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.