The Kaiser, Hunka and Bianchini Factor Similarity Coefficients: A Cautionary Note

Abstract

Kaiser, Hunka and Bianchini (1971) have given a method to compare two matrices of factor loadings based on the same variables, but different groups of individuals. They suggest expressing the factor similarity by the elements of the rotation matrix that optimizes the sum of inner products between corresponding columns or rows of the matrices. The optimal rotation involved in this method is examined from a mathematical point of view and, on the basis of this, the method is shown to be invalid.