Regression analysis for compositional data from perspective of the logratio approach

Eva Fiserova e Karel Hron

Palacky University, Olomouc, Czech Republic

Thursday 6th April 2017

14:00:00

Aula Seminari "F. Saleri" VI piano - MOX - Dipartimento di Matematica, Politecnico di Milano - Edificio 14

Regression analysis is an important tool for analysing the relationships between the response variable and known explanatory variables. When the response variables or explanatory variables are compositional, i.e. multivariate observations carrying only relative information (proportions, percentages), a special treatment in regression is necessary. Compositional data are characterized by the simplex sample space with the Aitchison geometry that forms the Euclidean structure. Proper statistical methodology for this kind of observations is the logratio methodology that enables to express the data isometrically in the real Euclidean space where it is possible to apply standard statistical tools (Aitchison, 1986; Pawlowsky-Glahn et al., 2015). The lecture is focused on three main regression tasks, where compositional data are involved: either regression with a compositional response variable, or regression with compositional explanatory variables, or regression between parts of a composition. The main methodological approach for dealing with compositional regression is based on orthonormal logratio coordinates. Although regression models in orthonormal logratio coordinates are theoretically well justified, both the normalizing constants to reach orthonormality and the natural logarithm itself result in quite a complex interpretation of the regression parameters. In the lecture, we will present new orthogonal logratio coordinates (Muller et al., 2017) in order to achieve better interpretability of regression parameters while preserving all important features of regression models for compositional data. Theoretical results will be applied to real-world examples. contatto: alessandra.menafoglio@polimi.it