Utilizing the Flexibility of the Epsilon-Skew-Normal Distribution for Tobit Regression Problems

Abstract

In this note, we extend the Tobit model first introduced by James Tobin in 1958. The Tobit model is a regression model used when the dependent variable is truncated or censored to the left and assumes the error term is normally distributed. It has been shown in subsequent research that even small violations of this assumption may lead to inconsistent estimators. The log and other Box–Cox transformations to the data are often utilized in an attempt to compensate for this weakness. However, we illustrate that for many biological applications this approach is oftentimes inadequate. An alternative approach is to consider other parametric models. We consider the utilizing the epsilon-skew-normal distribution to provide a more flexible model. We show this model provides consistent and efficient parameter estimates.

Keywords:

• Left-censoring
• Limit of detection
• Maximum likelihood estimation
• Regression modeling

Mathematics Subject Classification:

• Primary 62N01
• Secondary 62J05

Acknowledgments

The authors would like to thank Dr. Chris Andrews, Dr. Lili Tian, Dr. Greg Wilding, and the reviewer for reading the manuscript and providing helpful comments.