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

Mecatti, Fulvia; Singh, Avinash C.

Journal de la société française de statistique, Tome 155 (2014) no. 4, pp. 51-69.

Les enquêtes à bases multiples sont utiles afin de réduire les coûts pour une précision donnée ainsi que pour améliorer la (sous ou sur) couverture et pour le traitement des populations difficiles à joindre ou rares pour lesquelles il n’existe pas une base de sondage directe. Contrairement aux ajustements pour le biais de couverture traditionnellement utilisés pour les enquêtes à bases uniques pour lesquelles les sous-groupes d’unités sujets à des biais de couverture ne sont pas identifiables, les enquêtes à bases multiples font l’hypothèse que les sous-groupes d’unités sont identifiables et utilisent des bases de sondage supplémentaires ainsi que des ajustements pour la multiplicité afin de corriger le biais de sous-couverture. L’estimation ponctuelle et l’estimation de la variance présentent un certain défi dû à la multiplicité des unités provenant de bases chevauchantes et au possible problème de duplicata des unités dans l’échantillon. Une solution basée sur une unique base peut être utilisé pourvu que les unités échantillonnées à partir des bases supplémentaires soient dépistées lorsque présente sur la base principale. Cependant, cela n’est peut-être pas souhaitable en pratique car une partie importante du coût est déjà engagée afin de contacter les unités lors de l’étape de dépistage. Malgré l’attrait pratique des sondages à bases multiples, ils n’ont pas été couramment utilisés probablement en raison de leur nature complexe et non-standard et un manque de compréhension générale de l’estimation ainsi que de l’absence de consensus à propos d’une méthodologie préférée parmi les chercheurs. Cependant, il y a eu un regain d’intérêt récent pour les bases multiples en raison de la nécessité pratique d’atténuer l’augmentation des coûts de collecte des données et de l’utilisation des bases non-aréolaires telles que les téléphones cellulaires et les téléphones fixes . Dans cet article, nous présentons une revue simplifiée et unifiée des différentes méthodes existantes, qui permettront de mieux comprendre le choix d’une méthode appropriée dans n’importe quelle application, et d’encourager la promotion d’une utilisation de méthodes à bases multiples.

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.

Keywords: Coverage bias, Elusive/rare populations, GMHT-reg class, Horvitz-Thompson estimation, Imperfect frames, Zero functions
Mot clés : Bases imparfaites, Biais de couverture, class GMHT-reg, estimation d’Horvitz-Thompson, populations rares/difficiles à joindre

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