Dynamic Graphics of Parametrically Linked Multivariate Methods Used in Compositional Data Analysis

8 Pages Posted: 24 Apr 2008

See all articles by Michael Greenacre

Michael Greenacre

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Date Written: April 2008

Abstract

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods.

Keywords: compositional data, contingency tables, correspondence analysis, logratio transformation, singular value decomposition, spectral map, weighting

JEL Classification: C19, C88

Suggested Citation

Greenacre, Michael John, Dynamic Graphics of Parametrically Linked Multivariate Methods Used in Compositional Data Analysis (April 2008). Available at SSRN: https://ssrn.com/abstract=1124810 or http://dx.doi.org/10.2139/ssrn.1124810

Michael John Greenacre (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
34 93 542 25 51 (Phone)
34 93 542 17 46 (Fax)

Do you want regular updates from SSRN on Twitter?

Paper statistics

Downloads
65
Abstract Views
623
rank
455,138
PlumX Metrics