Composite Estimates from Incomplete and Complete Frames for Minimum-Mse Estimation in a Rare Population

Random digit dialing (RDD) can be costly for a rare population, but inexpensive convenience samples are unrepresentative by themselves. The authors combine biased estimates from an incomplete frame (a listed sample) with RDD estimates in a way that improves the accuracy (Mean Squared Error, MSE) of the RDD estimates compared to what would have been achieved without the incomplete frame data. Elliott and Haviland (2007) discuss this estimator when the bias of the incomplete frame estimator is known and discuss uncertainty in estimating bias; we describe an application that estimates incomplete frame bias relative to the RDD estimate for each parameter of interest, and conditions on that estimate. The authors discuss the extent to which this approach improves MSE relative to RDD alone and relative to a common alternative-stratified estimation based on whether a case appears in the incomplete frame. They surveyed 1,002 RDD and 1,023 listed households and examined the impact of incorporating listed estimates on MSE. Conditional on the bias estimate, MSE improved substantially for many outcomes because the estimated bias of listed sample estimates relative to RDD was small for most outcomes. For thirty-eight of forty-one estimates, including the listed sample (doubling the nominal sample size) produced MSEs equivalent to RDD sample sizes 1.22-1.85 times as large as the actual RDD sample size. Because the cost per listed complete was 20 percent of the cost per RDD complete, cost per effective sample size decreased relative to RDD alone for all but three estimates.