several valuable suggestions.
Rights and permissions
About this article
Cite this article
Rigdon, S.E., Tsutakawa, R.K. Parameter estimation in latent trait models. Psychometrika 48, 567–574 (1983). https://doi.org/10.1007/BF02293880
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293880