INTRODUCTION
Land is a human essential need in the earth. Everyone needs land for living,
work and many other activities. The role of land is more important than other
economic resources due to its necessary economic condition as well as a place
to stay. As an economic resource, appropriate land prices are important for
government to provide fair decisions. To analyze the land price data, statistical
approaches, such as regression models, are very useful to have right recommendations.
Many studies have highlighted that Ordinary Least Square (OLS) regression lack
the ability to consider spatial effect which then lead to biased and inefficient
estimations (Lochl and Axhausen, 2010). On the other
side, Geographically Weighted Regression (GWR) provides good alternative for
analyzing spatial data including land prices. The purpose of this research is
to compare the OLS and GWR approaches applied on the land price data in South
Tangerang, Indonesia.
Land prices, similar to house prices in general are variable depending on the
locations. Land price determinant is associated with many factors, not only
the environmental conditions but also government policies and the factors of
socioeconomic values. Some of the factors are the status of the land (certified,
not certified), the distance from highway gate, the distance from arteryroad,
developed/notdeveloped land, the social characteristic of area (safeness, proper/notproper,
crime rate) residence, the distance from market, the distance from public health
facility, the distance from security facility and the distance from education
facility. Many studies also indicated that land prices were highly correlated
with land use and the growth of regions (Luo and Wei, 2009).
Ignoring factors including areas determining land prices is ridiculous. Usually,
a simple approach is to run a linear regression model involving some possible
determinants as covariates, such as the distance from high way gate and/or many
social characteristics of the area. In the literature, this approach is known
as hedonic model of land or house prices (Cheshire and Sheppard,
1995; Lochl and Axhausen, 2010). The technique produces
single parameter estimate for each covariate which then called a global model.
Although the model provides useful information based on the parameter estimates,
it is not precise enough. Luo and Wei (2009) found that
the use of GWR improved significantly the global model in terms of model goodnessoffit
and residual autocorrelation. Also Saefuddin et al.
(2011) found that the GWR performed better than the OLS when applied on
poverty data in Indonesia. We, then implemented GWR to analyse land prices in
South Tangerang, Province of Banten, one of the urban areas in Indonesia which
is very fast moving.
The developments in Jakarta and its surroundings area called Bodetabek (Bogor, Depok, Tangerang and Bekasi) have showed a very rapid improvement since last decade. Physically, as the hinterland of Jakarta, Bodetabek has prime quality for residential area. The rapid development in Jakarta also has accelerated the urbanization process yielding the growth rate of economic investments, trade and industry in Bodetabek. Hence, Jakarta and its hinterland (Bodetabek) region have been continuing to develop into a Mega City Urban. Land prices in these areas are then very crucial to be analyzed.
This study is aimed at modeling the land price in South Tangerang area as a
part of BODETABEK. The analysis was based on several explanatory variables including
the status of the land (certified/not certified), the distance from highway
gate, the distance from arteryroad, developmental status (developed/notdeveloped
land), the characteristic of area (rural, ruralurban, urban), the social characteristics
(proper/notproper residence), the distance from market, the distance from public
health facility, the distance from security facility and the distance from education
facility. The data set was analyzed by ordinary regression (OLS) and Geographically
Weighted Regression (GWR). The results from both approaches were contrasted
using some statistical criteria.
MATERIALS AND METHODS
The data: The study area of this research was in South Tangerang, a district in Banten province, Indonesia. The location is in the border of Jakarta and Banten province. Therefore, South Tangerang has been developing rapidly since the last decade and many developers have expanded their properties in this area. Concerned with property and local government policy, the land prices have become an interesting and important topic to be analyzed. The data was taken from 1050 locationpoints in South Tangerang using variables listed in the Table 1. The data was obtained by a survey to the land owners and the heads of subdistricts in South Tangerang.
Methods
Geographically weighted regression (GWR): Compared to OLS, GWR
is considered more appropriate method for data of nonstationary regions. The
data is called in stationary condition if the data is homogenous across the
study region, otherwise it is called nonstationary.
Table 1: 
Variables used in the land price model 


