Journal of Official Statistics, Vol.10, No.4, 1994. pp. 381394

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Variance Estimation for the Regression Imputed Horvitz-Thompson Estimator

Imputation has found widespread use in surveys with missing data but can lead to incorrect inferences, e.g., invalid confidence intervals, unless care is exercised. This paper develops a procedure for valid variance estimation in surveys where regression imputation is used for the missing values. The imputed values are derived from the fit of a multiple regression model, with a multivariate auxiliary variable as predictor. Features of this new procedure are: (i) it is based on single value imputation (as opposed to the computationally more demanding multiple imputation); (ii) the variance estimation is valid for an arbitrary probability sampling design and for an arbitrary response mechanism of the unconfounded type; and (iii) the calculation of the variance estimate can be carried out with the standard formulas programmed in the existing computer packages for survey data.

Nonresponse; imputation; auxiliary information; unconfounded response mechanism; model assisted inference.

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