The need for rigorous and timely health and demographic summaries has led to an explosion in geographic studies, particularly in low and middle income countries. While household surveys are a major source of data in this context, they present challenges for statistical modeling. These challenges include biases due to oversampling certain population segments, nonlinear interactions between covariates, and multiple scales of prediction. However, many common statistical methods have never been tested rigorously in these settings.

In this context, we propose several models and model refinements, compare them under various simulation studies, and apply them to real data. First, we evaluate the predictions of a number of spatial models by simulating the full population of Kenya and datasets mimicking a Kenya Demographic Health Survey (DHS). These simulations are based on census population and demographic information. We describe a cluster level model with a discrete spatial smoothing prior that has not been previously used, but performs well. We find that including stratification and cluster level effects can improve predictions. In another simulation study, we formulate a Bayesian multi-resolution spatial model based on the popular `LatticeKrig' method intended for handling large datasets at multiple spatial scales, which we generalize to be able to handle non-Gaussian data. Lastly, we propose a new model for handling nonlinear interactions between several variables using simplex splines.