CANONICAL ANALYSIS FOR INCOMPLETE DATA MATRIX

形式上证明了两种最大化不完全测验成绩个体差异的方法的等价性。一种是基于最小二乘准则，考虑到测验难度的差异，尽可能地增大个体差异，从而得到综合得分;另一种是从方差分析模型的角度出发，易于推广到多因素情况。利用等价性的基本结果，说明了PGA算法对不完全数据矩阵的有效性。

Equivalence of two methods for maximizing individual differences with incomplete test scores is formally proved. One method is based on the least squares criterion and can get composite scores in such a way that individual differences become as large as possible allowing for differences between difficulties of tests.The other method is formulated from the viewpoint of ANOVA model, which is able to be easily extended to multi-component case. The basic result on the equivalence can be used to show the effective algorithm of PGA for incomplete data matrix.The algorithm is written in S-PLUS.