Calibrating on principal components in the presence of multiple auxiliary variables for nonresponse adjustment

Abstract

Nonresponse is a major impediment to valid inference in sample surveys. In the nonresponse scenario, the driver of successful estimation is the efficient use of available auxiliary information. As electronic devices provide considerable data storage capacities, at the estimation stage it is natural for survey statisticians to face large datasets of auxiliary variables. It is unwise to use all available data as doing so may lead to poor estimators, especially if some variables are strongly correlated. Furthermore, selecting a subset of available auxiliary variables may not be the best alternative given the issues related to selection criteria. In this paper, we propose reducing the dimensions of the original set of auxiliary variables by using principal components. The use of principal components in place of the original auxiliary variables is evaluated via two calibration approaches, linear calibration using no explicit response model and propensity calibration of a known response model. For the latter, we propose selecting components based on their canonical correlation with the model variables. The results of two simulation studies suggest that using principal components is appropriate, as it offers the great advantage of reducing the computational burden.