Predicting Spatial Patterns of House Prices Using LPR and Bayesian Smoothing

This article is motivated by the limited ability of standard hedonic price equations to deal with spatial variation in house prices. Spatial patterns of house prices can be viewed as the sum of many causal factors: Access to the central business district is associated with a house price gradient; access to decentralized employment subcenters causes more localized changes in house prices; in addition, neighborhood amenities (and disamenities) can cause house prices to change rapidly over relatively short distances. Spatial prediction (e.g., for an automated valuation system) requires models that can deal with all of these sources of spatial variation. We propose to accommodate these factors using a standard hedonic framework but incoporating a semiparametric model with structure in the residuals modeled with a partially Bayesian approach. The Bayesian framework enables us to provide complete inference in the form of a posterior distribution for each model parameter. Our model allows prediction at sampled or unsampled locations as well as prediction interval estimates. The nonparametric part of our model allows sufficient flexibility to find substantial spatial variation in house values. The parameters of the kriging model provide further insights into spatial patterns. Out–of–sample mean squared error and related statistics validate the proposed methods and justify their use for spatial prediction of house values.