1# RECORD 0d7a1f874f9358489f6f5882b5a4900f217742112# TITLE: SPATIAL HETEROGENEITY IN HOUSING MARKET: ANKARA METROPOLITAN AREA3# YEAR: 2022.0 VENUE: Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi DOI: 10.18070/erciyesiibd.11225684# AUTHORS: Tuğba Güneş; A. Apaydın5# PAGES: 8 CANDIDATE TABLE PAGES (1-based): [3, 4, 5, 6]6# ABSTRACT: Advanced statistical models have been widely used in real estate valuations for various purposes over the last fifty years, and hedonic approaches with their simple and easy interpretable features are still the most popular among these models. However, spatial heterogeneity and spatial autocorrelation are the two major features of the housing markets, and traditional regression cannot reflect these locational effects into the model sufficiently. This study employs a Geographically Weighted Regression (GWR) model to explore the spatial heterogeneity in the metropolitan area housing market in the city of Ankara. By applying a Gaussian kernel weighting function with adaptive bandwidth based on cross-validation approach on a house listing dataset, it is found that the GWR fit the data better than the traditional ordinary least squares regression which mostly ignore the spatial effects, and there is spatial heterogeneity in the housing market. Explanatory power of the GWR model and parameter estimations are non-stationary over the geographical area. The variations in the coefficients of the variables are depicted on the map and is supported with the spatial correlations between the housing prices and attributes as well.789===== PAGE 1 (score 7, numeric-paren 0, table-words 0, var-words 7) =====1011Araştırma Makalesi | Research Article12Yayın Tarihi: 30 Aralık 2022 | Published: December 30, 202213doi: 10.18070/erciyesiibd.112256814SPATIAL HETEROGENEITY IN HOUSING MARKET: 15ANKARA METROPOLITAN AREA16KONUT PİYASASINDA MEKANSAL HETEROJENLİK: 17ANKARA METROPOLİTEN ALANI18TUĞBA GÜNEŞ1* & AYŞEN APAYDIN2 191 Dr., Ankara Üniversitesi, gunest@ankara.edu.tr; https://orcid.org/ 0000-0002-7472-1017, 2 Prof. Dr., Ankara Üniversitesi, Uygulamalı Bilimler 20Fakültesi, Sigortacılık ve Aktüerya Bilimleri Bölümü, aapaydin@ankara.edu.tr; https://orcid.org/ 0000-0003-4683-045921Advanced statistical models have been widely used in real estate valuations for various purposes over 22the last fifty years, and hedonic approaches with their simple and easy interpretable features are still 23the most popular among these models. However, spatial heterogeneity and spatial autocorrelation 24are the two major features of the housing markets, and traditional regression cannot reflect these 25locational effects into the model sufficiently. This study employs a Geographically Weighted Regression 26(GWR) model to explore the spatial heterogeneity in the metropolitan area housing market in the 27city of Ankara. By applying a Gaussian kernel weighting function with adaptive bandwidth based on 28cross-validation approach on a house listing dataset, it is found that the GWR fit the data better than 29the traditional ordinary least squares regression which mostly ignore the spatial effects, and there is 30spatial heterogeneity in the housing market. Explanatory power of the GWR model and parameter 31estimations are non-stationary over the geographical area. The variations in the coefficients of the 32variables are depicted on the map and is supported with the spatial correlations between the housing 33prices and attributes as well.34İleri istatistiksel modeller, çeşitli amaçlarla gerçekleştirilen gayrimenkul değerleme çalışmalarında 35son elli yıldır yaygın olarak kullanılmakta olup, hedonik yaklaşımlar basit ve kolay yorumlanabilir 36özellikleri sebebiyle bu modeller arasında popüler hale gelmiştir. Ancak konut piyasalarında 37mekânsal heterojenlik ve mekânsal otokorelasyon durumları söz konusu olabilmektedir ve geleneksel 38regresyon analizinde bu konumsal etkiler modele yeterince yansıtılamamaktadır. Bu çalışmada 39Coğrafi Ağırlıklandırılmış Regresyon (CAR) analizi