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The Polyserial Correlation Coefficient

Published online by Cambridge University Press:  01 January 2025

Ulf Olsson ,
Fritz Drasgow  and
Neil J. Dorans
Ulf Olsson*
Affiliation:
The Swedish University of Agricultural Sciences
Fritz Drasgow*
Affiliation:
Yale University
Neil J. Dorans
Affiliation:
Educational Testing Service
*
Address reprint requests to Ulf Olsson, The Swedish University of Agricultural Sciences, Department of Economics and Statistics, S-750 07 Uppsala 7, SWEDEN, or, in North America, to Fritz Drasgow, Department of Psychology, University of Illinois, 603 E. Daniel Street, Champaign, IL 61820, U.S.A.
Address reprint requests to Ulf Olsson, The Swedish University of Agricultural Sciences, Department of Economics and Statistics, S-750 07 Uppsala 7, SWEDEN, or, in North America, to Fritz Drasgow, Department of Psychology, University of Illinois, 603 E. Daniel Street, Champaign, IL 61820, U.S.A.
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Abstract

The polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations. The relationship between the polyserial and point polyserial correlation is derived. The maximum likelihood estimator of the polyserial correlation is compared with a two-step estimator and with a computationally convenient ad hoc estimator. All three estimators perform reasonably well in a Monte Carlo simulation. Some practical applications of the polyserial correlation are described.

Keywords

point polyserial correlationdichotomous variablespolychotomous variableslatent variables
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 3 , September 1982 , pp. 337 - 347
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

By coincidence, the first author and the second and third authors learned that they were working independently on closely related problems and, consequently, decided to write a jointly authored paper.

References

References Notes

Nerlove, M. & Press, S. J. Univariate and multivariate log-linear and logistic models, 1973, Santa Monica: The Rand Corporation.Google Scholar
Gruvaeus, G. T. & Jöreskog, K. G. A computer program for minimizing a function of several variables, 1970, Princeton, NJ: Educational Testing Service.Google Scholar

References

Cox, N. R. Estimation of the correlation between a continuous and a discrete variable. Biometrics, 1974, 30, 171–178.CrossRefGoogle Scholar
Finney, D. J. Probit analysis, 1971, Cambridge: Cambridge University Press.Google Scholar
IMSL Library 1 (Ed. 5). Houston, Texas: International Mathematical and Statistical Libraries, 1975.Google Scholar
Jaspen, N. Serial correlation. Psychometrika, 1946, 11, 23–30.CrossRefGoogle ScholarPubMed
Jöreskog, K. G., & Sörbom, D. Lisrel V user's guide, 1981, Chicago: National Educational Resources.Google Scholar
Lancaster, H. O., & Hamdan, M. A. Estimation of the correlation coefficient in contingency tables with possibly nonmetrical characters. Psychometrika, 1964, 29, 383–391.CrossRefGoogle Scholar
Lazarsfeld, P. F. Latent structure analysis. In Koch, S. (Eds.), Psychology: A study of a science, Vol. 3, 1959, New York: McGraw-Hill.Google Scholar
Lord, F. M., Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass: Addison-Wesley.Google Scholar
Martinson, E. O., & Hamdan, M. A. Maximum likelihood and some other asymptotically efficient estimators of correlation in two way contingency tables. Journal of Statistical Computation and Simulation, 1971, 1, 45–54.CrossRefGoogle Scholar
Mosteller, E. Nonsampling errors. In Kruskal, W. H. & Tanur, J. M. (Eds.), International encyclopedia of statistics, 1978, New York: The Free Press.Google Scholar
NAG Fortran Library Manual, Mark 7, Oxford, NAG Ltd, 1979.Google Scholar
Olsson, U. Maximum likelihood estimation of the polychoric correlation coefficient. Psychometrika, 1979, 44, 443–460.CrossRefGoogle Scholar
Pearson, K. On a new method for determining the correlation between a measured character A and a character B. Biometrika, 1909, 7, 96–96.CrossRefGoogle Scholar
Pearson, K. On the measurement of the influence of “broad categories” on correlation. Biometrika, 1913, 9, 116–139.CrossRefGoogle Scholar
Silvey, S. D. Statistical inference, 1970, Harmondsworth: Penguin.Google Scholar
Tallis, G. The maximum likelihood estimation of correlation from contingency tables. Biometrics, 1962, 18, 342–353.CrossRefGoogle Scholar
Tate, R. F. The theory of correlation between two continuous variables when one is dichotomized. Biometrika, 1955, 42, 205–216.CrossRefGoogle Scholar
Tate, R. F. Applications of correlation models for biserial data. Journal of the American Statistical Association, 1955, 50, 1078–1095.CrossRefGoogle Scholar