CoDaPack: A tool for Compositional Data Analysis

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CoDaPack A tool for Compositional Data Analysis

• M. Comas-Cufí S. Thió-Henestrosa
• (marc.comas_at_udg.edu)
• Dept. Computer Sciences and Applied Mathematics
• University of Girona (UdG)
• Catalonia-Spain

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Whats coda?

• Vector xx1, x2,, xD
• Add to a constant 100, 1, 106, 109,
• Units percentage, part per one, ppm, ppb,
• Has positive elements
• Carry only relative information
• Examples
• Production (pieces) Ok, NonOk, Rework 87,
  1, 12
• Household budget () Food, Serv., Other
  1150, 623, 351
• Daily activities (h) Work, Sleep, Other
  7.5, 7.5, 9

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Sample space of coda simplex

• Compositional data live in the simplex (S)
  represented in ternary (D3), quaternary (D4),
  diagram

D3 S3
D4 S4
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Euclidean distance appropriate?
B
A
B2010 0.3, 0.4, 0.3
A2010 0.1, 0.2, 0.7
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Euclidean distance appropriate?
B
A
STOP PROD.
HALF PROD.
NON-STOP PROD.
NON-STOP PROD.
STOP PROD.
HALF PROD.
0.4
0.3
0.2
0.1
0.1
0.7
0.2
0.3
0.3
0.4
2009 2010
0.7
0.3
0.1
0.7
0.2
0.3
0.3
0.4
2009 ? 2010 Factory A Factory B
Stop Prod
Half Prod
Non-Stop Prod
-50
-25
100
33.3
0
0
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Euclidean distance appropriate?
STOP PROD.
Our interest lies on relative values A2010/A2009
1/2, 2, 1 B2010/B20093/4, 4/3, 1
Euclidian distance de(A) de(B) 0.14
B2009
A2009
B2010
A2010
Aitchison distance da(A)0.6276 da(B)
0.3970
HALF PROD.
NON-STOP PROD.
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Classical multivariate normal model appropriate?
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Log-ratio methodology

• Aitchison geometry to CODA is equivalent to
  classical euclidean geometry to log-ratio values.
  

Simplex (restricted space) ? Real space (non
restricted) x1,,xD
log(xi/xj), i,j 1,,D, j ? i
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CoDaPack 2
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Software

• CoDaPack software developed by the Departament
  of Computer Science and Applied Mathematics in
  the Universitat de Girona. Easy and intuitive.
• http//ima.udg.edu/codapack marc.comas_at_udg.edu
• compositions (R-package) analysis of
  compositional and positive data using different
  approaches.
• http//cran.r-project.org/ raimon.tolosana_at_upc.e
  du
• robCompositions (R-package) robust estimation
  for compositional data
• http//cran.r-project.org/ templ_at_tuwien.ac.at

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References

• Aitchison, J., 1986. The Statistical Analysis of
  Compositional Data. Chapman Hall, London.
  Reprinted in 2003 with additional material
  byBlackburn Press.
• Proceedings of CoDaWork, 2003-2005-2008-2011
  available in http//dugi-doc.udg.edu/handle/10256/
  150.
• CoDaWeb Compositional Data Analysis Web Site
  http//www.compositionaldata.com/