title: Some Results on Mean Square Error for Factor Score Prediction.
abstract: For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix Γp= Φ1/2Λp'Ψp-1ΛpΦ1/2. This matrix increases with the number of observable variables p. A necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of Γpor, equivalently, divergence of signal-to-noise (Schneeweiss & Mathes, 1995). The same condition is necessary and sufficient for convergence to zero of the positive definite MSE differences of factor predictors, convergence to zero of the distance between factor predictors, and convergence to the unit value of the relative efficiencies of predictors. Various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors.
authors.affiliation: University of Amsterdam, Amsterdam. P.W.vanRijn@uva.nl.|Department of Psychology, Psychological Methods, University of Amsterdam, Roetersstraat 15, 1018 WB, Amsterdam, The Netherlands. P.W.vanRijn@uva.nl.
authors.forename: Wim P
authors.initials: WP
authors.lastname: Krijnen
keywords: common factor analysis; confirmatory factor analysis; factor indeterminacy; relative efficiency