Optimal Allocation Under Anticipated Nonresponse

Abstract

Abstract Survey response rates have declined dramatically in recent years, increasing the costs of data collection. Despite this, there is little existing research on how to most efficiently allocate samples in a manner that incorporates response rate information. Existing mathematical theory on allocation for single-stage stratified sample designs generally assumes complete response. A common practice is to allocate sample under complete response, then to inflate the sample sizes by the inverse of the anticipated response rates. However, we show that this method can fail to improve upon an unadjusted allocation, due to ignoring the associated increase in the cost per interview. We provide mathematical theory on how to allocate single-stage designs in a manner that incorporates the effects of nonresponse on cost efficiency. We derive the optimal allocation for the poststratified estimator under nonresponse, which minimizes either the unconditional variance of our estimator or the expected costs, holding the other constant, and taking into account uncertainty in the number of respondents. We assume a cost model that incorporates effects of nonresponse. We provide theoretical comparisons between our allocation and common alternatives, which illustrate how response rates, population characteristics, and cost structure can affect the methods’ relative efficiency. In an application to a self-administered survey of US military personnel, the proposed allocation increases the effective sample size by 25 percent, compared with common practice.