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Incorporating spatial variation in housing attribute prices: a comparison of geographically weighted regression and the spatial expansion method

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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

  1. 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.

  2. 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.

  3. 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.

  4. This is a “pseudo”-R-squared, calculated as the squared correlation coefficient between the observed and predicted values for all 10,569 regressions.

  5. Almost all multi-story houses within Tucson are comprised of two stories.

References

  • Agterberg F (1984) Trend surface analysis. In: Gale G, Willmott C (eds) Spatial statistics and models. D. Reidel Publishing, Dordrecht, pp 147–171

    Google Scholar 

  • Anselin L (1988) Spatial econometrics, methods and models. Kluwer, Dordrecht

    Google Scholar 

  • Anselin L (1990) Spatial dependence and spatial structural instability in applied regression analysis. J Reg Sci 30:185–207

    Article  Google Scholar 

  • Bourassa S, Hoesli M, Peng V (2003) Do housing submarkets really matter? J Hous Econ 12:12–28

    Article  Google Scholar 

  • Bowen W, Mikelbank B, Prestegaard D (2001) Theoretical and empirical considerations regarding space in hedonic housing price model applications. Growth Change 32:466–490

    Article  Google Scholar 

  • Brunsdon C, Fotheringham S, Charlton M (1996) Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal 28:281–298

    Article  Google Scholar 

  • Can A (1992) Specification and estimation of hedonic house price models. Reg Sci Urban Econ 22:453–474

    Article  Google Scholar 

  • Can A, Mogbolugbe I (1987) Spatial dependence and house price index construction. J Real Estate Finance Econ 14:203–222

    Article  Google Scholar 

  • Cassetti E (1972) Generating models by the expansion method: applications to geographical research. Geogr Anal 4:81–92

    Article  Google Scholar 

  • Clapp J (2001) A semi parametric method for valuing residential locations: applications to automated valuation. J Real Estate Finance Econ 27:303–320

    Article  Google Scholar 

  • Dubin R, Sung C (1987) Spatial variation in the price of housing: rent gradients in non-monocentric cities. Urban Stud 24:193–204

    Article  Google Scholar 

  • Farber S, Yates M (2006) A comparison of localized regression models in an hedonic price context. Can J Reg Sci (in press)

  • Fik T, Ling D, Mulligan G (2003) Modeling spatial variation in housing prices: a variable interaction approach. Real Estate Econ 31:623–646

    Article  Google Scholar 

  • Fotheringham A, Brunsdon C (1999) Local forms of spatial analysis. Geogr Anal 31:340–358

    Article  Google Scholar 

  • Fotheringham A, Brunsdon C, Charlton N (2000) Quantitative geography: perspectives on spatial data analysis. Sage Publications, London

    Google Scholar 

  • Fotheringham A, Brunsdon C, Charlton N (2002) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, Chichester

    Google Scholar 

  • Freeman A (2003) The measurement of environmental and resource values. Resources for the Future, Washington

    Google Scholar 

  • Goodman A (1981) Housing submarkets within urban areas—definitions and evidence. J Reg Sci 21:175–185

    Article  Google Scholar 

  • Goodman A (1998) Housing market segmentation. J Hous Econ 7:121–143

    Article  Google Scholar 

  • Jones J, Cassetti E (1992) Applications of the expansion method. Routledge, London

    Google Scholar 

  • Michaels R, Smith V (1990) Market segmentation and valuing amenities with hedonic models: the case of hazardous waste sites. J Urban Econ 28:223–242

    Article  Google Scholar 

  • Mulligan G, Franklin R, Esparaza A (2002) Housing prices in Tucson, Arizona. Urban Geogr 23:446–470

    Article  Google Scholar 

  • National Association of Realtors (2006) Single-family spreadsheet. National Association of Realtors, Chicago

  • Orford S (1999) Valuing the built environment: GIS and house price analysis. Ashgate, Aldershot

    Google Scholar 

  • Páez A (2005) Local analysis of spatial relationships: a comparison of GWR and the expansion method. Lect Notes Comput Sci 3482:162–172

    Article  Google Scholar 

  • Páez A, Uchida T, Miyamoto K (2001) Spatial association and heterogeneity issues in land price models. Urban Stud 38(9):1493–1508

    Article  Google Scholar 

  • Pavlov A (2000) Space-varying regression coefficients: A semi-parametric approach applied to real estate markets. Real Estate Economics 28:249–283

    Article  Google Scholar 

  • Quigley J (1985) Consumer choice of dwelling, neighborhood and public services. Reg Sci Urban Econ 15:41–63

    Article  Google Scholar 

  • Schnare A, Struyk R (1976) Segmentation in urban housing markets. J Urban Econ 4:146–166

    Article  Google Scholar 

  • Thériault M, Des Rosiers F, Villeneuve P, Kestens Y (2003) Modelling interactions of location with specific value of housing attributes. Prop Manag 21:25–48

    Article  Google Scholar 

Download references

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Correspondence to Christopher Bitter.

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.

Table 8 Total variance explained

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.

Table 9 Rotated components

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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