Assessing Auxiliary Vectors for Control of Nonresponse Bias in the Calibration Estimator
Carl-Erik Särndal, Sixten Lundström,
This article develops a bias indicator, a computational tool useful for selecting auxiliary variables likely to be particularly effective for reducing nonresponse bias in estimates obtained by calibration.
The weights used in the calibration estimator are computed on information about a specified auxiliary vector. Even the best among the available auxiliary vectors will leave some bias remaining in the estimator. The objective is to reduce this remaining bias as far as possible, through the choice of a “best possible” auxiliary vector.
The theory in the article is inspired by the survey environment in the Nordic countries and in other North European countries, where many reliable administrative registers provide rich sources of auxiliary variables, in particular for surveys on individuals and households. The many potential auxiliary variables allow the statistician to compose a wide range of auxiliary vectors. There is a need to compare and rank these vectors to assess their effectiveness for bias reduction. The indicator examined in the article serves this purpose.
The indicator is computed on the auxiliary vector values known for the sampled units, responding and nonresponding. It has the advantage of being independent of the study variables, of which the survey may have many. A large value of the indicator suggests a low nonresponse bias, independently of the study variable.
The main body of the article explores the relationship existing between the indicator and the amount of bias in the estimator. The concluding sections are devoted to empirical studies. One of these involves a constructed finite population. The potential auxiliary vectors are ranked with the aid of the indicator. A second empirical illustration illustrates how the indicator is used for selecting auxiliary variables in a large survey at Statistics Sweden.
Calibration weighting, nonresponse adjustment, nonresponse bias, auxiliary variables, bias indicator