Truncated regression model
Encyclopedia
Truncated regression models arise in many applications of statistics
, for example in econometrics
, in cases where observations with values in the outcome variable below or above certain thresholds systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known.
Truncated regression models are often confused with censored regression model
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 is available.
ed). In such a case truncated regression has the considerable advantage of immediately providing consistent and unbiased estimates of the coefficients of the independent variables, as well as their standard errors, thereby allowing for further statistical inference, such as the calculation of the t-values of the estimates.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, for example in econometrics
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
, in cases where observations with values in the outcome variable below or above certain thresholds systematically excluded from the sample. Therefore, whole observations are missing, so that neither the dependent nor the independent variable is known.
Truncated regression models are often confused with censored regression model
Censored regression model
Censored regression models commonly arise in econometrics in cases where the variable ofinterest is only observable under certain conditions. A common example is labor supply. Data are frequently available on the hours worked by employees, and a labor supply model estimates the relationship between...
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 is available.
Example
One example of truncated samples come from historical military height records. Many armies imposed a minimum height requirement (MHR) on soldiers. This implies that men shorter than the MHR are not included in the sample. This implies that samples drawn from such records are perforce deficient i.e., incomplete, inasmuch as a substantial portion of the underlying population's height distribution is unavailable for analysis. Hence, without proper statistical correction any results obtained from such deficient samples, such as means, correlations, or regression coefficients are wrong (biasBias of an estimator
In statistics, bias of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased.In ordinary English, the term bias is...
ed). In such a case truncated regression has the considerable advantage of immediately providing consistent and unbiased estimates of the coefficients of the independent variables, as well as their standard errors, thereby allowing for further statistical inference, such as the calculation of the t-values of the estimates.