Convergence in mean square of factor predictors

Abstract

Sufficient conditions for mean square convergence of factor predictors in common factor analysis are given by Guttman, by Williams, and by Schneeweiss and Mathes. These conditions do not hold for confirmatory factor analysis or when an error variance equals zero (Heywood cases). Two sufficient conditions are given for the three basic factor predictors and a predictor from rotated principal components analysis to converge to the factors of the model for confirmatory factor analysis, including Heywood cases. For certain model specifications the conditions are necessary. The conditions are sufficient for the existence of a unique true factor. A geometric interpretation is given for factor indeterminacy and mean square convergence of best linear factor prediction.