Implications of Indeterminate Factor-Error Covariances for Factor Construction, Prediction, and Determinacy

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for indeterminate factor-error covariances to be arbitrarily small, for mean square convergence of the regression predictor of factor scores, and for the existence of a unique determinate factor and error variable. The determinate factor and error variable are uncorrelated and satisfy the defining assumptions of factor analysis. Several examples are given to illustrate the results. Requests for reprints should be sent to Wim P. Krijnen, Lisdodde 1, 9679 MC Scheemda, The Netherlands.