Spatially selected and dependent random effects for small area estimation with application to rent burden

Abstract 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 the 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.