Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-08T11:23:21.933Z Has data issue: false hasContentIssue false
  • English
  • Français

Parameter Estimation in Latent Trait Models

Published online by Cambridge University Press:  01 January 2025

Steven E. Rigdon  and
Robert K. Tsutakawa
Steven E. Rigdon
Affiliation:
University of Missouri
Robert K. Tsutakawa*
Affiliation:
University of Missouri
*
Requests for reprints should be sent to Robert K. Tsutakawa, Dept. of Statistics, University of Missouri, Columbia, MO 65211.
Get access Rights & Permissions [Opens in a new window]

Abstract

Latent trait models for binary responses to a set of test items are considered from the point of view of estimating latent trait parameters θ= (θ1, …, θn) and item parameters β=(β1, …, βk), where βj may be vector valued. With θ considered a random sample from a prior distribution with parameter ϕ, 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.

Keywords

EM algorithmempirical Bayeslatent traitRasch model
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 4 , December 1983 , pp. 567 - 574
Copyright
Copyright © 1983 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

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.

References

Andersen, E. B. Asymptotic properties of conditional maximum-likelihood estimators. Journal of the Royal Statistical Society, 1970, 32, 283–301.CrossRefGoogle Scholar
Andersen, E. & Madsen, M. Estimating the parameters of the latent population distribution. Psychometrika, 1977, 42, 357–374.CrossRefGoogle Scholar
Birnbaum, A. Some latent trait models. In Lord, F. M., & Novick, M. R. (Eds.), Statistical theories of mental test scores, Reading: Addison-Wesley, 1968.Google Scholar
Bock, R. D. & Aitkin, M. Marginal maximum likelihood estimation of item parameters: an application of an EM algorithm. Psychometrika, 1981, 46, 443–459.CrossRefGoogle Scholar
Conte, S. D. & de Boor, C. Elementary numerical analysis: an algorithmic approach, New York: McGraw-Hill, 1972.Google Scholar
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.CrossRefGoogle Scholar
Dempster, A. P., Rubin, D. B. & Tsutakawa, R. K. Estimation in covariance components models. Journal of the American Statistical Association, 1981, 76, 341–353.CrossRefGoogle Scholar
Finney, D. J. Probit analysis 3rd ed., New York: Cambridge University Press, 1971.Google Scholar
Lord, F. M. & Novick, M. R. Statistical theories of mental test scores, Reading: Addison-Wesley, 1968.Google Scholar
Mosteller, F. & Wallace, D. L. Inference and disputed authorship: The Federalist, Reading: Addison-Wesley, 1964.Google Scholar
Rasch, G. Probabilistic models for some intelligence and attainment tests, Copenhagen: Paedogogiske Institut., 1960.Google Scholar
Sanathanan, L. & Blumenthal, S. The logistic model and estimation of latent structure. Journal of the American Statistical Association, 1978, 73, 794–799.CrossRefGoogle Scholar
Wright, B. D. & Panchapakesan, N. A procedure for sample-free item analysis. Educational and Psychological Measurement, 1969, 29, 23–48.CrossRefGoogle Scholar