Methods of penalized regression for compositional data

Abstract

Compositional data consist of known vectors like compositions whose components are positive and defined in the interval (0,1) representing proportions or fractions of a "whole", where the sum of these components must be equal to one. Compositional data is present in different areas, as in geology, ecology, economy, medicine, among many others. In this way, there is a great interest in new modeling approaches for compositional data, principally when there is influence of covariates in this type of data. In this context, the main objective of this project is to propose the new approach of regression models applied in compositional data. The basic idea consists to develop of a marked method by penalized regression, in particular the Lasso (least absolute shrinkage and selection operator), for the estimation of parameters via classical and Bayesian inference. In particular, we envision developing this modeling for compositional data, with the number of explanatory variables exceeds the number of observations in the presence of large databases, and furthermore, when there is presence of components equal to zero. (AU)