# RECORD 03ae226b461f39ce77988b8e944f5ba8259156d3
# TITLE: Modelling hedonic residential rents for land use and transport simulation while considering spatial effects
# YEAR: 2010.0  VENUE: nan  DOI: 10.5198/jtlu.v3i2.117
# AUTHORS: Michael Löchl; K. Axhausen
# PAGES: 25  CANDIDATE TABLE PAGES (1-based): [14, 15, 16, 25]
# ABSTRACT: The application of UrbanSim requires land or real estate price data for the study area. These can be difficult to obtain, particularly when tax assessor data and data from commercial sources are unavailable. The article discusses an alternative method of data acquisition and applies hedonic modeling techniques in order to generate the required data. Many studies have highlighted that ordinary least square (OLS) regression approaches lack the ability to consider spatial dependency and spatial heterogeneity, consequently leading to biased and inefficient estimations. Therefore, a comprehensive data set is used for modeling residential asking rents by applying and comparing OLS, spatial autoregressive, and geographically weighted regression (GWR) techniques. The latter technique performed best with regard to model fit, but the issue of correlated coefficients favored a spatial simultaneous autoregressive model. Overall, the article reveals that when housing markets are a particular concern in UrbanSim applications, significant efforts are needed for the price data generation and modeling. The study concludes with further development potentials for UrbanSim.


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
http://jtlu.org
. 3 . 2 [Summer 2010] pp. 39–63
doi: 10.1598/jtlu.v3i2.117
Modeling hedonic residential rents for land use and transport
simulation while considering spatial effects
Michael Löchl
ETH Zürich a
Kay W. Axhausen
ETH Zürich b
Abstract:
ăe application of UrbanSim requires land or real estate price data for the study area. ăese
can be difficult to obtain, particularly when tax assessor data and data from commercial sources are un-
available. ăe article discusses an alternative method of data acquisition and applies hedonic modeling
techniques in order to generate the required data. Many studies have highlighted that ordinary least
square (OLS) regression approaches lack the ability to consider spatial dependency and spatial hetero-
geneity, consequently leading to biased and inefficient estimations. ăerefore, a comprehensive data set
is used for modeling residential asking rents by applying and comparing OLS, spatial autoregressive, and
geographically weighted regression (GWR) techniques. ăe latter technique performed best with re-
gard to model đt, but the issue of correlated coefficients favored a spatial simultaneous autoregressive
model. Overall, the article reveals that when housing markets are a particular concern in UrbanSim ap-
plications, signiđcanteffortsareneededforthepricedatagenerationandmodeling. ăestudyconcludes
with further development potentials for UrbanSim.
Keywords:
Hedonic technique; UrbanSim; asking rents; spatial effects; Switzerland
1
Introduction
One of the key components of UrbanSim is the use of land or real estate price data. ăese
are applied in the model system as an indicator of the relative market valuations for attributes
of housing, non-residential space, and location (Waddell and Ulfarsson 2003, 63). However,
đnding suitable data sources for real estate transaction prices and rents can be a challenge while
setting up an UrbanSim application when transaction and rent price data from data suppliers
are unavailable to researchers. As a minimum prerequisite for modeling purposes, sufficient in-
formation about a decent amount of properties is needed, including price (transaction cost or
rent) and some explanatory spatial variables to which the model system should be sensitive in
the application. ăese typically include at least some kind of regional accessibility, proximities,
and neighborhood characteristics. ăe hedonic approach is a suitable method to model price
values for every cell or parcel in the UrbanSim application based on such a sample. Moreover,
the analysis exposes the implicit prices of housing and location characteristics. In the case of the
UrbanSim application for Zürich (Löchl et al. 2007), tax assessor data and data from commer-
cial sources were unavailable. ăerefore, an alternative method of data acquisition was needed.
aloechl@ivt.baug.ethz.ch
baxhausen@ivt.baug.ethz.ch
Copyright 2010 Michael Löchl and Kay W. Axhausen.
Licensed under the Creative Commons Attribution – NonCommercial License 3.0.


