title: The use of sampling weights in Bayesian hierarchical models for small area estimation.
abstract: Hierarchical modeling has been used extensively for small area estimation. However, design weights that are required to reflect complex surveys are rarely considered in these models. We develop computationally efficient, Bayesian spatial smoothing models that acknowledge the design weights. Computation is carried out using the integrated nested Laplace approximation, which is fast. An extensive simulation study is presented that considers the effects of non-response and non-random selection of individuals, allowing examination of the impact of ignoring the design weights and the benefits of spatial smoothing. The results show that, when compared with standard approaches, mean squared error can be greatly reduced with the proposed methods. Bias reduction occurs through the inclusion of the design weights, with variance reduction being achieved through hierarchical smoothing. We analyze data from the Washington State 2006 Behavioral Risk Factor Surveillance System. The models are easily and quickly fitted within the R environment, using existing packages.
authors.affiliation: Department of Biostatistics, Brown University, USA. Electronic address: cici_bauer@brown.edu.
authors.forename: Cici
authors.initials: C
authors.lastname: Chen
authors.affiliation: Department of Statistics, University of Washington, USA; Department Biostatistics, University of Washington, USA. Electronic address: jonno@uw.edu.
authors.forename: Jon
authors.initials: J
authors.lastname: Wakefield
authors.affiliation: Department of Statistics, University of Auckland, New Zealand.
authors.forename: Thomas
authors.initials: T
authors.lastname: Lumely
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D001499:Bayes Theorem; D003920:Diabetes Mellitus / Q000453:epidemiology; D005260:Female; D015438:Health Behavior; D006801:Humans; D008297:Male; D008875:Middle Aged; D015233:Models, Statistical; D012044:Regression Analysis; D012107:Research Design / Q000706:statistics & numerical data*; D012307:Risk Factors; D012309:Risk-Taking; D012494:Sampling Studies; D015983:Selection Bias; D062206:Spatial Analysis; D014861:Washington / Q000453:epidemiology; D055815:Young Adult
keywords: Bayesian methods; Integrated nested Laplace approximation; Sample surveys; Spatial statistics