Psychometrika

, Volume 33, Issue 3, pp 335–345 | Cite as

Alpha-maximized factor analysis (alphamax): Its relation to alpha and canonical factor analysis

  • P. M. Bentler
Article

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.

Keywords

Internal Consistency Public Policy Statistical Theory Score Composite Factor Matrix 

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Copyright information

© Psychometric Society 1968

Authors and Affiliations

  • P. M. Bentler
    • 1
  1. 1.University of CaliforniaLos Angeles

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