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Shrinkage Estimation of Linear Combinations of True Scores

Published online by Cambridge University Press:  01 January 2025

Nicholas T. Longford
Nicholas T. Longford*
Affiliation:
De Montfort University, Leicester, England
*
Requests for reprints should be sent to Nicholas T. Longford, Department of Medical Statistics, De Montfort University, Leicester LE1 9BH, ENGLAND.
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Abstract

This paper is concerned with combining observed scores from sections of tests. It is demonstrated that in the presence of population information a linear combination of true scores can be estimated more efficiently than by the same linear combination of the observed scores. Three criteria for optimality are discussed, but they yield the same solution which can be described and motivated as a multivariate shrinkage estimator.

Keywords

mean squared errormeasurement errorobserved and true scoresshrinkage estimation
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 2 , June 1997 , pp. 237 - 244
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

Input from Eric Bradlow, Charles Lewis, and Linda Zeger is acknowledged. Research for this paper was funded by the Program Research Council (ETS). Suggestions of the Editor and of anonymous referees were instrumental in several improvements of the paper.

References

Battese, G. E., Harter, R. M., Fuller, W. A. (1988). An error-component model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association, 83, 28–36.CrossRefGoogle Scholar
Brandwein, A. C., Strawderman, W. E. (1990). Stein estimation: The spherically symmetric case. Statistical Science, 5, 356–369.CrossRefGoogle Scholar
Cronbach, L. J., Gleser, G. C., Nanda, H., Rajaratnam, N. (1972). The dependability of behavioral measurements: Theory of generalizability of scores and profiles, New York, NY: Wiley and Sons.Google Scholar
Dempster, A. P., Rubin, D. B., Tsutakawa, R. K. (1981). Estimation in covariance component models. Journal of the American Statistical Association, 76, 341–353.CrossRefGoogle Scholar
Efron, B. (1995). The statistical century. RSS News, 22(5), 1–2.Google Scholar
Kelley, T. L. (1927). Interpretation of educational measurements, New York, NY: World Book.Google Scholar
Longford, N. T. (1994). Reliability of essay rating and score adjustment. Journal of Educational and Behavioral Statistics, 19, 171–201.CrossRefGoogle Scholar
Longford, N. T. (1994). A case for adjusting subjectively rated scores in the Advanced Placement tests, Princeton, NJ: Educational Testing Service.CrossRefGoogle Scholar
Lord, F. M., Novick, M. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Mislevy, R. J., Bock, R. D. (1983). BILOG: Item analysis and test scoring with binary logistic models, Mooresville, IN: Scientific Software.Google Scholar
Rubin, D. B. (1980). Using empirical Bayes techniques in the law school validity studies. Journal of the American Statistical Association, 75, 801–827.CrossRefGoogle Scholar
Tsutakawa, R. K. (1988). Mixed model for analyzing geographic variability in mortality rates. Journal of the American Statistical Association, 83, 37–42.CrossRefGoogle ScholarPubMed