Socio-Demographic Network Varying Coefficient Fay-Herriot Model for Spatial Data

Music City Center 

The popular Fay-Herriot small area estimation model correlates area-level direct estimates with a set of area-level auxiliary covariates. Modifications, such as spatial Fay-Herriot models, allow for spatial correlation in these covariates, which are captured by introducing a spatial random effect term or by imposing a spatial correlation structure on the regression errors. The spatial variation assumed in these cases is based on a traditional nearest-neighbor approach. However, such methods may not fully capture the complexity of spatial dependencies. We propose an extension of the spatial Fay-Herriot model by introducing a varying coefficient structure, allowing the regression coefficients to vary systematically and smoothly for some of the area-level covariates. Instead of relying on geographical proximity to define network edges, we leverage node covariates in a latent socio-demographic space to infer the dependency network among auxiliary covariates. Unlike traditional approaches that impose predefined neighborhood structures, our model learns neighborhoods directly from data, and averages over all possible neighborhood structures. We showcase the flexibility and advantages of the proposed approach by presenting simulation results and applications to county-level American Community Survey data on median household income in the U.S. states of North Carolina and South Carolina.