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 systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known. This is in contrast to

censored regression model Censored regression models are a class of models in which the dependent variable 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 and nonp ...

s where only the value of the dependent variable is clustered at a lower threshold, an upper threshold, or both, while the value for

independent variables 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 deman ...

is available. Sample truncation is a pervasive issue in quantitative social sciences when using

observational data In fields such as epidemiology, social sciences, psychology and statistics, an observational study draws inferences from a sample to a population where the independent variable is not under the control of the researcher because of ethical concern ...

, and consequently the development of suitable estimation techniques has long been of interest 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. 8 ...

and related disciplines. In the 1970s,

James Heckman James Joseph Heckman (born April 19, 1944) is a Nobel Prize-winning American economist at the University of Chicago, where he is The Henry Schultz Distinguished Service Professor in Economics and the College; Professor at the Harris School of Pu ...

noted the similarity between truncated and otherwise non-randomly selected samples, and developed the

Heckman correction The Heckman correction is a statistical technique to correct bias from non-randomly selected samples or otherwise incidentally truncated dependent variables, a pervasive issue in quantitative social sciences when using observational data. Concep ...

. Estimation of truncated regression models is usually done via parametric maximum likelihood method. More recently, various semi-parametric and non-parametric generalisation were proposed in the literature, e.g., based on the local least squares approach or the local maximum likelihood approach, which are kernel based methods.

See also

References

Further reading