Balance and variable selection in regression with explicative compositional variables

G. Mateu-Figueras, J. Saperas Riera, J. A. Martín-Fernández

In penalized linear regression a penalty term is introduced in the cost function to shrink the coefficients of less relevant variables towards zero. LASSO regression, which applies an L1-norm penalty, is increasingly used for variable selection.

Recently, a compositional LASSO regression approach has been used for variable selection by considering a logcontrast model and the standard L1-norm. However, when dealing with regression involving compositional covariates, the geometry of the simplex needs to be considered.

In this work, we propose a new norm termed L1-pairwise . This new norm is defined as the sum of the absolute values of the pairwise logratios, being compatible with the properties of the Aitchison geometry. Using this new norm in the penalty term, our method aims to identify and split, instead of variables, the balances into two groups, those that influence the response variable and those that do not.

Keywords: Balance selection, penalized regression, L1-norm, Aitchison geometry

GT03.AMC3 Compositional Data
November 9, 2023  4:50 PM
CC3: Room 1

M. Comas Cufi, J. Palarea Albaladejo, J. A. Martín Fernández, G. Mateu Figueras

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