Censored regression models are a class of

models A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

in which the

dependent variable Dependent and independent variables are variables in mathematical modeling, statistical modeling and experimental sciences. Dependent variables receive this name because, in an experiment, their values are studied under the supposition or dema ...

is censored above or below a certain threshold. A commonly used likelihood-based model to accommodate to a censored sample is the Tobit model, but

quantile In statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile th ...

and nonparametric estimators have also been developed. These and other censored regression models are often confused with

truncated regression model Truncated regression models are a class of models in which the sample has been truncated for certain ranges of the dependent variable. That means observations with values in the dependent variable below or above certain thresholds are systematicall ...

s. Truncated regression models are used for data where whole observations are missing so that the values for the dependent and the independent variables are unknown. Censored regression models are used for data where only the value for the dependent variable is unknown while the values of the independent variables are still available. Censored dependent variables frequently arise in

econometrics Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. ...

. A common example is

labor supply In mainstream economic theories, the labour supply is the total hours (adjusted for intensity of effort) that workers wish to work at a given real wage rate. It is frequently represented graphically by a labour supply curve, which shows hypotheti ...

. Data are frequently available on the hours worked by employees, and a labor supply model estimates the relationship between hours worked and characteristics of employees such as age, education and family status. However, such estimates undertaken using

linear regression In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is cal ...

will be biased by the fact that for people who are unemployed it is not possible to observe the number of hours they would have worked had they had employment. Still we know age, education and family status for those observations.

See also

References

Further reading