Censored and Truncated Regression Models
A censored regression model is appropriate when the dependent variable is unavailable is above or below some threshold.
A truncated regression model is appropriate when cases are systemically not collected/unreported when the dependent variable is above or below some threshold.
The Tobit model, named for Tobin (1958), is a special case of a censored regression model.
Description
This is a modification of the OLS model, where the dependent variable Y is related to the independent variable(s) X as Yi = bXi + Ui.
Suppose that data is unobserved if the dependent variable is less than zero. The expected value is then expressed as E[Yi|Xi,Yi≥0] = bXi + E[Ui|Yi≥0].