Nonresponse Error

Simple Model

Although the nonresponse rate is important information used to evaluate the nonresponse error, that rate is only one component of the nonresponse error. The biasing effect of nonresponse error is also related to the difference between respondents and nonrespon-dents. A simple model for a sample mean can be used to illustrate this point.

Given a sample with n units, r of these n units participated in the survey and nr units did not: n = r + nr. Y is a metric characteristic, and r = mean estimated for the r respondents, n = mean estimated for all n sample units, and nr = mean estimated for the nr nonrespondents. The estimated mean for all the units in the sample (n) equals to a weighted sum of the estimated mean for the respondents (r) and the estimated mean for the nonrespondents (nr). The latter is weighted by the nonresponse rate (nr/n), the former by the response rate (r/n). This results in the following formal specification:

This expression makes it clear that the estimated mean for the respondents is equal to the estimated mean for all units in the sample plus a factor that expresses the biasing effect of the nonresponse error. When there is no nonresponse, then (nr = o→ r = n):r =n. In this situation, the estimated mean for the r respondents is equal to the mean estimated for all n sample units. This signifies that there is no non-response error. This is also the case when the estimated mean of the respondents and the nonrespondents are equal:r =nr. In this case, the decision to participate is uncorrelated with Y, and as far as Y is concerned, there is no difference between the group of respondents and the group of nonrespondents.

Although this nonresponse model for a sample mean is simple, it shows that the reduction of nonresponse error operationally is not straightforward. For example, with an incentive one can increase the response rate, but it is possible that some persons are more susceptible to the incentive than others. When the susceptibility to incentives is related to a substantive relevant characteristic, the use of the incentive will increase the difference between respondents and nonrespondents with respect to that characteristic, thus increasing nonresponse error. In this situation, a higher response rate due to the incentive does not result in a smaller nonresponse error; instead, just the opposite occurs.

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