Hierarchical Spatially Varying Coefficient Process Model

The spatially varying coefficient process model is a nonstationary approach to explaining spatial heterogen-eity by allowing coefficients to vary across space. In this article, we develop a methodology for generalizing this model to accommodate geographically hierarchical data. This article considers two-level hierarchical structures and allow for the coefficients of both low-level and high-level units to vary over space. We assume that the spatially varying low-level coefficients follow the multivariate Gaussian process, and the spatially varying high-level coefficients follow the multivariate simultaneous autoregressive model that we develop by extending the standard simultaneous autoregressive model to incorporate multivariate data. We apply the proposed model to transaction data of houses sold in 2014 in a part of the city of Los Angeles. The results show that the proposed model predicts housing prices and fits the data effectively.