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Efficient Estimation of Regression Coefficients With Missing Data
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Dissertation
Efficient Estimation of Regression Coefficients With Missing Data
1991
Overview
Several methods have been proposed for the treatment of missing variables in the context of linear regression estimation. This thesis surveys these methods and finds most of them inadequate due to their complexity and inadequate benefits. The most powerful methods (Minimum Distance and Maximum Likelihood) are potentially useful to the applied researcher.If the true model is known, ML is more efficient than all other methods, but in practice it has a greater computational cost and involves a greater risk of specification error, (new) denotes results which have not previously been published.1. OLSC (regression with the complete data only) is the standard, with low computational cost, no specification of auxilliary models, and it works just as easily for several missing variables.2. OLSI (missing variables replaced by imputed values) can potentially be more efficient than OLSC, but it has several complications which make it not work the effort:a. Difficulty in computing the correct coefficient standard errors.b. Naive standard errors are too large (new) or too small.c. Multiple imputation, while promising simpler computation of standard errors, is inconsistent (new).d. Possible specification error in the auxilliary imputation model.e. Often less efficient, or the efficiency gain is negligible.f. GLS is not worth the additional complications.3. PD (pairwise deletion estimation of moment matrices) is roughly the same as OLSI--it is potentially (but not necessarily) better, and it has impractical complications. The formula for its correct coefficient standard errors, previously derived asymptotically, is shown here to be exact for small samples (new).4. MD (minimum distance) offers efficiency gains with some robustness to heteroscedasticity, and is easier to compute than GLSI and ML (new).5. ML entails simultaneous estimation of the regression and imputation models for full efficiency. A specification test is derived (new). Examples with artifical data show a standard error reduction from OLSC to ML of from 2% to 43% for complete sample percentages of from 90% to 10%. Examples with real data show a larger standard error reduction--from 18% to 33% for complete percentages of from 70% to 50%.
Publisher
ProQuest Dissertations & Theses
Subject
ISBN
9798641912028
