Item


Changing the reference measure in the simplex and its weighting effects

Standard analysis of compositional data under the assumption that the Aitchison geometry holds assumes a uniform distribution as reference measure of the space. Weighting of parts can be done changing the reference measure. The changes that appear in the algebraic-geometric structure of the simplex are analysed, as a step towards understanding the implications for elementary statistics of random compositions. Some of the standard tools in exploratory analysis of compositional data analysis, such as center, variation matrix and biplots are studied in some detail, although further research is still needed. The main conclusion is that down-weighting some parts is approaching the geometry of the corresponding subcomposition, thus preserving a kind of coherence between standard and down-weighted analyses

Austrian Statistical Society

Author: Egozcue, Juan José
Pawlowsky-Glahn, Vera
Abstract: Standard analysis of compositional data under the assumption that the Aitchison geometry holds assumes a uniform distribution as reference measure of the space. Weighting of parts can be done changing the reference measure. The changes that appear in the algebraic-geometric structure of the simplex are analysed, as a step towards understanding the implications for elementary statistics of random compositions. Some of the standard tools in exploratory analysis of compositional data analysis, such as center, variation matrix and biplots are studied in some detail, although further research is still needed. The main conclusion is that down-weighting some parts is approaching the geometry of the corresponding subcomposition, thus preserving a kind of coherence between standard and down-weighted analyses
Document access: http://hdl.handle.net/2072/298005
Language: eng
Publisher: Austrian Statistical Society
Rights: Reconeixement 3.0 Espanya
Rights URI: http://creativecommons.org/licenses/by/3.0/es/deed.ca
Subject: Anàlisi multivariable
Estadística bayesiana
Multivariate analysis
Bayesian statistical decision
Title: Changing the reference measure in the simplex and its weighting effects
Type: info:eu-repo/semantics/article
Repository: Recercat

Subjects

Authors


Warning: Unknown: write failed: No space left on device (28) in Unknown on line 0

Warning: Unknown: Failed to write session data (files). Please verify that the current setting of session.save_path is correct (/var/lib/php5) in Unknown on line 0