Influence diagnostics in Birnbaum-Saunders nonlinear regression models

TL;DR

This paper develops influence diagnostics for Birnbaum-Saunders nonlinear regression models, extending previous linear model results to better assess the impact of observations in lifetime data analysis.

Contribution

It generalizes influence diagnostic methods from linear to nonlinear Birnbaum-Saunders regression models, including local influence, total local influence, and leverage measures.

Findings

Derived normal curvatures of local influence under various perturbations

Extended influence diagnostics to nonlinear models

Provided tools for better influence assessment in lifetime data

Abstract

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [2004, Influence diagnostics in log-Birnbaum-Saunders regression models. Journal of Applied Statistics, 31, 1049-1064] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures of local influence are derived under various perturbation schemes.