Zero-adjusted Birnbaum-Saunders regression model

TL;DR

This paper introduces a zero-adjusted Birnbaum-Saunders regression model that handles excess zeros and right-skewed data, providing a flexible framework for modeling such data with diagnostic tools.

Contribution

It proposes a new zero-adjusted Birnbaum-Saunders regression model that generalizes existing models and includes diagnostic and influence analysis methods.

Findings

Model effectively accounts for excess zeros and skewness.

Applications demonstrate the model's practical utility.

Diagnostic tools aid in model assessment.

Abstract

In this paper we introduce the zero-adjusted Birnbaum-Saunders regression model. This new model generalizes at least seven Birnbaum-Saunders regression models. The idea of this modeling is mixing a degenerate distribution at zero with a Birnbaum-Saunders distribution. Besides the capacity to account for excess zeros, the zero-adjusted Birnbaum-Saunders distribution additionally produces an attractive modeling structure to right-skewed data. In this model, the mean and precision parameter of the Birnbaum-Saunders distribution and the probability of zeros can be related to linear and/or non-linear predictors through link functions. We derive a type of residual to perform diagnostic analysis and a perturbation scheme for identifying those observations that exert unusual influence on the estimation process. Finally, two applications to real data show the potential of the model.