Using CostDistance Surfaces to Model Spatial Correlation in a Housing Price Model

1
Using Cost-Distance Surfaces to Model Spatial
Correlation in a Housing Price Model

• Jielai Ma
• GIS Master Project

2
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.

3
Abstract

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

4
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)

5
Euclidean Distance vs. Cost Distance
6
Cost Distance
7
Calculating Cost Distance between Points (CCDP)

• Calculate Cost Distance using Arc-Object

8
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

9
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

10
Data Process Diagram(Cost Distance Spatial Model)
11
Demo
12
Housing Price Literature

• Three major factors impact housing price
• Housing characteristics, local factors and time
  trend.
• There are 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.

13
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)
• H0 Can we use Cost Distances flexibility to
  improve the estimation result?

14
Housing Price Model

• Whats the reasonable cost distance surface, if
  we considering using spatial correlation in the
  residual?

15
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

16
Data Process Diagram
17
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.

18
Price and its kriging surface
19
Slope Surface and Cost Distance Surface
20
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

21
The Models

• SAR model
• SMA model
• CAR model

22
The Comparisons
23
Morans I coefficient

• OLS residuals Morans coefficient
• Spatial Regression Residuals Morans I

24
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.

25
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

26
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