Measuring Group Effect with Geographic Heterogeneity Using Complex Survey Data(In-Progress Draft)

Examining and explaining differences in the outcome of interest among subpopulations is a topic of interest in many research fields such as economics, social science, political science, and public health. The overall observed group difference in the outcome can be decomposed into two components: the difference that can be explained by the different distributions of other covariates associated with the outcome among individuals in the considered subpopulations and the unexplained difference (i.e., group effect). Besides the individual-level covariates, the overall group difference can also be explained by the different spatial distribution of the considered subpopulations. In this paper, we propose an innovative geo-additive model-based Peter-Belson (GGAM-PB) method to consider both individual-level and heterogeneous spatial effects when examining group effect using data from nationally representative surveys. We utilize bivariate splines over triangulations to capture the nonparametric spatial effect over the irregular two-dimensional target domain of the population and to account for the correlation among geographic areas. We prove the asymptotic consistency of the proposed GGAM-PB estimates of the nation-level and state-level group effect on the considered outcome and provide the corresponding Taylor-Linearization variance estimation under complex survey sample designs. Our simulation studies show that the proposed GGAM-PB method outperforms the traditional GLM-PB method, which uses fixed effects of residence locations to capture spatial effects. We apply the GGAM-PB method to estimate the group effect on the proportion of women receiving cancer screening among Non-Hispanic White and Non-Hispanic Black females in the Contiguous US.