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CoDaPack: A tool for Compositional Data Analysis M. Comas-Cuf & S. Thi -Henestrosa (marc.comas_at_udg.edu) Dept. Computer Sciences and Applied Mathematics – PowerPoint PPT presentation

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Title: CoDaPack: A tool for Compositional Data Analysis


1
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

2
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

3
Sample space of coda simplex
  • Compositional data live in the simplex (S)
    represented in ternary (D3), quaternary (D4),
    diagram

D3 S3
D4 S4
4
Euclidean distance appropriate?
B
A
B2010 0.3, 0.4, 0.3
A2010 0.1, 0.2, 0.7
5
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
6
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.
7
Classical multivariate normal model appropriate?
8
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
9
CoDaPack 2
10
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

11
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/
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