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Variance Estimators For Variables That Have Both Observed And Imputed Values

Sandra A. West, Diem-Tran Kratzke, and Kenneth W. Robertson


In this paper the results of theoretical and empirical investigations of different variance estimators, in the presence of imputed and observed values, are presented. Initially, it is assumed that all the missing data are imputed by the same method. The imputation methods considered include mean, hot deck, ratio, regression plus residual, and multiple imputation. Variance estimators considered include the standard, jackknife, and model based estimators, as well as an estimator developed in the paper. The data used for the empirical investigations are employment data from the Bureau of Labor Statistics census of establishments. Nonresponse patterns are simulated using the pattern observed on the universe data base. The first step is to see the effect on the standard variance estimator when the imputed data, which are obtained using a specific method, are treated in the same manner as the observed data. Alternative variance estimators are compared for each imputation method.