Nonresponse adjustment using auxiliary variables subject themselves to missing data

Nonresponse is a significant matter that cannot be denied in a sample survey. Declining response rates lead to increasing nonresponse bias which affects the estimated bias. Nonresponse adjustment can be used to deal with unit nonresponse by using nonresponse weight. Two possible models in which missingness in an ancillary database may be correlated with missingness in a survey are considered in this study for estimating the population mean when nonresponse occurs on both the study and auxiliary variables. Two auxiliary variables where one auxiliary variable is fully observed and some part of the other is missing are considered in the possible models. Simulation studies are carried on to see how the nonresponse adjustment using auxiliary variables that subject themselves to nonresponse work under the possible models. The simulation results show that the weighted mean performed the best in removing the bias and gave the minimum mean square error compared to the unweighted mean which was affected by nonresponse.