kullanılarak, Ankara ilinin metropoliten alanındaki 40konut piyasasında mekânsal heterojenlik incelenmiştir. Konut fiyatları ve özelliklerinden oluşan veri 41seti üzerinde Gauss kernel ağırlık fonksiyonu ve çapraz doğrulama yöntemine dayalı olarak belirlenen 42değişken (adaptif) bant genişliği kullanılmış, mekânsal etkileri çoğunlukla göz ardı eden en küçük 43kareler yöntemine dayalı geleneksel regresyon modeline kıyasla CAR modelinin daha başarılı sonuçlar 44elde ettiği ve konut piyasasında mekânsal heterojenlik olduğu görülmüştür. CAR modelinin konut 45fiyatlarını açıklama gücünün ve parametre tahminlerinin coğrafi olarak durağan olmadığı anlaşılmıştır. 46Parametrelerdeki bu değişimler harita üzerinde gösterilerek açıklanmış ve konut fiyatları ile özellikleri 47arasındaki mekânsal korelasyonlar yardımıyla bu sonuçlar desteklenmiştir. 48Keywords: spatial heterogeneity, housing market, geographically weighted regression49Anahtar Kelimeler: mekânsal heterojenlik, konut piyasası, coğrafi ağırlıklandırılmış regresyon50ABSTRACT51ÖZ52Editör / Editor:53Hatun KORKMAZ,54Erciyes Üniversitesi, Türkiye55Hakemler / Referees:56Emre EKİNCİ,57Yozgat Bozok Üniversitesi, Türkiye58Mehmet MARIN,59Mardin Üniversitesi, Türkiye60*Sorumlu Yazar / Corresponding Author:61Tuğba Güneş62gunest@ankara.edu.tr63JEL:64C31, R30, R3165Geliş: 28 Mayıs 202266Received: May 28, 202267Kabul: 8 Ekim 202268Accepted: October 8, 202269Yayın Tarihi: 30 Aralık 202270Published: December 30, 202271Atıf Önerisi / Cited as (APA):72Güneş, T. & Apaydın A. (2022),73Spatial Heterogeneity in Housing Market: 74Ankara Metropolitan Area,75Erciyes Üniversitesi İktisadi ve İdari Bilimler 76Fakültesi Dergisi, 63, 9-16,77doi: 10.18070/erciyesiibd.112256878Erciyes Üniversitesi79İktisadi ve İdari Bilimler Fakültesi Dergisi80ISSN: 1301-3688/e-ISSN: 2630-640981Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi82Erciyes University Journal of Faculty of Economics and Administrative Sciences83https://dergipark.org.tr/tr/pub/erciyesiibd848586===== PAGE 3 (score 29, numeric-paren 0, table-words 8, var-words 9) =====8788Spatial Heterogeneity in Housing Market: Ankara Metropolitan Area891190Sayı: 63 | Number: 6391Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi92Erciyes University Journal of Faculty of Economics and Administrative Sciences93https://dergipark.org.tr/tr/pub/erciyesiibd94ln y95x96i97k98ik99i100k101 102 103 104 105 106 1071080109(1)110where ln yi is the natural logarithm of the housing price of the 111i . sale, β0 is the intercept, βk is the k . coefficient (estimated 112parameter), xik is the k . variable for the i. housing sale, and εi is the 113error term of the i. housing sale. 114The OLS model includes all available data in one equation and 115assumes that this formula is constant everywhere in the study area. 116However, property attributes, prices and price drivers may show 117significant variations over a geographic space. Dummy variables might 118be included in the global OLS model to capture locational effects, but 119this will be insufficient to consider the spatial heterogeneity and spatial 120autocorrelation in property markets. The GWR, developed by Brunsdon 121et al. (1996) and Fotheringham, Brunsdon, and Charlton (2000); 122Fotheringham et al. (1998), is a technique allowing to take into account 123the spatial heterogeneity within the entire space of interest (Bitter et 124al., 2007). 125By following the Tobler (1970)’s First Law of Geography stating 126that “Everything is related to everything else, but near things are more 127related than distant things”, the GWR model gives a higher weight to 128the observations (houses) that are closer to a subject property (regression 129point) than to those are further away. Rather than specifying one single 130formula, the GWR estimates a separate model for each housing point 131and weight a subset of observations by their distances to this regression 132point (Brunsdon et al., 1996; Fotheringham et al., 2003). In essence, 133parameter