  The need for rigorous and timely health and demographic summaries has
provided the impetus for an explosion in geographic studies, with a common
approach being the production of pixel-level maps, particularly in low and
middle income countries. In this context, household surveys are a major source
of data, usually with a two-stage cluster design with stratification by region
and urbanicity. Accurate estimates are of crucial interest for precision public
health policy interventions, but many current studies take a cavalier approach
to acknowledging the sampling design, while presenting results at a fine
geographic scale. In this paper we investigate the extent to which accounting
for sample design can affect predictions at the aggregate level, which is
usually the target of inference. We describe a simulation study in which
realistic sampling frames are created for Kenya, based on population and
demographic information, with a survey design that mimics a Demographic Health
Survey (DHS). We compare the predictive performance of various commonly-used
models. We also describe a cluster level model with a discrete spatial
smoothing prior that has not been previously used, but provides reliable
inference. We find that including stratification and cluster level random
effects can improve predictive performance. Spatially smoothed direct
(weighted) estimates were robust to priors and survey design. Continuous
spatial models performed well in the presence of fine scale variation; however,
these models require the most "hand holding". Subsequently, we examine how the
models perform on real data; specifically we model the prevalence of secondary
education for women aged 20-29 using data from the 2014 Kenya DHS.
