Hierarchical spatially varying coefficient process models with application to housing market analysis

Abstract

We propose a methodology for extending the spatially varying coefficient process, which is a famous non-stationary approach for explaining the spatial heterogeneity by allowing coefficients to vary across the space, to accommodate geographically hierarchical data. We consider two-level hierarchical structures and assume that the coefficients of low-level units and high-level units follow the multivariate Gaussian process and multivariate simultaneous autoregressive model, respectively. We applied the proposed method to house transaction data sold in 2014 in a part of the city of Los Angeles. To compare the performance of the proposed method with the classic spatially varying coefficients process and hierarchical simultaneous autoregressive model, Markov Chain Monte Carlo simulations are conducted. The comparison results show that our proposed model predicts the housing selling prices and fits the data more effectively than the competitive models.