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
()
Table 2: Estimated OLS parameters (N = 8592).
Y = Ln(RENT)
Model 1
Model 2
Explanatory Variable
Estimate
SE
sig.
VIF
Estimate
SE
sig.
VIF
(Constant)
5.214
3.638
Ln(SQM)
0.777
0.005 ***
1.392
0.776
0.005 ***
1.394
LIFT
0.026
0.004 ***
1.160
0.024
0.005 ***
1.159
FIREPLACE
0.108
0.010 ***
1.167
0.118
0.011 ***
1.167
BALCONY
0.033
0.004 ***
1.186
0.033
0.004 ***
1.186
GTERRACE
0.105
0.015 ***
1.013
0.107
0.016 ***
1.013
ISHOUSE
0.133
0.013 ***
1.153
0.125
0.013 ***
1.153
BUILTBEF21
0.077
0.006 ***
1.230
0.109
0.006 ***
1.209
BUILT21TO30
0.086
0.011 ***
1.062
0.094
0.011 ***
1.061
BUILT81TO90
0.018
0.005 ***
1.199
0.018
0.005 ***
1.199
BUILT91TO05
0.067
0.005 ***
1.305
0.067
0.005 ***
1.306
Ln(CARTT_CBD)
−0.294
0.007 ***
2.089
CARACC
0.119
0.005 ***
2.471
PTACC
0.006
0.001 ***
1.472
0.011
0.001 ***
1.493
Ln(RAILSTATION)
−0.012
0.002 ***
1.184
−0.012
0.003 ***
1.232
AUTOBAHN
−0.060
0.013 ***
1.033
−0.067
0.013 ***
1.033
AIRNOISE
−0.039
0.006 ***
1.281
−0.096
0.006 ***
1.276
Ln(HOTREST_JOBS)
0.020
0.002 ***
2.339
0.032
0.002 ***
2.447
Ln(POP_DENS)
−0.028
0.002 ***
1.242
−0.026
0.002 ***
1.243
FOREIGNERS (logit)
−0.018
0.002 ***
1.340
−0.023
0.002 ***
1.338
Ln(TAXLEVEL)
−0.130
0.014 ***
1.326
−0.223
0.015 ***
1.292
SLOPE (logit)
0.016
0.002 ***
1.285
0.026
0.002 ***
1.255
Ln(VIEW_LAKE)
0.008
0.001 ***
1.759
0.012
0.001 ***
1.944
Ln(VIEW_ALL)
0.005
0.002
**
1.450
−0.001
0.002
1.528
Ln(SOLAR_EVE)
0.037
0.003 ***
1.107
0.018
0.003 ***
1.089
1Q_04
0.080
0.013 ***
1.195
0.079
0.014 ***
1.195
2Q_04
0.038
0.012 ***
1.228
0.032
0.013
**
1.228
3Q_04
0.059
0.009 ***
1.618
0.057
0.009 ***
1.618
4Q_05
0.032
0.007 ***
2.612
0.033
0.007 ***
2.613
1Q_05
0.045
0.007 ***
2.616
0.044
0.007 ***
2.616
2Q_05
0.026
0.007 ***
2.035
0.024
0.008 ***
2.035
3Q_05
0.037
0.007 ***
2.526
0.034
0.007 ***
2.526
Adjusted R-square
0.854
0.836
F -test
1677.000
***
1460.000
***
Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1


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Modeling hedonic residential rents

