Equivalence of Two Methods for Maximizing Individual Differences with Incomplete Test scores

Abstract

Equivalence of two methods for obtaining composite scores that maximize individual differences from incomplete test scores is formally proved. One method is based on the least squares criterion and can get composite scores in such a way as to maximize individual differences while allowing for differences between difficulties of tests. The other method is formulated from the viewpoint of ANOVA model and thus can be easily extended to multi-component case. The basic result of the equivalence is shown to be available for developing an effective algorithm of PCA for incomplete data matrix.