Comprehensive Regression and Diagnostics for Non-Negative Data Using the BCSreg Package

Abstract

Continuous positive data characterized by high skewness and heavy tails frequently arise in applied statistics. In other applications, these characteristics are accompanied by a point mass at zero, resulting in a non-negative response with a mixed discrete-continuous distribution. Standard regression models often fail to capture these complex features adequately, requiring more flexible approaches. In this paper, we introduce the BCSreg package for R, which provides a comprehensive and unified computational framework for fitting Box-Cox symmetric and log-symmetric regression models for positive continuous data and their zero-adjusted extensions for mixed non-negative data. These broad classes of models accommodate varying degrees of skewness and tail-heaviness while allowing the parameters to be interpreted directly on the original scale of the data. Through a user-friendly multi-part formula interface, the BCSreg package allows practitioners to simultaneously specify regression structures for the scale parameter (which is proportional to the quantiles of the response), the relative dispersion, and, when appropriate, the probability of zero occurrences. Furthermore, the package provides a complete suite of diagnostic tools specifically tailored to these classes of models, including randomized quantile residuals, simulated envelopes, and influence diagnostics. The package's features and capabilities are illustrated through applications to real data.