Efficient estimation for surveys with nonresponse follow-up using dual-frame calibration
Singh, A. C., Iannacchione, V. G., & Dever, J. A. (2003, August). Efficient estimation for surveys with nonresponse follow-up using dual-frame calibration. Presented at American Statistical Association Meeting, Section on Survey Reserach Methods, San Francisco, CA.
In surveys where response rates are low, a follow-up survey of nonrespondents may be used to augment the respondents from the main survey. Using the theory of double sampling for stratification, estimatesfrom this combined sample provide a less-biased alternative to nonresponse-adjusted estimates from the main survey. This is due to the bias-correction limitations of the main survey nonresponse model inthe presence of high nonresponse. However, when cost considerations require that the follow-up sample size be small, the reduction in bias of estimates obtained from the combined sample may be negatedby the increase in sampling variance due to variability in selection probabilities between the main and the follow-up samples. In this situation, a possible solution might be to trim the extremeweights to reduce the mean square error (MSE) associated with key survey estimates. However, it is not clear how to define a model to measure andcontrol bias introduced by trimming. We present an alternative in which we make more efficient use of information in the data to construct estimates by minimizing MSE under joint designand model-based randomization. Analogous to the small area estimation setting, our goal is to obtain a composite estimator that strikes a balance between variance of the unstable estimator based on the main and follow-up samples and bias of the stable estimator based on the main sample only. However, this situation it is a large area and not a small areaproblem, and so the dual frame estimation framework can be used for its formulation. Moreover, composite weights can be obtained from weight calibration with built-in controls for extreme weights whilepreserving the known population control totals as well as zero control totals for difference estimates from the two samples for a key set of study variables. The proposed method is illustrated for a survey ofGulf War veterans with a nonresponse follow-up survey.