The technique of multicrossvalidation, an extension of the method of double crossvalidation was discussed and compared with analytical "formulae" methods for estimation of shrinkage of the multiple coefficient of correlation. The computer implementation of the suggested multicrossvalidation algorithm was described. The validity of analytical estimates was evaluated jointly with multicrossvalidated R's within the framework of amorphous and prestructured data sets.
Get full access to this article
View all access options for this article.
References
1.
Browne, M. W.Predictive validity of a linear regression equation . British Journal of Mathematical and Statistical Psychology, 1975, 28, 79-87.
2.
Cattin, P.Estimation of the predictive power of a regression model . Journal of Applied Psychology, 1980, 65, 407-414.
3.
Cooley, W. W. and Lohnes, P. R.Multivariate data analysis. New York: Wiley, 1971.
4.
Crombach, L. J.The two disciplines of scientific psychology . American Psychologist, 1957, 12, 671-684.
5.
Drehmer, D. E. and Morris, G. W.Cross validation with small samples: An algorithm for computing Gollob's estimator. Educational and Psychological Measurement, 1981, 41, 195-200.
6.
Fisher, R. A.Statistical methods for research workers. (14th edition). New York: Hafner, 1970.
7.
Gollob, H. F.Cross validation using samples of size one . Paper presented at the American Psychological Association meeting in Washington, D.C., September, 1967.
8.
Horst, P.An overview of the essentials of multivariate analysis methods. In R. B. Cattell (Ed.) Handbook of multivariate experimental psychology. Chicago: Rand McNally, 1966, pp. 129-152.
9.
Kerlinger, F. M. and Pedhazur, E. J.Multiple regression in behavioral research. New York: Holt, 1973.
10.
Krus, D. J. and Ceurvorst, R. W.Computer assisted construction of X variable norms. Educational and Psychological Measurement, 1978, 38, 815-818.
11.
Lord, F. M. and Novick, M. R.Statistical theories of mental test scores. Reading, Mass: Addison-Wesley, 1968.
12.
Mosier, C. I.Problems and designs of crossvalidation . Educational and Psychological Measurement, 1951, 11, 5-11.
13.
Olkin, I. and Pratt, J. W.Unbiased estimation of certain correlation coefficients. Annals of Mathematical Statistics, 1958, 29, 201-211.
14.
Roseboom, W. W.The estimation of crossvalidated multiple correlation: A clarification . Psychological Bulletin, 1978, 85, 1348-1351.
15.
Tatsuoka, M. M.The use of multiple regression equations. Champaign, Ill.: IPAT, 1969.
16.
Thurstone, L. L.Multiple factor analysis. Chicago: U of Chicago Press, 1947.
17.
Weiss, D. J.Multivariate procedures. In M. D. Dunnette (Ed.) Handbook of industrial and organizational psychology. Chicago: Rand McNally, 1976, pp. 327-362.
18.
Wherry, R. J.A new formula for predicting the shrinkage of the coefficient of multiple correlation . Annals of Mathematical Statistics, 1931, 2, 440-451.