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

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.