CANONICAL ANALYSIS FOR INCOMPLETE DATA MATRIX

正式证明了两种方法在不完全考试成绩下个体差异最大化的等价性。一种方法是基于最小二乘标准，可以以这样一种方式得到综合分数，使个体差异尽可能大，允许不同难度的测试差异。另一种方法是从方差分析模型的角度出发，易于推广到多组分情况。等效性的基本结果可用于证明PGA算法在不完全数据矩阵下的有效性。该算法采用S-PLUS语言编写。

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.