Doing More with Less: Recent Advances in Small Area Estimation

Small area estimation is necessarily model-based. Much of the literature is based on normal mixed effects models. However, normality is often justified only after a suitable transformation. The present talk will focus on variance stabilizing transformations which achieve the dual objective of getting closer to normality as well as known sample variances. 

Area-level models for small area estimation typically rely on areal random effects to shrink design-based direct estimates towards a model-based predictor. Incorporating the spatial dependence of the random effects into these models can further improve the estimates when there are not enough covariates to fully account for spatial dependence of the areal means. A number of recent works have investigated models that include random effects for only a subset of areas, in order to improve the precision of estimates. However, such models do not readily handle spatial dependence. In this paper, we introduce a model that accounts for spatial dependence in both the random effects as well as the latent process that selects the effects. We show how this model can significantly improve predictive accuracy via an empirical simulation study based on data from the American Community Survey, and illustrate its properties via an application to estimate county-level median rent burden. 

Small area estimation often relies on model-based approaches to stabilize estimates of subgroups with small sample sizes. The model-based approaches can be hierarchical models or introduce prior distributions in a Bayesian paradigm to borrow information across subgroups. Rich literature work has made important contributions to SAE methods, especially with applications to complex sample surveys. However, due to recent data collection challenges, survey data alone cannot meet analytic demands. Combining multiple data sources has become a research priority. SAE methods need to account for data collection tailored to each data source and integrate all relevant information to improve inference. We consider a few scenarios, where multiple data sources collect different measure components and participant groups, and develop a Bayesian SAE framework. We will compare with alternatives and use simulation and application studies to illustrate the improvement.