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We propose a Bayesian approach to estimate finite population means for smallareas. The proposed methodology improves on the traditional sample surveymethods because, unlike the traditional methods, our proposed method borrowsstrength from multiple data sources. Our approach is fundamentally differentfrom the existing small area Bayesian approach to the finite populationsampling, which typically assumes a hierarchical model for all units of thefinite population. We assume such model only for the units of the finitepopulation in which the outcome variable is observed; because for these units,the assumed model can be checked using existing statistical tools. Modelingunobserved units of the finite population is challenging because the assumedmodel cannot be checked in the absence of data on the outcome variable. To makereasonable modeling assumptions, we propose to form several cells for eachsmall area using factors that potentially influence the outcome variable ofinterest. This strategy is expected to bring some degree of homogeneity withina given cell and also among cells from different small areas that areconstructed with the same factor level combination. Instead of modeling trueprobabilities for unobserved individual units, we assume that population meansof cells with the same combination of factor levels are identical across smallareas and the population mean of true probabilities for a cell is identical tothe mean of true values for the observed units in that cell. We apply ourproposed methodology to a real-life COVID-19 survey, linking information frommultiple disparate data sources to estimate vaccine-hesitancy rates(proportions) for 50 US states and Washington, D.C. (small areas). We alsoprovide practical ways of model selection that can be applied to a wider classof models under similar setting but for a diverse range of scientific problems.

Hierarchical Bayes estimation of small area means using statistical linkage of disparate data sources