Spatial Prediction of House Prices Using Lpr and Bayesian Smoothing

Abstract

This paper is motivated by the limited ability of hedonic price equations to deal with spatial variation in house prices. Host (1999) divides spatial processes into low and high frequency components, inspiring the methods developed here. We further divide Host's low frequency spatial patterns into truly low frequency components, typically modeled parametrically with distance to the CBD or other points of interest, and medium frequency components, modeled here non-parametrically, with local polynomial regressions (LPR). Host, on the other hand, uses LPR for both low and medium frequency variation. LPR gives sufficient flexibility to find substantial spatial variation in house values.

We adopt a partially Bayesian approach to modeling high frequency spatial association. The Bayesian framework enables us to provide complete inference in the form of a posterior distribution for each model parameter. It allows for prediction at sampled or unsampled locations as well as prediction interval estimates.

Out-of-sample mean squared error and related statistics validate the proposed methods. The model is shown to provide insights into the spatial variation of house value.

Keywords: Land values; house prices; prediction; spatial modeling; Bayesian spatial modeling; local polynomial regression; smoothing regressions; nonparametric methods; semiparametric models.

JEL Classification: C4, H2, R1, R5