  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.
