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Using Cost-Distance Surfaces to Model Spatial Correlation in a Housing Price Model Jielai Ma GIS Master Project

Introduction § We are trying to use cost distance to revisit the spatial correlation concept in econometrics analysis § We explore the issue of using Visual Basic, Arc -Object, Rcom server, to connect Arc-GIS software with statistics software R package. § We conduct cost-distance spatial econometrics model on a small sample of housing price data.

Abstract § § Euclidean Distance vs. Cost Distance Estimation: Connecting Arc-GIS and R Example: Housing Price Data Demo

Distance § First Law of Geography (Waldo Tobler, 1970) § "Everything is related to everything else, but near things are more related than distant things. " § This concept has been widely used in spatial analysis § Effort distance (Falk and Abler 1980), social network distance (Stanley Wasserman, Katherine Faust 1994 ), cost distance (Meyerson, Adam; Munagala, Kamesh; Plotkin, Serge 2000)

Euclidean Distance vs. Cost Distance

Cost Distance

Calculating Cost Distance between Points (CCDP) § Calculate Cost Distance using Arc-Object

The Spatial Model in R § Spatial Econometrics Packages: (Esri), Geoda, Matlab, Sata and R spdep library § Strengths and limitations of R § Models that available in R spdep package § SAR, SAR(Lag), CAR, Spatial random coefficient and SMA…

Connecting R and Arc-GIS § The powerful statistics computation and flexibility of R package § The user friendly Arc-GIS software § Rcom Client Interface and internal COM Server maintained by Thomas Baier

Data Process Diagram (Cost Distance Spatial Model)

Demo

Housing Price Literature § Three major factors impact housing price: § Housing characteristics, local factors and time trend. § There a lot of local factors will affect housing price, such as air quality, water quality, transportation network, visibility reading… § We use spatial autocorrelation to model the unobservable factors.

Cost Distance vs. Eclidean Distance § Beron (2004) reported that introducing localize spatial dependence did little to help reduce the variability in housing price model. § Micro level data has higher variability than macro data set (Bell et al, 2000) § H 0: Can we use Cost Distance’s flexibility to improve the estimation result?

Housing Price Model § What’s the reasonable cost distance surface, if we considering using spatial correlation in the residual?

Defining Local Communities § Highway system § Census tract or block group demographic characteristics § Regression estimated coefficients § Other external environmental variables § We use prior housing price pattern to reflect the definition of local communities

Data Process Diagram

Kriging and Slope Function § We use ordinary kriging method in Arc. GIS to model the surface (spherical model with 12 nearest neighbors, output cell size is 66) § We use the degree of slope as the measure when using slope function.

Price and its kriging surface

Slope Surface and Cost Distance Surface

Pilot Sample § Total 136 observations § Price § § Minimum: 80500 Maximum: 305000 Mean: 134956. 33 Standard Deviation: 38067. 725312 § Total Observations in 2000 § § § Count: 19266 Minimum: 0 Maximum: 3800000 Mean: 157697. 648396 Standard Deviation: 162186. 068983

The Models § SAR model § SMA model § CAR model

The Comparisons Land area Years old Living area Cost Dist Euc Dist Coefficient 3. 2188 e-05 3. 5614 e-05 -0. 0058191 -0. 0064353 4. 7606 e-04 4. 8162 e-04 AIC criteria -45. 574 -33. 168 -18. 981 -3. 1554 -151. 2 -150. 79 24. 005 11. 599 35. 254 19. 428 0. 87967 0. 47302 26. 78690 20. 58386 13. 49028 5. 577685 79. 59936 79. 39604 Sigma 0. 19333 0. 20429 0. 21255 0. 22767 0. 13446 0. 13483 Coefficient 3. 4556 e-05 3. 6353 e-05 -0. 0064725 -0. 0069836 4. 7739 e-04 4. 7920 e-04 AIC criteria -45. 885 -34. 986 -16. 96 -4. 9931 -151. 15 -150. 99 LR test 24. 317 13. 418 33. 233 21. 266 0. 82775 0. 67312 Log Likelihood 26. 94273 21. 49323 12. 48014 6. 496565 79. 5734 79. 49608 Sigma CAR model Euc Dist Log Likelihood SMA model Cost Dist LR test SAR model Euc Dist 0. 20188 0. 20865 0. 22453 0. 23298 0. 13502 0. 13512 Coefficient 3. 5236 e-05 3. 8059 e-05 -0. 0063421 -0. 0069231 4. 7696 e-04 4. 8295 e-04 AIC criteria -37. 371 -28. 5 -7. 2077 5. 0665 -151. 14 -150. 7 LR test 15. 802 6. 9316 23. 481 11. 207 0. 82472 0. 37615 22. 68529 18. 24996 7. 603839 1. 466754 79. 57189 79. 3476 0. 2009 0. 20868 0. 22404 0. 23622 0. 13428 0. 13485 Log Likelihood Sigma

Moran’s I coefficient § OLS residuals Moran’s coefficient Land area Years old Living area Intercept Coefficient Standard Error Land area Intercept Years old Intercept Living area 1. 137 4. 165 e-05 12. 083 -0. 008 1. 093 e+01 4. 869 e-04 -45. 574*** -33. 168*** 0. 136*** 0. 003*** 4. 742 e-02*** 2. 642 e-05*** R square 0. 2708 0. 037 0. 717 Residual Standard Error 0. 2187 0. 251 0. 136 Moran’s I (Euc Dist) 0. 065 0. 012 0. 103 Moran’s I (Cost Dist) 0. 140 0. 023 0. 188 § Spatial Regression Residuals’ Moran’s I Land area Years old Living area Moran’s I (Euc Dist Model) 0. 088 0. 123 0. 004 Moran’s I (Cost Dist Model) 0. 048 0. 079 0. 000

Future Research § Combine cost-distance surface and econometrics diagnostics test to define the homogenous housing sub-market. § Incorporate cost-distance model in FGLS estimation. § Consider adding policy impact variable as a shock of housing market. § Use the cost-distance model to analyze other distance related social economics issue. § Add more models and summit the program.

Conclusion § We are trying to use cost distance to revisit the spatial correlation concept in econometrics analysis § With Visual Basic, Arc-Object, Rcom server, we successfully connect Arc-GIS software with statistics software R package. § A user friendly software has been developed, which can run spatial econometrics model directly from Arc-GIS software. § The pilot sample of housing price data shows a promising result of cost-distance spatial model

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