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Factor score predictors are to be computed when the individual scores on thefactors are of interest. Conditions for a perfect inter-correlation of theregression/best linear factor score predictor, the best linear conditionallyunbiased predictor, and the determinant best linear correlation-preservingpredictor are presented. When these three types of factor score predictors areperfectly correlated for corresponding factors, the factor score predictorscomputed from one method will have the virtues of the factor score predictorscomputed from the other methods. A Schmid-Leiman based transformation for whichthe three types of factor score predictors are perfectly correlated forcorresponding orthogonal factors is proposed.

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