On a tobit–Birnbaum–Saunders model with an application to medical data

ABSTRACT

The tobit model allows a censored response variable to be described by covariates. Its applications cover different areas such as economics, engineering, environment and medicine. A strong assumption of the standard tobit model is that its errors follow a normal distribution. However, not all applications are well modeled by this distribution. Some efforts have relaxed the normality assumption by considering more flexible distributions. Nevertheless, the presence of asymmetry could not be well described by these flexible distributions. A real-world data application of measles vaccine in Haiti is explored, which confirms this asymmetry. We propose a tobit model with errors following a Birnbaum–Saunders (BS) distribution, which is asymmetrical and has shown to be a good alternative for describing medical data. Inference based on the maximum likelihood method and a type of residual are derived for the tobit–BS model. We perform global and local influence diagnostics to assess the sensitivity of the maximum likelihood estimators to atypical cases. A Monte Carlo simulation study is carried out to empirically evaluate the performance of these estimators. We conduct a data analysis for the mentioned application of measles vaccine based on the proposed model with the help of the R software. The results show the good performance of the tobit–BS model.

KEYWORDS:

• Birnbaum–Saunders distribution
• diagnostics
• likelihood-based methods
• R software
• residuals
• tobit models

Acknowledgements

The authors thank the Editors and referees for their constructive comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Paulo Scalco http://orcid.org/0000-0002-0667-0422.

Additional information

Funding

This study was partially supported by CAPES and CNPq from the Brazilian government and by FONDECYT 1160868 from the Chilean government.