Estimation in Multiple Frame Surveys: A Simplified and Unified Review using the Multiplicity Approach

Multiple frame surveys are useful for reducing cost for given precision constraints, improving coverage (under or over) and dealing with elusive or rare populations for which a direct sampling frame may not exist. Unlike model-based coverage bias adjustments traditionally used for single-frame surveys where domains of units subject to coverage bias are not identificable, multiple frame surveys assume identifiability of such domains, and supplementary sampling frames along with multiplicity adjustments are used to deal with the coverage bias. Point and variance estimation for multiple frame surveys are somewhat challenging because of multiplicity of units due to overlapping frames, and possible duplication of units in the sample. A simple single-frame solution can be used if selected units from the supplementary frame are screened out whenever they are listed in the main frame. However, this may not be desirable in practice because a major portion of the cost is already incurred in contacting the selected unit for the screening information. Despite the practical appeal of multiple frame surveys, they have not been commonly used possibly because of non-standard complex nature and a lack of general understanding of estimation as well as lack of consensus about a preferred methodology among researchers. However, there has been a recent resurgence of interest in multiple frame due to the practical necessity of mitigating increased cost in data collection and use of non-area frames such as cell and landline telephones. In this paper, we provide a simplified and unified review of different existing methods which should help in a better understanding in choosing a suitable method in any application, and promoting more use of multiple frames in practice.