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

TL;DR

This paper introduces a Schmid-Leiman based transformation that ensures perfect inter-correlation among three types of factor score predictors, enhancing their consistency and reliability in factor analysis.

Contribution

It proposes a novel transformation method that achieves perfect correlation among different factor score predictors for orthogonal factors, improving their comparability.

Findings

The three types of factor score predictors can be perfectly correlated with the proposed transformation.

The transformation enhances the virtues of each predictor type by aligning their scores.

It provides conditions under which perfect inter-correlation is achieved.

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.