Hierarchical Bayes Modeling of Survey-Weighted Small Area Proportions

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Benmei Liu, Partha Lahiri and Graham Kalton ^{Note 1}

Abstract

The paper reports the results of a Monte Carlo simulation study that was conducted to compare the effectiveness of four different hierarchical Bayes small area models for producing state estimates of proportions based on data from stratified simple random samples from a fixed finite population. Two of the models adopted the commonly made assumptions that the survey weighted proportion for each sampled small area has a normal distribution and that the sampling variance of this proportion is known. One of these models used a linear linking model and the other used a logistic linking model. The other two models both employed logistic linking models and assumed that the sampling variance was unknown. One of these models assumed a normal distribution for the sampling model while the other assumed a beta distribution.  The study found that for all four models the credible interval design-based coverage of the finite population state proportions deviated markedly from the 95 percent nominal level used in constructing the intervals.

Key Words

Weighted proportions; Hierarchical Bayes modeling; Beta distribution; credible interval.

Table of content

• 1. Introduction
• 2. Notation
• 3. Models Studied
• 4. Simulation Study
• 5. Simulation Results
• 6. Discussion
• Acknowledgements
• Appendix
• References

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Notes

1. Benmei Liu, Division of Cancer Control and Population Sciences, National Cancer Institute, 9609 Medical Center Drive Room 4E524, Bethesda, Maryland 20892; E-mail: liub2@mail.nih.gov; Partha Lahiri, JPSM, University of Maryland, 1218 Lefrak Hall, College Park, Maryland 20742; Graham Kalton, Westat, 1600 Research Boulevard, Rockville, Maryland 20850. The majority of this research took place while the first author was a graduate student in the Joint Program in Survey Methodology at the University of Maryland.