Fig. 1: 
Stationary versus nonstationary 
Fotheringham et al. (2002) named this phenomenon
is the spatial nonstationarity. Figure 1 indicates parameter
of stationary and nonstationary regions.
In the case of spatial nonstationarity, the same stimulus (determinant) provokes
different response in different parts of the region which then the approach
is termed local specific models as opposed to global models. Fotheringham
et al. (2002) listed differences between local and global models
which are important to consider in analyzing spatial data.
Global model is a linear regression in which the simple one with formula as
y_{i} = β_{o}+β_{1}x_{1} is used for
all locations assuming regional stationarity. The parameter estimates do not
change across areas, have singlevalued statistics, cannot be mapped, Geographic
Information System (GIS) unfriendly and aspatial (Fotheringham
et al., 2002; Yu and Wei, 2004). On the other
hand, GWR has the formula as y_{i} = β_{io}+β_{i1}x_{1}
in which the betas are not the same for each location and hence, called as local
models. Every location has its own parameter estimates. This local statistics
are different across space, has multivalued statistics and can be mapped using
GIS.
Let global regression have an equation as follows:
where, y_{i} is the value of dependent variable for observation i, β_{o} is the intercept, β_{k} is the parameter for variable k, x_{ik} is the value of the kth variable for i and ε_{i} is the error term. Instead of calibrating a single regression equation, GWR generates a separate regression equation for each observation. Each equation is calibrated using a different weighting of the observations contained in the data set. Each GWR equation may be expressed as:
where, (u_{i}, v_{i}) captures the coordinate location of i
(Fotheringham et al., 1998). Following Tobler
(1970) observations nearby one another have a greater influence on one another’s
parameter estimates than observations farther apart. The weight assigned to
each observation is then based on a distance decay function centered on observation
i. In the case of areal data, the distance between observations is calculated
as the distance between polygon centroids.
Parameter estimation: In linear regression, the parameter estimates obtained in the calibration of a model are constant over space:
while in GWR which the equation is as follows:
with the estimator
where, W(i) is a matrix of weights specific to location i such that observations
nearer to i are given greater weight than observations further away. An example
of W(i) is as the following:
where, w_{in} is the weight given to data point n for the estimate of the local parameters at location i. Numerous weighting schemes can be used although they tend to be Gaussian or ‘Gaussianlike’ reflecting the type of dependency found in most spatial processes.
Weighting schemes can be either fixed or adaptive. A fixed weighting schemes has w_{ij} as:
where, d_{ij} is the distance between locations i and j and h is the bandwidth as h increases, the gradient of the kernel becomes less steep and more data points are included in the local calibration. For fixed weighting schemes, h is fixed for all location i. We need to find the optimal value of h in the GWR routine.
A spatially adaptive weighting function has w_{ij} as:
if j is one of the Nth nearest neighbours of i otherwise 
The optimal value of h has to be found by minimizing a crossvalidation score (CV) or the Akaike Information Criterion (AIC).
The distance decay function which may take a variety of forms is modified by a bandwidth setting in which distance the weight rapidly approaches zero. Bandwidth is a distance between center of a polygon or grid to a particular border. There are two types bandwidth, i.e., fixed or adaptive. The bandwidth may be manually chosen by the analyst or using an algorithm that seeks to minimize a crossvalidation score:
where, n is the number of observations and observation i is omitted from the calculation so that in areas of sparse observations the model is not calibrated solely on i. Alternatively, as mentioned before, the bandwidth may be chosen by minimizing the Akaike Information Criteria (AIC) score, given as:
where, tr(S) is the trace of the hat matrix. The AIC method has the advantage of taking into account the fact that the degrees of freedom may vary among models centred on different observations. In addition, the user may choose a fixed bandwidth for every observation or a variable bandwidth that expands in areas of sparse observations and shrinks in areas of dense observations. Optimal bandwidth selection is a tradeoff between bias and variance. Too small a bandwidth leads to large variance in the local estimates and too large a bandwidth leads to large bias in the local estimates.
Because the regression equation is calibrated independently for each observation,
a separate parameter estimate, tvalue and goodnessoffit is calculated for
each observation. These values can thus be mapped, allowing the analyst to visually
interpret the spatial distribution of the nature and strength of the relationships
among explanatory and dependent variables (Fotheringham et
al., 2002). The map of parameter estimates was facilitated in Rsoftware
developed by Bivand and Yu (2011).
Result of ordinary regression: This section gives the results of OLS
and GWR computation. The outcome (land price) was transformed using natural
logarithmic to be normally distributed.
Figure 2 is the normal QQ Plot of the dependent variable
(land price). The result of natural logarithmic transformation (Fig.
2b) indicated its normality. Furthermore, modeling analysis used natural
logarithmic (ln) of land prices as the dependent variable. The analysis was
implemented based on the logarithmic scale.

