Premium
MULTIVARIATE ANALYSIS OF COMPOSITIONAL DATA: APPLIED COMPARISONS FAVOUR STANDARD PRINCIPAL COMPONENTS ANALYSIS OVER AITCHISON'S LOGLINEAR CONTRAST METHOD
Author(s) -
TANGRI D.,
WRIGHT R. V. S.
Publication year - 1993
Publication title -
archaeometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.716
H-Index - 67
eISSN - 1475-4754
pISSN - 0003-813X
DOI - 10.1111/j.1475-4754.1993.tb01026.x
Subject(s) - compositional data , principal component analysis , mathematics , multivariate statistics , spurious relationship , statistics , correspondence analysis , contrast (vision) , transformation (genetics) , log linear model , multivariate analysis , econometrics , linear model , computer science , artificial intelligence , biochemistry , chemistry , gene
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.