Weighting

Why Weighting for Nonresponse is Necessary

Essentially all surveys suffer from nonresponse. This occurs either when elements (persons, households, companies) in the selected sample do not provide the requested information or when the provided information is useless. The situation in which all requested information on a sampled element is missing is called unit nonresponse.

As a result of unit nonresponse, estimates of population characteristics may be biased. This bias occurs if (a) some groups in the population are over- or underrepresented in the sample because of their differential response/nonresponse rates and (b) these groups are different with respect to the variables being measured by the survey. As a consequence, wrong conclusions are drawn from the survey results.

It is vital to try to reduce the amount of nonresponse in the field work as much as possible. Nevertheless, in spite of all these efforts, a substantial amount of nonresponse usually remains. To avoid biased estimates, some kind of correction procedure must be carried out. One of the most important correction techniques for nonresponse is weighting. It means that every observed object in the survey is assigned a weight, and estimates of population characteristics are obtained by processing weighted observations instead of the (unweighted) observations themselves.

Basics of Weighting to Correct for Nonresponse

Suppose that the objective of a survey is to estimate the population mean, , of a variable Y. Suppose further that a simple random sample of size n is selected with equal probabilities and without replacement from a population of size N. The sample can be represented by a series of N indicators t1, t2,…, tn, where the k-th indicator tk assumes the value 1 if element k is selected in the sample, and otherwise it assumes the value 0. In case of complete response, the sample mean,

is an unbiased estimator of the population mean. In case of nonresponse, this estimator may be biased. Assuming that every element, k, in the population has an unknown probability, pk, of response when invited to participate in the survey, the bias of the mean R of the available observations is equal to

where RpY is the correlation between the values of the survey variable and the response probabilities, Sy is the standard deviation of the Y, and Sp is the standard deviation of the response probabilities.

Weighting is a frequently used approach to reduce this nonresponse bias. Each observed element, k, is assigned a weight, Wk-Thus, the response mean, yR, is replaced by a new estimator,

Correction weights are the result of the application of some weighting technique. The characteristics of the correction weights should be such that the weighted estimator has better properties than the unweighted response mean.

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