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A comparison of localized regression models in a hedonic house price context.

Article Excerpt
Abstract

This paper compares the use of several local regression models using residential property valuation as a case study. The dataset consists of 19,007 housing sales observations occurring between July 2000 and June 2001 within the City of Toronto. Presently, assessment offices rely on a vast number of structural variables in order to sufficiently model market values. Building on the earlier findings of the authors, namely that local models using a small set of variables have a similar performance to the models used in industry, the aim of this paper is to compare the results of several localised regression models. Global OLS models are compared to a variety of local models including spatially autoregressive techniques (SAR), geographically weighted regression (GWR), moving window regression (MWR), and a spatial model of error heterogeneity. The models are all calibrated using a small set of parsimonious and defendable variables. Spatial autocorrelation amongst the residuals, as measured with Moran's Index, is used as an indicator of spatial bias in the estimates. The results show that GWR produces the most accurate and least spatially biased estimates. MWR, the simpler alternative, produced results that rivaled those of GWR without incorporating the unknown effects of distance-decaying weights. This indicates that the conceptual cost of abstraction associated with the use of a distance weighting scheme of GWR may not be worth the additional estimation accuracy.

Resumes

Cet article compare l'utilisation de nombreux modeles Iocaux de regression en utilisant l'etude de cas de l'evaluation de la propriete privee. La serie de donnees provient de l'observation de 19 007 ventes residentielles ayant eu lieu entrejuillet 2000 et juin 2001 a travers la ville de Toronto. Actuellement, les bureaux d'evaluation dependent d'un vaste nombre de variables structurelles dans le but de modeliser suffisamment les valeurs du marche. Se basant sur les decouvertes precedentes des auteurs, a savoir que les modeles locaux utilisant une petite serie de variables ont des performances similaires aux modeles utilises dans l'industrie, le but de cet article est de comparer les resultats de differents modeles de regression localises. Les modeles OSL globaux sont compares a une variete de modeles locaux comprenant des techniques autoregressives spatiales, des regressions geographiquement ponderees (GWR), des regressions en mouvement de fenetre (MWR) et un modele spatial d'heterogeneite d'erreur. Les modeles sont tous calibres a l'aide d'une petite serie de variables parcimonieuses et defendables. L'autocorrelation spatiale au sein des residus, telle que mesuree avec l'indice de Moran, est utilisee en tant qu'indicateur d'un prejuge spatial dans les estimes. Les resultats demontrent que la GWR produit les estimes les plus precis et les moins spatialement partiaux. MWR, l'alternative plus simple, produit des resultats qui rivalisent ceux de la GWR sans incorporer les effets inconnus des poids s'effritant avec la distance. Ceci indique que le cout conceptuel de l'abstraction associee a l'utilisation d'un schema de GWR considerant la distance peut ne pas valoir la precision additionnelle de l'estimation.

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It is the nature of spatial analysis to be concerned with local variations in a 'global' context. Analysts are compelled by the notion that objects nearer to each other are usually more similar and have greater influence on each other than objects farther apart--that is, that there is invariably some spatial autocorrelation in the data (Cliff and Ord 1981). 'Global' models, frequently based on ordinary least-squares (OLS) regression, assume that a single best equation can be found that characterizes the relationships between variables in a dataset pertaining to objects or locations in a particular geographic space. However, recent spatial multivariate regression models have emphasised that parameters identified in local models may not resemble the stationary parameters estimated in 'global' models. That is, they are often nonstationary (Brundsdon et al 1996; Fotheringham et a1 2002; Paez 2003).

This paper, based on the methodology and results of Farber (2004), compares the results of the application of a number of spatial multivariate models to two 'global' models in a hedonic house price context--that is, the adequacy of two models with nonstationary parameters are compared with two with stationary parameters. Although level of 'adequacy', or fit, is often in the eye of the beholder, in this case the comparisons are made with a number of distinct measures: multiple [R.sup.2] (or pseudo-[R.sup.2]), (1) and its counterpart the sum-of-squared errors (Paez et al 2002a and b); and, the Moran Coefficient (MC), which in this study is used to measure the spatial autocorrelation in the pattern of residuals for each model (Goodchild 1986; Cliffand Ord 1973; Moran 1948).

The models are applied...

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