An Empirical Comparison of Performance of the Unified Approach to Linearization of Variance Estimation after Imputation with Some Other Methods

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 naϊve estimators. After using most of common imputation methods، mean and total (imputation estimators) are still unbiased. However their variances (imputation variances) are underestimated by naϊve variance estimators. Sampling mechanism and response variable values are variation sources which have been hidden in naϊve variance estimators. While missing mechanism and imputation processes are other sources which are created after imputation. The naϊve 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 estimator 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 imputation 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.