Some new results on correlation-preserving factor scores prediction methods

Anderson and Rubin and McDonald have proposed a correlation-preserving meth od of factor scores prediction which minimizes the trace of a residual cova riance matrix for variables. Green has proposed a correlation-preserving me thod which minimizes the trace of a residual covariance matrix for factors. Krijnen, Wansbeek and Ten Berge have proposed minimizing the determinant r ather than the trace of the latter covariance matrix, and offered an iterat ive procedure to that effect. In the present paper it is shown that the ite rative procedure can be replaced by a closed-form solution. When all unique variances are strictly positive, this solution is the same as McDonald's, The solution coincides with Green's solution in certain special cases, for instance, when the factors are orthogonal. (C) 1999 Published by Elsevier S cience Inc. All rights reserved.