A common problem in applied regression analysis is that covariate values may be missing for some observations but imputed values may be available. This situation generates a trade-off between bias and precision: the complete cases are often disarmingly few, but replacing the missing observations with the imputed values to gain precision may lead to bias. In this paper we formalize this trade-off by showing that one can augment the regression model with a set of auxiliary variables so as to obtain, under weak assumptions about the imputations, the same unbiased estimator of the parameters of interest as complete-case analysis. Given this augmented model, the bias-precision trade-off may then be tackled by either model reduction procedures or model averaging methods. We illustrate our approach by considering the problem of estimating the relation between income and the body mass index (BMI) using survey data affected by item non-response, where the missing values on the main covariates are filled in by imputations.
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Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number
150.
Length: 13 pages Date of creation: 08 Oct 2009 Date of revision:
08 Oct 2009 Handle: RePEc:rtv:ceisrp:150
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Find related papers by JEL classification: C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Other
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