  The model implied by factor score predictors does not reproduce the
non-diagonal elements of the observed covariance matrix as well as the factor
loadings. It is therefore investigated whether it is possible to estimate
factor loadings for which the model implied by the factor score predictors
optimally reproduces the non-diagonal elements of the observed covariance
matrix. Accordingly, loading estimates are proposed for which the model implied
by the factor score predictors allows for a least-squares approximation of the
non-diagonal elements of the observed covariance matrix. This estimation method
is termed Score predictor factor analysis and algebraically compared with
Minres factor analysis as well as principal component analysis. A population
based and a sample based simulation study was performed in order to compare
Score predictor factor analysis, Minres factor analysis, and principal
component analysis. It turns out that the non-diagonal elements of the observed
covariance matrix can more exactly be reproduced from the factor score
predictors computed from Score predictor factor analysis than from the factor
score predictors computed from Minres factor analysis and from principal
components. Moreover, Score predictor factor analysis can be helpful to
identify factors when the factor model does not perfectly fit to the data
because of model error.