Table 3: OLS diagnostics (N = 8592).
Model 1
Model 2
Measure
Value
sig.
Value
sig.
LogLik
3685.653
3183.261
AIC
−7307.306
−6302.522
Global Moran’s I
0.213
***
0.287
***
LMerr
2164.867
***
3918.393
***
LMlag
454.444
***
977.235
***
Robust LMerr
1722.903
***
2981.065
***
Robust LMlag
12.480
***
39.907
***
Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1
plots of the model indicated a problem with heteroscedasticity, as very low and very high ob-
served asking rents tended to be overestimated. ăe problem may have been caused by missing
and unavailable crucial structural variables, such as information about building conditions or
the landlord. However, the standard error of the OLS model was compared to the results based
on the heteroscedasticity consistent covariance matrix and did not show any signiđcant differ-
ence (for the procedure in R, see Bivand 2008, 290). ăerefore, heteroscedasticity was not
considered to be a serious problem in this case.
Since the data points were not randomly located and sometimes spaced widely about (see
Figure 1), an adaptive kernel was used for the GWR approach. As there was no prior justiđca-
tion for supplying a particular bandwidth, the two available options for đnding the most appro-
priate bandwidth were tested: 1) minimization of the cross-validation (CV) score and 2) min-
imization of the AIC measure (Fotheringham et al. 2002, 212). Both methods suggested the
same bandwidth. In Table 4, the results of the OLS, SARerr, SARmix, and GWR estimations,
based on the variable selection in Model 2, are shown. For the GWR model, the mean and the
standard deviations of the parameter values are presented. ăe parameter estimates do not vary
dramatically among the models (exceptions are CARACC, AIRNOISE, and VIEW_ALL, for
which the GWR model indicates a large spatial variation of those variables indicated by mul-
tiple standard deviation values compared to the mean of the estimates). For model evaluation
purposes, boththesumofsquaresoftheerrors(SSE)andtheAIChavebeencalculated. Inboth
measures, smaller values indicate better model đt. In this case, both measures identify the best
model đt for the GWR estimates; second best, the SARmix model. However, four explanatory
variables (PTACC, AIRNOISE, TAXLEVEL, and SOLAR_EVE) are not signiđcant in the
SARmix (as indicated by the values marked with a * in Table 4), whereas AIRNOISE even has
a counter-intuitive sign. Particularly with regard to the envisaged application of the hedonic
model in UrbanSim, the insigniđcance of the public transport accessibility coefficient creates a
major limitation of the model.
In order to further assess and compare the predictive accuracy of spatial autoregressive ap-
proaches and the GWR model, the predicted rents were compared with the observed values.
ăe results of this analysis (presented in Table 5), show that the OLS approach has the low-
est accuracy. Less than 66 percent of the predictions were within the range of ±2 percent of
the actual rent price and it showed the lowest accuracy within ±5 percent and ±10 percent as


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
()
Table 4: Comparison of coefficients from various modeling approaches.
Y = Ln(RENT)
GWR
Explanatory variable
OLS
Estimate
SARerr
Estimate
SARmix
Estimate
Estimate
mean
Std.dev.Ʋ
(Constant)
3.638
3.611
1.329
3.954
Ln(SQM)
0.776
0.773
0.773
0.772
0.055
LIFT
0.024
0.026
0.025
0.022
0.017
FIREPLACE
0.118
0.085
0.088
0.096
0.038
BALCONY
0.033
0.030
0.030
0.031
0.011
GTERRACE
0.107
0.094
0.097
0.098
0.073
ISHOUSE
0.125
0.137
0.141
0.138
0.047
BUILTBEF21
0.109
0.082
0.075
0.091
0.026
BUILT21TO30
0.094
0.075
0.070
0.084
0.042
BUILT81TO90
0.018
0.019
0.020
0.026
0.024
BUILT91TO05
0.067
0.080
0.085
0.078
0.023
CARACC
0.119
0.113
0.068
0.011
0.098
PTACC
0.011
0.006
0.002*
0.039
0.034
Ln(RAILSTATION)
−0.012
−0.013
−0.016
−0.009
0.016
AUTOBAHN
−0.067
−0.076
−0.079
−0.071
0.066
AIRNOISE
−0.096
−0.083
0.032*
−0.014
0.032
Ln(HOTREST_JOBS)
0.032
0.029
0.014
0.025
0.017
Ln(POP_DENS)
−0.026
−0.028
−0.028
−0.029
0.014
FOREIGNERS (logit)
−0.023
−0.014
−0.013
−0.018
0.007
Ln(TAXLEVEL)
−0.223
−0.201
−0.002*
−0.160
0.268
SLOPE (logit)
0.026
0.016
0.007
0.010
0.009
Ln(VIEW_LAKE)
0.012
0.010
0.003
0.008
0.007
Ln(VIEW_ALL)
−0.001*
0.008*
0.017
0.006
0.024
Ln(SOLAR_EVE)
0.018
0.012
0.006*
0.024
0.027
1Q_04
0.079
0.078
0.079
0.072
0.034
2Q_04
0.032
0.046
0.044
0.040
0.036
3Q_04
0.057
0.067
0.066
0.060
0.021
4Q_05
0.033
0.038
0.036
0.032
0.020
1Q_05
0.044
0.050
0.049
0.048
0.020
2Q_05
0.024
0.027
0.026
0.024
0.018
3Q_05
0.034
0.040
0.039
0.037
0.022
Lambda
0.637
Rho
0.599
SSE
239.781
182.655
179.700
174.202
AIC
−6302.522 −8169.980 −8319.190 −8392.987
* Not signiđcant at 0.05 level
Ʋ Standard deviation of coefficient values across study area


