2004 Fiscal Year Final Research Report Summary

CANONICAL ANALYSIS FOR INCOMPLETE DATA MATRIX

Research Project

Project/Area Number	15500184
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Statistical science
Research Institution	Niigata University
Principal Investigator	SHIBAYAMA Tadashi Niigata University, Faculty of Education and Human Sciences, Associate Professor, 教育人間科学部, 助教授 (70240752)
Project Period (FY)	2003 – 2004
Keywords	CANONICAL ANALYSIS / ANOVA / MISSING VALUES / INCOMPETE DATA / INDIVIDUAL DIFFERENCES / PCA
Research Abstract	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.

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