Survey Methodology
Bayesian predictive inference of small area proportions under selection bias

by Seongmi Choi, Balgobin Nandram and Dalho KimNote 1

  • Release date: June 24, 2021
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Abstract

In a previous paper, we developed a model to make inference about small area proportions under selection bias in which the binary responses and the selection probabilities are correlated. This is the homogeneous nonignorable selection model; nonignorable selection means that the selection probabilities and the binary responses are correlated. The homogeneous nonignorable selection model was shown to perform better than a baseline ignorable selection model. However, one limitation of the homogeneous nonignorable selection model is that the distributions of the selection probabilities are assumed to be identical across areas. Therefore, we introduce a more general model, the heterogeneous nonignorable selection model, in which the selection probabilities are not identically distributed over areas. We used Markov chain Monte Carlo methods to fit the three models. We illustrate our methodology and compare our models using an example on severe activity limitation of the U.S. National Health Interview Survey. We also perform a simulation study to demonstrate that our heterogeneous nonignorable selection model is needed when there is moderate to strong selection bias.

Key Words:   Biserial correlation; Metropolis-Hastings algorithm; Nonignorable selection model; Official statistics; Selection probabilities.

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How to cite

Choi, S., Nandram, B. and Kim, D. (2021). Bayesian predictive inference of small area proportions under selection bias. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 47, No. 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2021001/article/00001-eng.htm.

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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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Published by authority of the Minister responsible for Statistics Canada.

© Her Majesty the Queen in Right of Canada as represented by the Minister of Industry, 2021

Use of this publication is governed by the Statistics Canada Open Licence Agreement.

Catalogue No. 12-001-X

Frequency: Semi-annual

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Table of contents

Abstract - Article main page
Section 1. Introduction
Section 2. Review
Section 3. Heterogeneous nonignorable selection model
Section 4. Numerical studies
Section 5. Concluding remarks
Acknowledgements
References

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