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| The '''Tobit model''', named for [[EstimationOfRelationshipsForLimitedDependentVariables|Tobit (1958)]], is a special case of a censored regression model. | The '''Tobit model''', named for [[EstimationOfRelationshipsForLimitedDependentVariables|Tobin (1958)]], is a special case of a censored regression model. |
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| This is a modification of the [[Statistics/OrdinaryLeastSquares|OLS model]], where the dependent variable ''Y'' is related to the independent variable(s) ''X'' as ''Y,,i,, = bX,,i,, + U,,i,,''. Suppose that data is unobserved if the dependent variable is less than zero. The expected value is then expressed as ''E[Y,,i,,|X,,i,,,Y,,i,,≥0] = bX,,i,, + E[U,,i,,|Y,,i,,≥0]''. |
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].