Survey Methodology
Bayesian inference for multinomial data from small areas incorporating uncertainty about order restriction
by Xinyu Chen and Balgobin NandramNote 1
- Release date: June 21, 2022
Abstract
When the sample size of an area is small, borrowing information from neighbors is a small area estimation technique to provide more reliable estimates. One of the famous models in small area estimation is a multinomial-Dirichlet hierarchical model for multinomial counts. Due to natural characteristics of the data, making unimodal order restriction assumption to parameter spaces is relevant. In our application, body mass index is more likely at an overweight level, which means the unimodal order restriction may be reasonable. The same unimodal order restriction for all areas may be too strong to be true for some cases. To increase flexibility, we add uncertainty to the unimodal order restriction. Each area will have similar unimodal patterns, but not the same. Since the order restriction with uncertainty increases the inference difficulty, we make comparison with the posterior summaries and approximated log-pseudo marginal likelihood.
Key Words: Bayesian computation; Contingency tables; Log-pseudo marginal likelihood; Monte Carlo method; Small areas; Unimodal order restrictions.
Table of contents
- Section 1. Introduction
- Section 2. Hierarchical multinomial Dirichlet
- Section 3. Hierarchical multinomial Dirichlet model incorporated uncertainty about order restrictions
- Section 4. Application to body mass index data
- Section 5. Simulated BMI
- Section 6. Concluding remarks
- Appendix
- References
How to cite
Chen, X., and Nandram, B. (2022). Bayesian inference for multinomial data from small areas incorporating uncertainty about order restriction. Survey Methodology, Statistics Canada, Catalogue No. 12-001-X, Vol. 48, No. 1. Paper available at http://www.statcan.gc.ca/pub/12-001-x/2022001/article/00004-eng.htm.
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