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https://hdl.handle.net/2142/68821
Description
Title
Corrections for Sample Selection Bias
Author(s)
Dunbar, Stephen Barnes
Issue Date
1982
Department of Study
Education
Discipline
Education
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Education, Tests and Measurements
Abstract
Statistical adjustments of correlation coefficients and regression parameters developed to correct for the effects of sample selection bias are examined for robustness to violations of assumptions in this Monte Carlo study. Corrections derived by Pearson (1903) for cases of explicit and incidental selection are found to be sensitive to variations in (1) the linearity of the regression of a criterion variable on the explicit selection variable, (2) the homoscedasticity of that regression, (3) the way in which sample selection takes place, and (4) the severity of selection. Two major findings are noted. First, in spite of the fact that systematic directional biases in the adjusted estimates of population parameters were detected, the dominant tendency is for Pearson's corrections to yield conservative estimates of those parameters. This is argued in the case of explicit selection on the basis of the fact that the available explicit selection variable is usually an imperfectly correlated proxy for a hypothetical true selection variable. Regardless of violated assumptions, such imperfect knowledge of the true selection variable will yield conservative estimates according to simulation results. It is argued in the case of incidental selection on the basis of the likely characteristics of the relevant bivariate regressions when linearity and homoscedasticity assumptions are violated at the same time. Second, the stability of Pearson's corrections for both explicit and incidental selection is threatened by violated assumptions and by severe selection. In extreme cases, corrected estimates are sufficiently unstable to jeopardize any advantage gained by using a less biased estimate of a population value. An alternative procedure for the case of incidental selection, developed by Heckman (1979) is also described and evaluated with respect to selected assumptions by Monte Carlo methods. Heckman's approach is found to be suitable in many situations for which it was designed, especially since it requires no direct knowledge of the true selection variable. However, under conditions of severe selection, Heckman's approach yields estimates with standard errors so high that they have little utility for inferential purposes. The application of reduced-variance regression techniques to this problem is considered.
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