Alpha factor analysis of infallible variables

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 betweenF andF*, viz.,F*=AF whereA 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 analysisF* andF are related byF*=AF. Empirical examples for which the corresponding elements ofF* andAF are equal to two decimal places are presented. The implications of the equality ofF* andAF for alpha factor analysis are discussed.I wish to acknowledge the generous assistance of Drs. Chester W. Harris and Henry F. Kaiser in the execution of the research reported in this paper.