A Schmid-Leiman based transformation resulting in perfect inter-correlations of three types of factor score predictors

Abstract: Factor score predictors are to be computed when the individual scores on the factors are of interest. Conditions for a perfect inter-correlation of the regression/best linear factor score predictor, the best linear conditionally unbiased predictor, and the determinant best linear correlation-preserving predictor are presented. When these three types of factor score predictors are perfectly correlated for corresponding factors, the factor score predictors computed from one method will have the virtues of the factor score predictors computed from the other methods. A Schmid-Leiman based transformation for which the three types of factor score predictors are perfectly correlated for corresponding orthogonal factors is proposed.