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Modeling hedonic residential rents

well. ăe other three models performed considerably better, whereas around 73 percent are
in the ±2 percent range and slightly above 98 percent are in the ±5 percent range. ăe GWR
approach had the best predictive accuracy in the two tighter ranges but its performance was
slightly inferior in the ±8 percent range, although the differences were only marginal among
the models. ăe SARerr model is more accurate in the ±2 percent range than the SARmix
model, but slightly lower in the ±5 percent and ±8 percent range. Finally, the residuals of all
four models were tested for autocorrelation, measured by the Moran’s I test. Besides the OLS,
the GWR approach seems not to solve the autocorrelation, while there is essentially no auto-
correlation observable anymore in the residuals of the SARerr and the SARmix model.
Table 5: Predictive accuracy of models: Percentage of predicted rents within speciđed range of actual
asking rents (Ln(RENT)) and Moran’s I of the residuals.
2% range
5% range
8% range
Moran’s I
OLS
65.77
96.81
99.91
0.287
SARerr
72.65
98.02
99.93
−0.018
SARmix
72.59
98.14
99.94
−0.016
GWR
73.79
98.46
99.92
0.119
ăe fact that the GWR approach does not solve the autocorrelation in the residuals is
alarming. Wheeler and Tiefelsdorf (2005, 186) emphasize that spatially auto-correlated resid-
uals can produce severely correlated local regression coefficients. ăis is proven by a further
investigation of the correlation matrix of the regression coefficients. In the correlation matrix,
signiđcant values beyond ±0.5 can be found in almost 8 percent of the cases and values beyond
±0.6 in 4 percent. ăerefore, the issue of multicollinearity among the coefficients clearly exists
in the GWR results. ăis raised strong doubts as to whether the GWR method is the most
suitable and reliable approach here despite its good model đt. ăe SARmix model has some
limitations as well, namely that four explanatory variables, including public transport accessi-
bility, are insigniđcant. Given that the SARerr model accuracy is almost as good as the SARmix
model, it is preferred here and suggested for the next update of the UrbanSim application for
Zürich.
6
Conclusions
Setting up an UrbanSim application for a metropolitan area is a major task and includes, in
particular, a signiđcant data collection effort. ăis article focused on hedonic residential rent
modeling in order to establish a housing price surface for the UrbanSim application in Zürich.
ăe task was particularly difficult since there was no tax assessor data or data from commer-
cial sources available for the study area at the required spatial resolution. Eventually, publicly
available residential asking rents from a web-based portal were used. ăe variable selection
was found by considering signiđcant explanatory variables while strictly controlling for mul-
ticollinearity. Spatial autocorrelation later proved to be a problem and several spatial simul-
taneous autoregressive models and the GWR approach were therefore tested. Although all
goodness-of-đt measures indicated slightly better performance for the GWR model compared
to the spatial simultaneous autoregressive models, its residuals were still auto-correlated. Ad-


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Modeling hedonic residential rents

Appendix: Additional variable data
Table 6: Estimated OLS parameters for models with spatial explanatory variables only.
Model 3
Model 4
Measure
Value
Sig.
Value
Sig.
(Constant)
9.515
***
8.366
***
Ln(CARTT_CBD)
−0.258
***
CARACC05
0.064
***
PTACC05
−0.012
***
−0.004
Ln(RAILSTATION)
−0.019
***
−0.015
**
AUTOBAHN
−0.061
**
−0.064
**
AIRNOISE
−0.009
−0.053
***
Ln(HOTREST_JOBS)
0.000
0.020
***
Ln(POP_DENS)
−0.093
***
−0.091
***
FOREIGNERS (logit)
−0.087
***
−0.091
***
Ln(TAXLEVEL)
−0.289
***
−0.368
***
SLOPE (logit)
0.018
***
0.027
***
Ln(VIEW_LAKE)
0.015
***
0.018
***
Ln(VIEW_ALL)
0.007
0.005
Ln(SOLAR_EVE)
0.071
***
0.056
***
Adjusted R-square
0.235
0.215
F -test
208.800
***
182.200
***
Moran’s I
0.165
***
0.185
***
Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1