ABSTRACT
Multiple imputation procedure is used in handling of item non-response. The imputation procedure is affected by model misspecification and leads to loss in efficiency and biased results. The inclusion of auxiliary variables in the sampling design helps to avoid sensitivity of inference to model misspecification and improves the precision of estimate of population mean. The main aim of this study was to incorporate auxiliary variables in the Multiple Imputation to improve the accuracy of the values imputed and the efficiency of point estimators. The twostep semi- parametric multiple imputation procedure was considered and modified to incorporate the axiliary variables. In the first step a non-parametric model was used to generate a posterior predictive model that includes both item level missingness and auxiliary information. The size variables in a sample were replicated using a Constrained Bayesian Bootstrap. A Constrained Weighted Finite Population Bayesian Bootstrap was then used to create a population of size variables which was considered to be the value of an auxiliary variables that is closely associated with the survey outcome variable. The imputed size variables were then used in a linear regression model to predict the survey outcome variables for the synthetic population. A parametric model was used to impute the missing data on the survey outcome variables in the second step. A simulation study was conducted using single stage probability-proportionate-to-size without replacement sampling design. The asymptotic properties of the estimator of the population mean were compared to those obtained using the existing two-step semi-parametric multiple imputation procedure. The proposed procedure reduced bias and resulted in gain in efficiency. The 95 % confidence interval coverage rates of the proposed estimator were close to nominal level when the sample size was small.
