1 / 11

CoDaPack : A tool for Compositional Data Analysis

CoDaPack : A tool for Compositional Data Analysis. M. Comas- Cufí & S. Thió-Henestrosa ( marc.comas@udg.edu ) Dept. Computer Sciences and Applied Mathematics University of Girona ( UdG ) Catalonia-Spain. What’s coda?.

patriciap
Download Presentation

CoDaPack : A tool for Compositional Data Analysis

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CoDaPack: A toolforCompositional Data Analysis M. Comas-Cufí & S. Thió-Henestrosa (marc.comas@udg.edu) Dept. Computer Sciences and Applied Mathematics University of Girona (UdG) Catalonia-Spain

  2. What’s coda? We are interested in relative values ; total sum is not informative. • Vector x=[x1, 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 (D=3), quaternary (D=4), … diagram x = [0.45,0.35,0.2] x=[0.2,0.25,0.2 ,0.35] D=3 S3 D=4 S4

  4. Euclidean distance appropriate? B A STOP PROD. HALF PROD. NON-STOP PROD. STOP PROD. HALF PROD. NON-STOP PROD. A2009= [0.2, 0.1, 0.7] B2009= [0.4, 0.3, 0.3] B2010= [0.3, 0.4, 0.3] A2010= [0.1, 0.2, 0.7] A2010- A2009= B2010- B2009= [-0.1, 0.1, 0] de(A)=de(B)=0.14  measures the absolute difference

  5. Euclidean distance appropriate? B A STOP PROD. HALF PROD. NON-STOP PROD. NON-STOP PROD. STOP PROD. HALF PROD. 2009 2010 0.1 0.2 0.7 0.7 0.4 0.4 0.3 0.3 0.3 0.1 0.2 0.3 0.7 0.3 0.3 0.4 0.1 0.2 -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/B2009=[3/4, 4/3, 1] Euclidian distance: de(A) = de(B) = 0.14 B2009 B2010 A2009 A2010 Aitchisondistance: 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@udg.edu compositions (R-package): analysis of compositional and positive data using different approaches. http://cran.r-project.org/ raimon.tolosana@upc.edu robCompositions (R-package): robust estimation for compositional data http://cran.r-project.org/ templ@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/

More Related