MULTIVARIATE ANALYSIS OF COMPOSITIONAL DATA: APPLIED COMPARISONS FAVOUR STANDARD PRINCIPAL COMPONENTS ANALYSIS OVER AITCHISON'S LOGLINEAR CONTRAST METHOD
作者:
D. TANGRI,
R. V. S. WRIGHT,
期刊:
Archaeometry
(WILEY Available online 1993)
卷期:
Volume 35,
issue 1
页码: 103-112
ISSN:0003-813X
年代: 1993
DOI:10.1111/j.1475-4754.1993.tb01026.x
出版商: Blackwell Publishing Ltd
关键词: PRINCIPAL COMPONENTS ANALYSIS;LOGLINEAR TRANSFORMATION;COMPOSITIONAL DATA
数据来源: WILEY
摘要:
There has been debate about whether standard principal components analysis is appropriate for the multivariate analysis of compositional data (e.g. oxide composition of glass), Loglinear transformation has been recommended by Aitchison as a prerequisite. This paper argues that previous comparisons of methodological merits have tended to circularity of argument by making assumptions about the form of a good multivariate result. To break the circularity of argument the authors have introduced randomized variables into five data sets. A good result must recognize these randomized variables as noise and place them near the centroid of the principal components scattergram of variable loadings. Standard principal components analysis is found to perform better than loglinear transformation in its ability to recognize the randomized variables. It is concluded that loglinear transformation tends to introduce spurious structure into a table of compositional data.This paper is followed by a comment by M. J. Baxter.
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