Abstract:
Imputation is one of the most common methods to reduce item
non-response effects. Imputation results in a complete data set, and then it
is possible to use nalve estimators. After using most of common imputation
methods, mean and total (imputation estimators) are still unbiased. However
their variances (imputation variances) are underestimated by naive variance
estimators. Sampling mechanism and response variable values are variation
sources which have been hidden in naive variance estimators. While missing
mechanism and imputation processes are other sources which are created af-
ter imputation. The naive estimator does not account for these new variation
sources. In this paper, a recent method of unified approach to linearization
imputation variance estimation is explained. In this method, imputation es-
timator is linearized with respect to nuisance parameters estimators. Then
linear estimator is asymptotically equal to imputation estimator. Variance
estimators are also asymptotically equal. The unified approach can cover all
deterministic and stochastic imputation methods, except nearest neighbors
method. By a simulation study, imputation variance estimators of multiple
imputation, model-assisted, bootstrap and unified approach are compared
when regression imputation has been implemented. Performance of the im-
putation variance estimators are compared with respect to relative efficiency
and coverage probability. Findings of the study show that unified approach
and model-assisted are close in values of efficiencies and give more stable
results through either increasing sample size or non-response rate.