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A Maximum Likelihood Approach to Test Validation with Missing and Censored Dependent Variables

Published online by Cambridge University Press:  01 January 2025

Alan L. Gross
Alan L. Gross*
Affiliation:
Department of Educational Psychology, Graduate Center, City University of New York
*
Requests for reprints should be sent to Alan L. Gross, Graduate Center, City University of New York, 33 West 42 Street, New York, NY 10036.
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Abstract

A maximum likelihood approach is described for estimating the validity of a test (x) as a predictor of a criterion variable (y) when there are both missing and censored y scores present in the data set. The missing data are due to selection on a latent variable (ys) which may be conditionally related to y given x. Thus, the missing data may not be missing random. The censoring process in due to the presence of a floor or ceiling effect. The maximum likelihood estimates are constructed using the EM algorithm. The entire analysis is demonstrated in terms of hypothetical data sets.

Keywords

missing datacensored dataEM algorithmrestriction of range

Information

Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 3 , September 1990, pp. 533 - 549
Copyright
Copyright © 1990 The Psychometric Society

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References

Amemiya, T. (1985). Advanced econometrics, MA: Harvard University Press.Google Scholar
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, 39, 1–38.CrossRefGoogle Scholar
Gross, A. L. (1982). Relaxing the assumptions underlying restriction of range. Educational and Psychological Measurement, 42, 795–801.CrossRefGoogle Scholar
Heckman, J. J. (1976). The common structure of statistical models of truncation, sample selection, and limited dependent variables, and a simple estimator for such models.. Annals of Economic and Social Measurement, 5, 475–492.Google Scholar
Heckman, J. J. (1979). Sample selection bias as a specification error. Econometrika, 47, 153–161.CrossRefGoogle Scholar
IMSL, Library (1987). User's Manual Math/Library, Houston, TX: Author.Google Scholar
Keats, J. A., & Lord, F. M. (1962). A theoretical distribution for mental test scores. Psychometrika, 27, 59–72.CrossRefGoogle Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Reading, MA: Addison-Wesley.Google Scholar
Maddala, G. S. (1983). Limited dependent variables and qualitative variables in econometrics, New York: Cambridge University Press.CrossRefGoogle Scholar
Muthén, B., & Jöreskog, K. G. (1983). Selectivity problems in quasi-experimental studies. Evaluation Review, 7, 139–174.CrossRefGoogle Scholar
Rosenbaum, S. (1961). Moments of a truncated bivariate normal distribution. Journal of the Royal Statistical Society, 23(2), 405–408.CrossRefGoogle Scholar
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63, 581–592.CrossRefGoogle Scholar