Mean regression for (0,1) responses via beta scale mixtures

TL;DR

This paper introduces a beta scale mixture model to enhance flexibility in modeling heavy-tailed bounded responses, allowing for greater skewness and kurtosis, and demonstrates its superior performance through experiments.

Contribution

The paper proposes a novel beta scale mixture model that extends beta regression by incorporating a mixing variable for improved flexibility in response distribution modeling.

Findings

Outperforms classical beta regression in simulations

Achieves better fit on real datasets

Handles heavy-tailed and skewed responses effectively

Abstract

To achieve a greater general flexibility for modeling heavy-tailed bounded responses, a beta scale mixture model is proposed. Each member of the family is obtained by multiplying the scale parameter of the conditional beta distribution by a mixing random variable taking values on all or part of the positive real line and whose distribution depends on a single parameter governing the tail behavior of the resulting compound distribution. These family members allow for a wider range of values for skewness and kurtosis. To validate the effectiveness of the proposed model, we conduct experiments on both simulated data and real datasets. The results indicate that the beta scale mixture model demonstrates superior performance relative to the classical beta regression model and alternative competing methods for modeling responses on the bounded unit domain.