Best linear predictors for factor scores

Abstract

From the literature three types of predictors for factor scores are available. These are characterized by the constraints: linear, linear conditionally unbiased, and linear correlation preserving. Each of these constraints generates a class of predictors. Best predictors are defined in terms of Lowner's partial matrix order applied to matrices of mean square error of prediction. It is shown that within the first two classes a best predictor exists and that it does not exist in the third.

Keywords:

• Löwner's partial matrix order
• mean square error
• conditional unbiasedness
• correlation preservation