Variance estimation by multivariate imputation methods in complex survey designs

In this paper, we consider variance estimation of the sample mean when the missing data have been imputed with multivariate imputation methods. Modern multivariate imputation methods to missing data are complicated and computationally expensive. These multivariate imputation methods do not require the normality assumption to impute the missing values. Under this assumption free condition, we compare the performance of variance estimation of six modern multivariate imputation methods including copula imputation, random forest imputation, principal component analysis imputation, and k-nearest neighbors imputation methods in complex sampling designs such as stratified sampling, cluster sampling and resampling approach to variance estimation by jackknife and bootstrap methods in stratified sampling. We conducted simulation studies using National Health and Nutrition Survey data considering 5% and 15% missing completely at random (MCAR) rates. Based on our 500 times resampling simulation study of the mean squares errors of the sample mean in complex survey designs, the percent relative efficiency (RE(%)) of the random forest (RF) imputation method appears to outperform other imputation methods overall when the data has high skewness at the 5% missing rate and when the data has high excessive kurtosis at the 15% missing rate whereas the principal component analysis (PCA) imputation method appears to outperform other imputation methods when the data has high skewness at the 5% and 15% missing rates. Especially, the RE(%) of the multivariate imputation methods appears to be efficient in the cluster sampling design when the data has high skewness or excessive kurtosis at the 15% missing rate.