Abstract

The development of Multiple Frame (MF) surveys, spanning more than six decades, is systematically reviewed and critically discussed, from their first appearance in the 1960s–1970s literature to their role in today’s fast-evolving landscape of sampling statistics and emerging data needs. Traditional survey methodology assumes a single frame with complete coverage for sample selection. In contrast, an MF survey uses two or more frames, which may have partial coverage and usually overlap, but together adequately cover the study population. MF surveys are especially useful when no single complete frame exists and there is insufficient information or resources to construct one through linkage. Still, MF surveys can be cost-effective even when a full frame is available, which was, in fact, the practical motivation behind their initial introduction in the sampling statistics literature.
Since then, MF surveys have undergone significant evolution in their objectives, application areas, and estimation approaches. The initial cost-saving motivation has expanded to include applications to difficult-to-sample populations (e.g., undocumented immigrants), to handle attrition in longitudinal studies, to agricultural surveys combining satellite and field data, and to MF-based strategies to address long-standing challenges in sample surveys, such as rising costs and declining response rates. A parallel evolution in MF estimation has occurred, mainly due to inherent methodological difficulties in dealing with complex survey designs and notational cumbersomeness. This initially led to several seemingly disconnected estimation approaches, which can now be simplified and unified under the Multiplicity approach and the Generalized Multiplicity-Adjusted Horvitz–Thompson framework.
With the emergence of the unprecedented availability of new digital and BigData sources, a recent surge of interest in combining information from probability and non-probability samples, to address budget constraints, the demand for timely information, and lack of respondent cooperation, calls for a re-assessment of MF practices, leveraging the ease of access to administrative and voluntary Internet data sources and outlining directions for future research.