estimations of a GWR are conducted by an enhanced form of 134weighted least squares (WLS) approach. The GWR model is expressed 135as136ln137( ,138)139( ,140)141y142u v143u v144i145i146i147k148i149i150k151i152 153 154 155 156 157 1581590160(2)161where ui and vi denote longitude and latitude of house i , 162βk163i164i165u v166( ,167) is the parameter of the kth explanatory variable of house 168i to be estimated. To produce local parameters for each observation, a 169spatial weighting matrix is determined including all observations falling 170within a specific bandwidth around a regression point ( ,171)172u v173i174i175. The 176bandwidth can be determined by number of neighbors, by distance or 177by a kernel function which can be fixed or adaptive. As the bandwidth 178increases, the number of observations to be included in each regression 179increases and the GWR model gets closer to the global OLS model. On 180the other hand, if the bandwidth is identified narrower, then the GWR 181model becomes more local; however, the risk of insufficient subsample 182size may arise in this case. Kernel functions optimize the bandwidth to 183find the most appropriate number of neighboring points to be included 184in each regression. Minimization of the Akaike Information Criterion 185(AIC) and a cross-validation (CV) are the two most common methods 186in identifying the optimal bandwidth (Fotheringham et al., 2003).187GWR model estimations are undoubtedly sensitive to the choice of 188bandwidth and kernel function (Guo, Ma, & Zhang, 2008). Bujanda 189and Fullerton (2017) stated that using adaptive kernel bandwidths is 190recommended when regression points are not uniformly distributed 191in the study area because an adaptive kernel tries to find a certain 192number of neighboring points to ensure a constant subsample size in 193each location while a fixed kernel include all observations within the 194specified fixed radius around each regression point. In this study, we 195use a Gaussian kernel weighting function with adaptive bandwidth by 196adopting both CV and AIC approaches.197DATA AND STUDY AREA198Real estate transaction prices in the official records in Türkiye do not 199reflect the actual prices. According to the current legislations, buyers 200and sellers must report the actual price during the transaction, and this 201price cannot be lower than the tax value of the real property. However, 202buyers and sellers usually report the tax values as the actual prices to 203avoid paying high land registry fees because real estate tax values are 204significantly lower than their market values. Furthermore, housing 205attributes are also not available in the official records. Due to lack of 206reliable data for house prices and attributes, we used a cross-sectional 207dataset provided by hepsiemlak.com, one of the most popular websites 208for all types of real estate listings in Türkiye. The dataset includes listing 209prices and attributes of 2784 residential properties as of November 13, 2102021 in the Ankara metropolitan area where the majority of the real 211estate transactions in the city occur according to the official records 212of the Land Registry and Cadastre Agency (Tapu ve Kadastro Genel 213Müdürlüğü). As seen in Table 1, in the last five years annually more 214than 80 percent of the property sales transactions were made in this 215particular area consisting of eight counties. Figure 1 shows the Ankara 216metropolitan districts included in this study (a), and distribution (b) and 217density (c) of dwellings on the map. In addition to our main data set, 218POI (points of interest) data we considered in this study was retrieved 219from the OpenStreetMap.220TABLE 1 | Distribution of Real Estate Transactions in