1998 Fiscal Year Final Research Report Summary

A psychometric study on principal components analysis of categorical data

Research Project

Project/Area Number	09610114
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	教育・社会系心理学
Research Institution	Nagoya University
Principal Investigator	MURAKAMI Takashi School of Education, Nagoya University, Professor, 教育学部, 教授 (70093078)
Project Period (FY)	1997 – 1998
Keywords	Principal components analysis / Multiple correspondence analysis / Theory of quantification / Orthomax rotation / Meet and join / Rating scales
Research Abstract	Non-metric principal components analysis with relaxed rank restrictions, originally proposed by De Leeuw and van Rijckevorsel (1988), is investigated from both theoretical and practical view points. A new alternating least squares algorithm for large sample cases and a procedure of rotations of a matrix of loadings from two directions are formulated. It is also shown that the method minimizes three different loss functions, and relations of the method with principal component analysis (PCA) and multiple correspondence analysis (MCA) are explored in the context of join-loss and meet-loss in the sense of Gifi (1990) . Numerical examples show that the method not only produces more interpretable results than those from MCA, but also explains the differences between solutions of PCA and MCA.