Survey Methodology
Approximate hierarchical Bayes small area estimation using Natural Exponential Family with Quadratic Variance Function and poststratification

by Soumojit Das and Partha LahiriNote 1

  • Release date: December 23, 2025
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Abstract

We propose an approximate hierarchical Bayes approach that uses the Natural Exponential Family with Quadratic Variance Function (NEF-QVF) in combining information from multiple sources to improve traditional survey estimates of finite population means for small areas. Unlike other Bayesian approaches in finite population sampling, we do not assume a model for all units of the finite population and do not require linking sampled units to the finite population frame. We assume a model only for the finite population units in which the outcome variable is observed; because, for these units, the assumed model can be checked using existing statistical tools. We do not posit an elaborate model on the true means for unobserved units. Instead, we assume that population means of cells with the same combination of factor levels are identical across small areas, and that the population mean for a cell is identical to the mean of the observed units in that cell. We apply our proposed methodology to a real-life survey, linking information from multiple disparate data sources. We also provide practical ways of model selection that can be applied to a wider class of models under similar setting but for a diverse range of scientific problems.

Key Words:    Administrative data; Finite population sampling; Informative sampling; Multi-level modeling; Multiple surveys; Nonprobability surveys; Synthetic estimation.

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How to cite

Das, S. and Lahiri, P. (2025). Approximate hierarchical Bayes small area estimation using Natural Exponential Family with Quadratic Variance Function and poststratification. Survey Methodology, 51(2), 399-423. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2025002/article/00011-eng.pdf.

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ISSN : 1492-0921

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Survey Methodology publishes articles dealing with various aspects of statistical development relevant to a statistical agency, such as design issues in the context of practical constraints, use of different data sources and collection techniques, total survey error, survey evaluation, research in Survey Methodology, time series analysis, seasonal adjustment, demographic studies, data integration, estimation and data analysis methods, and general survey systems development. The emphasis is placed on the development and evaluation of specific methodologies as applied to data collection or the data themselves. All papers will be refereed. However, the authors retain full responsibility for the contents of their papers and opinions expressed are not necessarily those of the Editorial Board or of Statistics Canada.

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© His Majesty the King in Right of Canada, as represented by the Minister of Industry, 2025

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Catalogue No. 12-001-X

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