Abstract
The problem of determining linear functions for two sets of variables so as to maximize the correlation between the two functions has been solved by Hotelling. This article presents a more efficient computational solution for the case of two sets of variables and a generalized solution for any number of sets. Applications are discussed and a numerical example is included to demonstrate the solution for more than two sets.
Similar content being viewed by others
References
Horst, P. Servant of the human sciences. Seattle: Division of Counseling and Testing Services, Univ. Washington, 1953. (Duplicated manuscript.)
Hotelling, H. Analysis of a complex of statistical variables into principal components.J. educ. Psychol., 1933,24, 417–441, 498–520.
Hotelling, H. The most predictable criterion.J. educ. Psychol., 1935,26, 139–142.
Hotelling H. Relations between two sets of variates.Biometrika, 1936,28, 321–277.
Mees, H. L. Preliminary steps in the construction of factor scales for the MMPI. Unpublished doctoral dissertation, Univ. Washington, 1959.
Roy, S. N. and Bargmann, R. E. Tests of multiple independence and the associated confidence bounds.Ann. math. Statist., 1958,29, 491–502.
Thurstone, L. L. and Thurstone, T. G. Factorial studies of intelligence.Psychometric Monogr., No. 2, 1941.
Tucker, L. R. An inter-battery method of factor analysis.Psychometrika, 1958,23, 111–136.
Wilks, S. S. On the independence ofk sets of normally distributed statistical variables.Econometrica, 1953,3, 309–326.
Wright, C. E. Principal axis factor analysis program for the IBM Type 650. Tech. Rep., Office of Naval Res. Contr. Nonr-477(08), Univ. Washington Division of Counseling and Testing Service, 1957.
Wrigley, C. and Neuhaus, J. O. The matching of two sets of factors.Amer. Psychologist, 1955,10, 418–419.
Author information
Authors and Affiliations
Additional information
This study was supported in part by Office of Naval Research Contract Nonr-477(08) and Public Health Research Grant M-743(C4), Paul Horst, Principal Investigator. The author is also indebted to Dennis Hamilton and Glenn Roudabush for programming the procedure for the IBM 650, to Charlotte MacEwan for preliminary desk calculations and for assuming editorial responsibility in preparing the manuscript for publication, and to Helen Haukeness and Dolores Payton for typing the manuscript.
Rights and permissions
About this article
Cite this article
Horst, P. Relations amongm sets of measures. Psychometrika 26, 129–149 (1961). https://doi.org/10.1007/BF02289710
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02289710