Fig. 2(ab): 
The normal QQ plot of the dependent variable (land price
and land for natural logarithmic (land price) 
Table 2: 
OLS parameter estimation for all explanatory variables 

Significant at ^{#}1, : 0.1, *0.5, **0.01, ***0.001 
Table 2 was the result of OLS showing that not all explanatory variables were statistically significant. Furthermore, to simplify the analysis, regression modeling was continued based on the significant variables, i.e., the distance from highway gate, the distance from arteryroad, developmental characteristic (developed/notdeveloped area), social characteristic (proper/notproper residence) and the distance from public health facility. The result was presented in Table 3. This model was used to predict the land price in the study area shown by Fig. 4a. However, since it is a global model, the parameter estimate for each explanatory variable were the same over the region. Hence, map was only available for land price prediction, but not for the parameter estimates. On the hand, GWR approach may produce map for parameter estimates as shown the section of GWR result.
The result of GWR: Similar to the previous model, GWR of land prices
used only determinant (explanatory variables) having statistically significant
effect obtained by the OLS method.
Table 3: 
OLS parameter estimation for significant explanatory variables 

Valuer are significant at **0.01 and ***0.001 
Table 4: 
The Summary of GWR coefficient estimates 

The explanatory variables in the model were the distance from highway gate
(meter), the distance from arteryroad (meter), developmental status (developed/notdeveloped
area), social characteristic (proper/notproper residence) and the distance
from public health facility (meter).
As an advantage of analysis using GWR is mappable output. The map provides
specific information for each area including parameter estimates which impossible
in the case of global models. In this study, we created maps for the parameter
estimates and land price predictions. The usefulness of GWR in terms of expressing
parameter estimates using GISmap was discussed by Mennis
(2006). Similar to this study, ignoring spatial nonstationarity may blur
the differences of parameter estimates. Hence, we realized the effect of spatial
nonstationarity was not trivial The summary of the parameter estimates obtained
by GWR was listed in Table 4 with the Bandwidth is 1159.857
of the CV score equals 240.9669. AIC: 1307.714, Residual sum of squares: 195.3455
and Quasiglobal Rsquare: 0.3809504. The GWR procedure followed Charlton
et al. (2003) and the software obtained from Bivand
and Yu (2011).
Figure 3 is the maps of local regression parameters of GWR
for (a) highway, (b) artery, (c) developmental status, (d) social properness
and (e) health, while the land prices may be seen in Fig. 3f.
The figures indicated that coefficient parameters of highway, artery, properness
and health are not the same for all locations. The coefficient parameters of
highway were high in the northwest area, but pretty low in the west area. The
coefficient parameters of artery were high in the center and west of South Tangerang,
but low in the northwest area. The coefficient parameters of properness were
high in the center and northeast area and they were low in the southeast area.
The coefficient parameters of health were high in the east and southeast area
and lower in other areas. Meanwhile, the coefficient parameters of developmental
land status were almost uniform high in all locations.

Fig. 3(af): 
Maps of (a, b, c, d, e) local regression parameters (GWR)
and (f) values of land prices 

Fig. 4(ab): 
(a) Map OLS and (b) GWR land price estimations 
Figure 4a was the predicted values based on OLS, while Fig.
4b was based on GWR. These Fig. 4a and b
showed that the GWR based land prices were better than OLS based, in which the
former had small differences with the real prices. The predicted land prices
based on OLS overestimated in all areas. The result was also supported by the
residual analysis of OLS and GWR showed by Fig. 5.

Fig. 5(ab): 
(a) Map of OLS and (b) GWR residuals 
The colors of locations in the Fig. 5b are lighter than
the color in the Fig. 5a indicating that residuals in Fig.
5b are nearer to zero than residuals in Fig. 5a.
CONCLUSION
The map of parameter estimates provided clear explanation about spatial nonstationarity expressed well by GWR. In addition, the model using GWR provided smaller error than that from the OLS. In this study, the OLS based land price prediction were overestimated. GWR approach of land price models provided better performance statistically compared to the OLS one. Therefore, in the analysis hedonic models of land price, GWR was recommended.
The land price in South Tangerang was influenced by the distance from highway gate, the distance from arteryroad, developmental characteristic (developed/notdeveloped area), social characteristic (proper/notproper residence) and the distance from public health facility. The distance from the market facility did not have a significant effect to the land price. Following to a geographic research, the district has many mini markets spread in almost every 2 kilometers and hence the market centers were equivocal. The negative sign of land development indicated that buyers preferred an empty land compared to land with private houses. The local government may use the information in order to have a realistic land price regulation.
ACKNOWLEDGMENT
Dr. Bivand and Yu are acknowledged for allowing us to use the GWR software.