Hierarchical Spatially Varying Coefficient Process Model

ABSTRACT

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.

KEYWORDS:

• Hierarchical data
• Markov chain Monte Carlo
• Multivariate simultaneous autoregressive model
• Spatial heterogeneity
• Spatially varying coefficient process

Acknowledgments

This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (2015R1C1A1A02037090). The authors thank the referees, associate editor, and editor for reviewing the manuscript and providing valuable comments.