CoDaPack: A tool for Compositional Data Analysis

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CoDaPack: A tool for Compositional Data Analysis

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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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