Basic Concepts
The Tobit regression model (aka the censored regression model) is designed to model the linear relationship between independent variables and a censored dependent variable. Censoring can occur from above (right) or below (left) or both.
For example, suppose we want to be able to predict the dividend of a stock based on the company’s earnings. Since the lowest dividend is zero, even for a company with poor earnings, the dividend will still be zero (censoring from below). Thus, the data for such companies hides useful information for such poor-performing companies.
A test used by the government measures pollutants in drinking water. The measuring device is only capable of measuring amounts up to 100 parts per million. Thus, pollutants above this value will report a value of 100. This is censoring from above.
Using ordinary linear regression will tend to distort the relationship between the variables. Tobit regression is used to provide a better estimate of the relationship.
Topics
- Model description
- Real Statistics capabilities
- Technical information (using calculus)
Under construction
References
Shanaev, S. (2021) Tobit model explained: censored regression (Excel)
https://www.youtube.com/watch?v=QS3OAYML2nM
Munk-Nielson, A. (2016) The Tobit model
https://www.youtube.com/watch?v=IwsE8Rr6l6E
Demeritt, J. (2024) Tobit model
https://jdemeritt.weebly.com/uploads/2/2/7/7/22771764/tobit1.pdf
Greene, W. (2003) Econometric analysis. New Jersey: Prentice Hall.
Wikipedia (2024) Tobit model
https://en.wikipedia.org/wiki/Tobit_model
SAS (1999) Computing predicted values for a Tobit model
https://www.sfu.ca/sasdoc/sashtml/stat/chap36/sect24.htm
Olsen, R. J. (1978) Note on the uniqueness of the maximum likelihood estimator for the Tobit model
Greene, W. (2014) Censoring, Tobit and two part models
https://pages.stern.nyu.edu/~wgreene/DiscreteChoice/2014/DC2014-10-Censoring&Truncation.pdf