Japan Womenfs University Journal (Faculty of Integrated Arts and Social Sciences), Vol. 16 (2005), 43-50
On the Special Type of Principal Component Analysis:
It should belong to factor analysis
YASUHARU OKAMOTO
Abstract
There are two types of criteria used in principal components analysis (PCA), (1) criteria of one by one extraction of components and (2) the join loss criterion. There are also two types of variables, observed and unobserved. In this paper, the two types of criteria are connected respectively with the two types of variables, and distinctive features of the join loss criterion are discussed. Both types of criteria are proposed to extract the major part of the information in the data. But, one of distinctive features of criterion (2) against criterion (1) is that criterion (2) is set for latent variables, while criterion (1) is set for linear combinations of the observed variables. It is also pointed out that the solution of criterion (2) can be rotated, although rotation of the solution of criterion (1) is inhibited. Rotation is a common procedure in factor analysis. In this paper, based on these features, criterion (2) is proposed to be considered as that for factor analysis. Positive evaluation of correlated errors, which result from criterion (2), is also discussed.
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