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The Role of Collateral Information about Examinees in Item Parameter Estimation

Published online by Cambridge University Press:  01 January 2025

Robert J. Mislevy  and
Kathleen M. Sheehan
Robert J. Mislevy*
Affiliation:
Educational Testing Service
Kathleen M. Sheehan
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Robert J. Mislevy, Educational Testing Service, Princeton, NJ 08541.
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Abstract

Standard procedures for estimating item parameters in item response theory (IRT) ignore collateral information that may be available about examinees, such as their standing on demographic and educational variables. This paper describes circumstances under which collateral information about examinees may be used to make inferences about item parameters more precise, and circumstances under which it must be used to obtain correct inferences.

Keywords

item response theorymaximum likelihoodmissing datamissing information principle
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 4 , December 1989 , pp. 661 - 679
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the United States Government. We are indebted to Tim Davey, Eugene Johnson, and three anonymous referees for their comments on earlier versions of the paper.

References

Andersen, E. B. (1973). Conditional inference and models for measuring, Copenhagen: Danish Institute for Mental Health.Google Scholar
Andersen, E. B. (1977). Sufficient statistics and latent trait models. Psychometrika, 42, 69–81.CrossRefGoogle Scholar
Bartholomew, D. J. (1988). The sensitivity of latent trait analysis to choice of prior distribution. British Journal of Mathematical and Statistical Psychology, 41, 101–107.CrossRefGoogle Scholar
Beaton, A. E. (1987). The NAEP 1983-84 technical report, Princeton, NJ: Educational Testing Service.Google Scholar
Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: An application of an EM algorithm. Psychometrika, 46, 443–459.CrossRefGoogle Scholar
Bradley, R. A., & Gart, J. J. (1962). The asymptotic properties of ML estimators when sampling from associated populations. Biometrika, 49, 205–214.CrossRefGoogle Scholar
Cohen, L. (1979). Approximate expressions for parameter estimates in the Rasch model. British Journal of Mathematical and Statistical Psychology, 32, 113–120.CrossRefGoogle Scholar
Cressie, N., & Holland, P. W. (1983). Characterizing the manifest probabilities of latent trait models. Psychometrika, 48, 129–141.CrossRefGoogle Scholar
de Leeuw, J., & Verhelst, N. (1986). Maximum likelihood estimation in generalized Rasch models. Journal of Educational Statistics, 11, 183–196.CrossRefGoogle Scholar
Engelen, R. J. H. (1987). Semiparametric estimation in the Rasch model, Twente, The Netherlands: Department of Education, University of Twente.Google Scholar
Kelderman, H. (1984). Loglinear Rasch model tests. Psychometrika, 49, 223–245.CrossRefGoogle Scholar
Kendall, M., Stuart, A. (1979). The advanced theory statistics, Volume 2, New York: MacMillan.Google Scholar
Kiefer, J., & Wolfowitz, J. (1956). Consistency of the maximum likelihood estimator in the presence of infinitely many incidental parameters. Annals of Mathematical Statistics, 27, 887–903.CrossRefGoogle Scholar
Lindsay, B. (1987). Semiparametric estimation in the Rasch model, University Park, PA: Department of Statistics, Pennsylvania State University.Google Scholar
Little, R. J. A., & Rubin, D. B. (1987). Statistical analysis with missing data, New York: Wiley.Google Scholar
Louis, T. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, 44, 226–233.CrossRefGoogle Scholar
Mislevy, R. J. (1987). Exploiting auxiliary information about examinees in the estimation of item parameters. Applied Psychological Measurement, 11, 81–91.CrossRefGoogle Scholar
Mislevy, R. J., & Bock, R. D. (1983). BILOG: Item analysis and test scoring with binary logistic models, Mooresville, IN: Scientific Software.Google Scholar
Mislevy, R. J., & Sheehan, K. M. (in press). The information matrix in latent-variable models. Journal of Educational Statistics.Google Scholar
Neyman, J., & Scott, E. L. (1948). Consistent estimates based on partially consistent observations. Econometrika, 16, 1–32.CrossRefGoogle Scholar
Orchard, T., & Woodbury, M. A. (1972). A missing information principle: Theory and applications, Berkeley: University of California Press.Google Scholar
Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests, Copenhagen: Danish Institute for Educational Research.Google Scholar
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.CrossRefGoogle Scholar
Tjur, T. (1982). A connection between Rasch's item analysis model and a multiplicative Poisson model. Scandanavian Journal of Statistics, 9, 23–30.Google Scholar
Tsutakawa, R. K. (1984). Estimation of two-parameter logistic item response curves. Journal of Educational Statistics, 9, 263–276.CrossRefGoogle Scholar