Linear Models with Compositions in R

Compositional Data Analysis: Theory and Applications

Volumn , Issue , 2011, Pages 356-371

  Tolosana Delgado, Raimon ^a   van den Boogaart, Karl Gerald ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b TU BERGAKADEMIE FREIBERG   (Germany)

Author keywords

Classical concept of linear combination meaningless on the simplex, and classical linear combination giving negative predictions; Compositional summary geometric centre and variation matrix; Descriptive analysis of compositional characteristics; Explanatory binary variable dependence of a composition on a factor; Explanatory categorical variable extended to factors, with more than two levels; Explanatory composition, within scope of regression and linear models, CODA data set playing role of set of covariates; Explanatory variables, categorical variables analysis of the variance (ANOVA), or analysis of the covariance (ANCOVA); Fitting a linear model on the simplex using package 'compositions' and basic linear model functionality of R; Linear models with compositions in R checking intrinsic relations between (sets of) variables; Package compositions, used in conjunction with standard R routines, as response or as explanatory variables

Indexed keywords

EID: 84872068964     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9781119976462.ch26     Document Type: Chapter

References (11)

1. Aitchison J 1986 The Statistical Analysis of Compositional Data.Monographs on Statistics and Applied Probability. Chapman and Hall Ltd (reprinted 2003 with additional material by The Blackburn Press), London (UK). 416 p.
2. Eaton ML 1983 Multivariate Statistics. A Vector Space Approach. John Wiley & Sons, Ltd, New York, NY (USA). 512 p.
3. Fahrmeir L and Hamerle A (ed.) 1984 Multivariate Statistische Verfahren. Walter de Gruyter, Berlin (Germany). 796 p.
4. Grantham JH andVelbelMA1988 The influence of climate and topography on rock-fragment abundance in modern fluvial sands of the southern Blue Ridge Mountains,North Carolina. Journal of Sedimentary Petrology 58, 219-227.
5. Krzanowski WJ 1988 Principles of Multivariate Analysis: A User's Perspective. Clarendon Press, Oxford (UK). 563 p.
6. Mardia KV, Kent JT and Bibby JM 1979 Multivariate Analysis. Academic Press, London (UK). 518 p.
7. Pawlowsky-Glahn V 2003 Statistical modelling on coordinates. In Proceedings of CoDaWork'03, The 1st Compositional Data Analysis Workshop (ed. Thió-Henestrosa S and Martín-Fernández JA). http://ima.udg.es/Activitats/CoDaWork03/. University of Girona. Girona (Spain). CD-ROM.
8. Pawlowsky-Glahn V and Egozcue JJ 2001 Geometric approach to statistical analysis on the simplex. Stochastic Environmental Research and Risk Assessment (SERRA) 15(5), 384-398.
9. R Development Core Team 2004 R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna (Austria).
10. Tolosana-Delgado R and von Eynatten H 2010 Simplifying compositional multiple regression: Application to grain size controls on sediment geochemistry. Computers & Geosciences 36(5), 577-589.
11. van den Boogaart KG and Tolosana-Delgado R 2008 "compositions": a unified R package to analyze compositional data. Computers & Geosciences 34(4), 320-338.