An extension of log-symmetric regression models: R codes and applications

Abstract

In the context of regression models, the data for which the response variable is continuous, strictly positive, and asymmetric are commonly employed in various fields of practice. The recent proposal of log-symmetric regression models can be used to describe this kind of data, because it allows that the median and the skewness (or the relative dispersion) of the response variable distribution are explicitly modelled. The purpose of this paper is to flexibilize the log-symmetric regression models by allowing that the median and the skewness (or the relative dispersion) may be described using an arbitrary number of non-parametric additive components, where the latter are approximated by P-splines and/or natural cubic splines with an arbitrary number of knots. An iterative process of parameter estimation based on Fisher scoring, expectation–maximization (EM) and backfitting algorithms is described. A computational implementation of the proposed methodology in the statistical computing environment is also presented. A real data set is analized to illustrate the flexibility of the addressed statistical and computational tools.