A general and unified class of gamma regression models

Abstract

The usual mean linear regression provides the average relationship between a response variable and explanatory variables, but it is not always the best metric for modeling right-skewed data in regression. In this paper, we extend the usual mean gamma regression model using a general and unified parameterization of this distribution that is indexed by some central tendency measure. Unlike the traditional gamma regression model, which focuses on the arithmetic mean, this new parameterization accommodates different measures of central tendency, including the median, mode, and geometric mean, harmonic mean along with a precision parameter. We consider a regression structure for both components. The model provides a robust framework for regression, allowing for greater adaptability to different data characteristics. Estimation is performed by maximum likelihood. Furthermore, we discuss residuals. A Monte Carlo experiment is conducted to evaluate the performances of these estimators and residuals in finite samples with a discussion of the obtained results. The methods developed are applied to two real data sets from minerals and nutrition.