Alpha Factor Analysis of Infallible Variables

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Abstract
The relationship between the factor pattern, F, derived from fallible (containing measurement error) observations on variables and the factor pattern, F*, derived from infallible observations on variables is investigated. A widely believed relationship between F and F*, viz.,F* = AF where A is a diagonal matrix containing the inverses of the square roots of the reliabilities of the variables, is shown to be false for several factor analytic techniques. Under suitable assumptions, it is shown that for Kaiser and Caffrey's “alpha factor analysis”F* and F are related by F* = AF. Empirical examples for which the corresponding elements of F* and AF are equal to two decimal places are presented. The implications of the equality of F* and AF for alpha factor analysis are discussed.

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