Truncated regression model
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Truncated regression models arise in econometrics in cases where whole observations are missing, so that neither the dependent nor the independent variable is known.
Truncated regression models are often confused with censored regression models where only the value of the independent variable is unknown while the value for dependent variables is available.
One example of truncated samples come from historical military height records. Military imposed a minimum height requirement (MHR) on soldies. 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. 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.
[edit] References
- Brian A’Hearn, 2004. A Restricted Maximum Likelihood Estimator for Truncated Height Samples. Economics and Human Biology 2, 1, 5-20.
- John Komlos, 2004. How to (and How Not to) Analyze Deficient Height Samples: an Introduction. Historical Methods, 37, No. 4, Fall, 160-173.
The definition of 'censored regression' is wrongly put when it was used to compare with 'truncated regression models'(appears in the link). There, Censored regression was wringly defined as a model where the values of independent variables are unknown and that of the dependent variable is available. Rather,the definition should be the reverse.
