Hostname: page-component-6bf8c574d5-w79xw Total loading time: 0 Render date: 2025-02-22T08:21:39.541Z Has data issue: false hasContentIssue false
  • English
  • Français

The Theory of Abstract Partials: An Introduction

Published online by Cambridge University Press:  01 January 2025

William W. Rozeboom
William W. Rozeboom*
Affiliation:
University of Alberta
Get access Rights & Permissions [Opens in a new window]

Abstract

It is customary in multivariate analysis to search out relational structure by partitioning measures of total variation or overall relatedness into components variously attributable to different sources. Although the multivariate systems most familiar today–notably, linear correlational analysis, analysis of variance, and Information theory–base their decompositions upon very different substantive quantities, they all embody the very same abstract mathematical structure which, moreover, is capable of generating potentially fruitful patterns of data analysis in many other substantive applications as well.

Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 2 , June 1968 , pp. 133 - 167
Copyright
Copyright © 1968 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.)

References

Anderson, T. W. Introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Attneave, F. Applications of information theory to psychology, New York: Holt-Dryden, 1959.Google Scholar
DuBois, P. H. Multivariate correlational analysis, New York: Harper & Bros., 1957.Google Scholar
Fhanér, S. Some comments in connection with Rozeboom's linear correlation theory. Psychometrika, 1966, 31, 267–270.CrossRefGoogle Scholar
Garner, W. R. Uncertainty and structure as psychological concepts, New York: Wiley, 1962.Google Scholar
Garner, W. R., and McGill, W. J.. The relation between information and variance analysis. Psychometrika, 1956, 21, 219–228.CrossRefGoogle Scholar
Lazarsfeld, P. F. The algebra of dichotomous systems. In Solomon, H. (Eds.), Studies in item analysis and prediction, Stanford, Calif.: Stanford University Press, 1961.Google Scholar
McGill, W. J. Multivariate information transmission. Psychometrika, 1954, 19, 97–116.CrossRefGoogle Scholar
Ross, J. Informational coverage and correlational analysis. Psychometrika, 1962, 27, 297–306.CrossRefGoogle Scholar
Rozeboom, W. W. Linear correlations between sets of variables. Psychometrika, 1965, 30, 57–71.CrossRefGoogle ScholarPubMed
Rozeboom, W. W. Foundations of the theory of prediction, Homewood, Ill.: Dorsey Press, 1966.Google Scholar
Rozeboom, W. W. Scaling theory and the nature of measurement. Synthese, 1966, 16, 170–233.CrossRefGoogle Scholar
Shannon, C. E. A mathematical theory of communication. Bell System Technical Journal, 1948, 27, 379–423.CrossRefGoogle Scholar
Watanabé, S. Information theoretical analysis of multivariate correlation. IBM Journal of Research and Development, 1960, 4, 66–82.CrossRefGoogle Scholar
Watanabé, S. A note on the formation of concept and of association by information-theoretical correlation analysis. Information and Control, 1961, 4, 291–296.CrossRefGoogle Scholar