Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-08T12:23:22.257Z Has data issue: false hasContentIssue false
  • English
  • Français

The Evaluation of Multiple and Partial Correlation Coefficients from the Factorial Matrix

Published online by Cambridge University Press:  01 January 2025

P. S. Dwyer
P. S. Dwyer*
Affiliation:
The University of Michigan
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper shows how to compute multiple correlation coefficients, partial correlation coefficients, and regression coefficients from the factorial matrix. Special emphasis is given to computation technique and to approximation formulas. The method is extremely flexible in application since it may be applied to any subset of the original set of observed variables. It is also extremely useful when many of these coefficients are desired.

Type
Original Paper
Information
Psychometrika , Volume 5 , Issue 3 , September 1940 , pp. 211 - 232
Copyright
Copyright © 1940 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Editor's Note: The reader will recognize the subject-matter treated in this article as closely allied to that of an article by Louis Guttman, “Multiple Rectilinear Prediction and the Resolution into Components,” in the June, 1940 issue of this journal. Although there is considerable overlapping in the topics considered in these two articles, it was felt that some readers would be more interested in one approach, while others would gain more from the other approach and that still others would find both presentations of value. Guttman's article is somewhat more concerned with the theoretical aspects of the problem, while Dwyer's article emphasizes the technique of computation and approximation. The manuscript for Dwyer's article was received while Guttman's article was in press. At Dwyer's request, Guttman made available to him a pre-publication copy of his manuscript so that Dwyer was able to insert in his manuscript references to the earlier one.

References

Kurtz, A. K. The use of the Doolittle method in obtaining related multiple correlation coefficients. Pschometrika, 1936, 1, 45–51.CrossRefGoogle Scholar
Dwyer, P. S. The simultaneous computation of groups of regression equations and associated multiple correlation coefficients. Annals Math. Stat., 1937, 8, 224–231.CrossRefGoogle Scholar
Tolley, H. R. and Ezekial, Mordeca. The Doolittle method for solving multiple correlation equations versus the Kelley-Salisbury iteration method. J. Am. Stat. Ass., 1927, 22, 497–500.Google Scholar
Kelley, T. L. Statistical method, New York: Macmillan, 1923.Google Scholar
Thurstone, L. L. The vectors of mind, Chicago: Univ. Chicago Press, 1935.Google Scholar
Wilson, E. B. and Worcester, Jan. Note on factor analysis. Psychometrika, 1939, 4, 133–148.CrossRefGoogle Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1935, 1, 1–6.CrossRefGoogle Scholar
Dwyer, P. S. The determination of the factor loadings of a given test from the known factor loadings of other tests. Psychometrika, 1937, 2, 173–178.CrossRefGoogle Scholar
Dwyer, P. S. An analysis of 19 occupational scores, etc.. J. Appl. Psychol, 1938, 22, 8–16.CrossRefGoogle Scholar
Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation. Psychometrika, 1939, 4, 163–171.CrossRefGoogle Scholar
Frisch, R. Statistical confluence analysis by means of complete regression systems. Oslo, 1934.Google Scholar
Guttman, Loui. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99.CrossRefGoogle Scholar