Studies have found that the level of association between an area-level covariate and an outcome can vary depending on the spatial scale (SS) of a particular covariate. However, covariates used in regression models are customarily modeled at the same spatial unit. In this dissertation, we developed four SS model selection algorithms that select the best spatial scale for each area-level covariate. The SS forward stepwise, SS incremental forward stagewise, SS least angle regression (LARS), and SS lasso algorithms allow for the selection of different area-level covariates at different spatial scales, while constraining each covariate to enter at most one spatial scale. We applied our methods to two real applications with area-level covariates available at multiple scales to model variation in the following outcomes: 1) nitrate concentrations in private wells in Iowa and 2) body mass index z-scores of pediatric patients of the Virginia Commonwealth University Medical Center. In both applications, our SS algorithms selected covariates at different spatial scales, producing a better goodness of fit in comparison to traditional models, where all area-level covariates were modeled at the same scale. We evaluated our methods using simulation studies to examine the performance of the SS algorithms and found that the SS algorithms generally outperformed the conventional modeling approaches. These findings underscore the importance of considering spatial scale when performing model selection.
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