T. Tsagris, Michail and Preston, Simon and T.A. Wood, Andrew (2011): A databased power transformation for compositional data. Published in: Proceedings of the 4th international workshop on Compositional Data Analysis, Girona, Spain (May 2011)

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Abstract
Compositional data analysis is carried out either by neglecting the compositional constraint and applying standard multivariate data analysis, or by transforming the data using the logs of the ratios of the components. In this work we examine a more general transformation which includes both approaches as special cases. It is a power transformation and involves a single parameter�. The transformation has two equivalent versions. The �first is the stayinthesimplex version. This expression is the power transformation as de�fined by Aitchison (1986). The second version, which is a linear transformation of the stayinthesimplex, is a BoxCox type transformation. We call the second version the isometric �alphatransformation because of the multiplication with the Helmert submatrix. We discuss a parametric way of estimating the value of alpha�, which is maximization of its pro�le likelihood (assuming multivariate normality of the transformed data) and the equivalence between the two versions is exhibited. Other ways include maximization of the correct classi�cation probability in discriminant analysis and maximization of the pseudoR2 in linear regression. We examine the relationship between the transformation, the raw data approach and the isometric logratio transformation. Furthermore, we also de�fine a suitable family of metrics corresponding to the family of �alphatransformation and consider the corresponding family of Fr�echet means.
Item Type:  MPRA Paper 

Original Title:  A databased power transformation for compositional data 
English Title:  A databased power transformation for compositional data 
Language:  English 
Keywords:  Compositional data, power transformation, alpha, Frechet mean 
Subjects:  C  Mathematical and Quantitative Methods > C8  Data Collection and Data Estimation Methodology ; Computer Programs > C89  Other 
Item ID:  53068 
Depositing User:  Mr Michail Tsagris 
Date Deposited:  20 Jan 2014 17:21 
Last Modified:  27 Sep 2019 21:04 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/53068 