Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T09:51:26.739Z Has data issue: false hasContentIssue false
  • English
  • Français

Alpha-Maximized Factor Analysis (Alphamax): Its Relation to Alpha and Canonical Factor Analysis

Published online by Cambridge University Press:  01 January 2025

P. M. Bentler
P. M. Bentler*
Affiliation:
University of California, Los Angeles
Get access Rights & Permissions [Opens in a new window]

Abstract

An alpha-O coefficient of internal consistency is defined for an observed score composite. Maximizing alpha-O leads to a system of psychometric (vs. statistical) factor analysis in which successive factors describe dimensions of successively less internal-consistency. Factoring stops when alpha-O is zero or less. In contrast to Kaiser-Caffrey's alpha-C analysis, when the factored matrix is rank 1, alpha-O does not reach unity; it can approach unity only as the number of variables reach infinity. The relative usefulness and domains of generalization of alpha-C and alpha-O are compared. Basically, alpha-C analysis is concerned with the representativeness of factors while alpha-O analysis is concerned with the assessibility of factors. Consequently, either system of factoring can and should be summarized by both the alpha-C and alpha-O coefficients. Not surprisingly, alpha-O analysis is computationally analogous to Rao's canonical factor analysis.

Type
Original Paper
Information
Psychometrika , Volume 33 , Issue 3 , September 1968 , pp. 335 - 345
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

Cliff, N. Orthogonal rotation to congruence. Psychometrika, 1966, 31, 33–42.CrossRefGoogle Scholar
Cronbach, L. J., and Gleser, G. C. The signal/noise ratio in the comparison of reliability coefficients. Educational and Psychological Measurement, 1964, 24, 467–480.CrossRefGoogle Scholar
Green, B. F. Jr. A note on the calculation of weights for maximum battery reliability. Psychometrika, 1950, 15, 57–61.CrossRefGoogle Scholar
Harris, C. W. Some Rao-Guttman relationships. Psychometrika, 1962, 27, 247–263.CrossRefGoogle Scholar
Kaiser, H. F., and Caffrey, J. Alpha factor analysis. Psychometrika, 1965, 30, 1–14.CrossRefGoogle ScholarPubMed
Novick, M. R., and Lewis, C. Coefficient alpha and the reliability of composite measurements. Psychometrika, 1967, 32, 1–13.CrossRefGoogle ScholarPubMed
Peel, E. A. Prediction of a complex criterion and battery reliability. British Journal of Psychology, 1948, 1, 84–94.Google Scholar
Rao, C. R. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar
Schönemann, P. H. A generalized solution of the orthogonal Procrustes problem. Psychometrika, 1966, 31, 1–10.CrossRefGoogle Scholar
Thomson, G. H. Weighting for battery reliability and prediction. British Journal of Psychology, 1940, 30, 357–366.Google Scholar