The Trade-Off Between Factor Score Determinacy and the Preservation of Inter-Factor Correlations

Regression factor score predictors have the maximum factor score determinacy, that is, the maximum correlation with the corresponding factor, but they do not have the same inter-correlations as the factors. As it might be useful to compute factor score predictors that have the same inter-correlations as the factors, correlation-preserving factor score predictors have been proposed. However, correlation-preserving factor score predictors have smaller correlations with the corresponding factors (factor score determinacy) than regression factor score predictors. Thus, higher factor score determinacy goes along with bias of the inter-correlations and unbiased inter-correlations go along with lower factor score determinacy. The aim of the present study was therefore to investigate the size and conditions of the trade-off between factor score determinacy and bias of inter-correlations by means of algebraic considerations and a simulation study. It turns out that under several conditions very small gains of factor score determinacy of the regression factor score predictor go along with a large bias of inter-correlations. Instead of using the regression factor score predictor by default, it is proposed to check whether substantial bias of inter-correlations can be avoided without substantial loss of factor score determinacy using a correlation-preserving factor score predictor. A syntax that allows to compute correlation-preserving factor score predictors from regression factor score predictors, and to compare factor score determinacy and inter-correlations of the factor score predictors is given in the Appendix.