Gradient boosting for Dirichlet regression models

Abstract

In various real-world applications, researchers often work with compositional data which appears as proportions, amounts or rates. As a framework for dealing with the unique nature of compositional data, Dirichlet regression models have been introduced. In this article, we propose a novel model-based gradient boosting approach for Dirichlet regression models embedded in the framework of generalized additive models for location, scale and shape. This approach allows for data-driven variable selection in low- as well as high-dimensional data settings. Moreover, the implementation enables the direct calculation of marginal effects for different predictor variables. Thus, it provides an alternative estimation procedure besides the well-established approach based on the maximum likelihood principle. After conducting detailed simulation studies to evaluate the performance of the estimation procedure regarding prediction accuracy and variable selection in low- and high-dimensional settings, we present a real-world application concerning the changes in election results in the Great Recession utilizing a large-scale European dataset. Using our proposed approach, we investigate the effect of protests on voting proportions of distinct party families while identifying important socioeconomic variables and their effect on those voting proportions via variable selection.