  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.
