Modeling Random Effects Using Global–Local Shrinkage Priors in Small Area Estimation

ABSTRACT

Small area estimation is becoming increasingly popular for survey statisticians. One very important program is Small Area Income and Poverty Estimation undertaken by the United States Bureau of the Census, which aims at providing estimates related to income and poverty based on American Community Survey data at the state level and even at lower levels of geography. This article introduces global–local (GL) shrinkage priors for random effects in small area estimation to capture wide area level variation when the number of small areas is very large. These priors employ two levels of parameters, global and local parameters, to express variances of area-specific random effects so that both small and large random effects can be captured properly. We show via simulations and data analysis that use of the GL priors can improve estimation results in most cases. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Bayesian model
• Fay–Herriot model
• Poverty rate
• Spike-and-slab prior

Acknowledgements

The authors thank Drs. G. Datta, A. Mandal, A. Chakraborty, and J. Maples for providing the datasets, and the editor, associate editors, and three anonymous reviewers for insightful comments and suggestions which improved the article significantly.

Additional information

Funding

Ghosh’s research was partially funded by SES-1327359.