Abstract
Hedonic house price models typically impose a constant price structure on housing characteristics throughout an entire market area. However, there is increasing evidence that the marginal prices of many important attributes vary over space, especially within large markets. In this paper, we compare two approaches to examine spatial heterogeneity in housing attribute prices within the Tucson, Arizona housing market: the spatial expansion method and geographically weighted regression (GWR). Our results provide strong evidence that the marginal price of key housing characteristics varies over space. GWR outperforms the spatial expansion method in terms of explanatory power and predictive accuracy.
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Notes
This is often referred to as a trend surface analysis (TSA). Agterberg (1984) provides a good overview of the development and applications of this technique.
The lot size calculations were validated by comparing the value calculated based on parcel polygon area to the value in the assessor file when present. In almost all cases the values were reasonably close.
Many of the interaction terms exhibit high degrees of multicollinearity which increases the variances of the estimated coefficients. A stepwise regression could be used to ameliorate this effect, however, because of the large size of our sample we felt that this was unnecessary.
This is a “pseudo”-R-squared, calculated as the squared correlation coefficient between the observed and predicted values for all 10,569 regressions.
Almost all multi-story houses within Tucson are comprised of two stories.
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Appendix
Appendix
A principal component analysis was performed in order to reduce the number of explanatory variables while mitigating potential omitted variables bias. Eight housing attributes were entered into the PCA. Our objective was to reduce these variables to as few factors as possible due to computational limitations imposed by GWR. We retained the two components with eigenvalues greater than one for use in the regression models (Table 8), which together explain 56% of the variance in the original eight variables.
The extracted components were rotated via the varimax method with Kaiser normalization (Table 9). Component one loads negatively on age, and positively on refrigerated air conditioning, enclosed garages, and number of bathroom fixtures per room in the home. This component represents homes with modern features. We expect a positive relationship between this factor and housing prices. Component two has a high negative loading on the number of rooms per square foot of living space (large rooms), and positive loadings on homes with pools and patios. This component represents a specific style of housing, with a spacious design and outdoor amenities. A positive association between this component and housing prices is anticipated.
While 44% of the variance in the original eight variables is lost in the PCA, we find this to be acceptable as the two factors appear to capture the most important dimensions of this set of variables. The R-squared in our base model drops only slightly from 0.884 to 0.883 when the reduced variable set is specified.
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Bitter, C., Mulligan, G.F. & Dall’erba, S. Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method. J Geograph Syst 9, 7–27 (2007). https://doi.org/10.1007/s10109-006-0028-7
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DOI: https://doi.org/10.1007/s10109-006-0028-7