Ankara221Districts22220172232018224201922520202262021227Çankaya22813.25%22913.80%23014.47%23115.00%23215.57%233Keçiören23413.59%23513.25%23613.04%23713.44%23812.97%239Mamak24012.54%24112.24%24212.10%24311.67%24411.62%245Etimesgut24610.20%2479.50%24810.02%24911.13%25010.97%251Yenimahalle25210.45%25310.49%25411.46%25510.94%25610.33%257Sincan2589.48%2598.66%2608.93%2619.22%26210.06%263Altındağ2648.48%2658.91%2668.63%2677.98%2687.54%269Pursaklar2703.33%2713.55%2723.58%2733.52%2743.38%275Total27681.31%27780.40%27882.24%27982.88%28082.43%281FIGURE 1 | Study Area (a), Housing Units Distribution (b) 282and Density (c) Maps283(a)284(b)285(c)286Our final data set includes the listing prices (Turkish Lira) of each 287housing unit and their structural and locational characteristics including 288the geolocations. Variables were selected primarily on the basis of 289literature review and previous research. Structural variables are net 290surface area of the dwelling in square meters (net.area), numbers of 291292293===== PAGE 4 (score 79, numeric-paren 15, table-words 14, var-words 19) =====294295Güneş, T. & Apaydın A.29612297Sayı: 63 | Number: 63298Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi299Erciyes University Journal of Faculty of Economics and Administrative Sciences300https://dergipark.org.tr/tr/pub/erciyesiibd301bedrooms (bedroom) and living rooms (livingroom), floor number in 302four categories (basement level, ground floor, top floor, and middle 303floors between the top and ground floors), number of views (east, 304west, south, north) of the dwelling (num.views), a categorical variable 305representing whether the dwelling has one or more than one bathroom 306(bath), total number of floors in the building (total.floor), age of the 307building in years (age), whether or not the building has an indoor 308or outdoor parking area (carpark.indoor and carpark.outdoor), and 309whether it is located in a gated community (gated.community). Several 310locational variables to reflect the attractiveness of the building by the 311distances to selected points are also included: distances of the building 312in kilometers to the closest transportation station (dist.transportation), 313primary school (dist.school), shopping mall (dist.mall), hospital (dist.314hospital), university (dist.university), and police station (dist.police). 315Dependent variable is natural logarithm (to correct for skewing) of 316asking prices (price in Turkish Lira) of each housing unit. An overview 317of the included variables is given in Table 2.318EMPRICIAL ANALYSIS319We first performed a standard ordinary least squares (OLS) regression 320model that is a global regression and serves as the benchmark model. 321Afterwards, we employed geographically weighted regression (GWR) 322to lay down that parameter estimations are not constant over the space 323and spatial data is not stationary. All analyses were performed in R 324software. 325The traditional OLS regression results are shown in Table 3. Thirteen 326out of independent variables were found statistically significant. 327Adjusted R2 of the model is 0.695 which means that the explanatory 328variables can explain 69.5% of the variation of the housing prices 329(dependent variable). Multicollinearity does not seriously exist as all 330global variance inflation factor values (GVIF) are lower than five, 331except for the variable of the distance to the closest primary school. 332However, global OLS regression model assumes that marginal prices of 333property attributes are constant throughout the study area. Also, Moran’s 334I value was calculated 0.149 (p-value < 0.000), which indicates that the 335residuals generated from the global OLS regression are not statistically 336random. In other words, housing prices in this study have significant 337agglomeration characteristics and positive spatial autocorrelation. 338To explore the spatial heterogeneity, we perform a GWR for further 339analysis.340TABLE 3 | Global OLS Regression Results341Variables342Coef.343Std. Error344t value345p value346GVIF347(Intercept)34813.015***3490.065350199.7723510.000352-353net.area3540.004***3550.00035613.8633570.0003582.051359bedroom360-0.0133610.015362-0.8623630.3893641.932365livingroom366-0.0483670.052368-0.9163690.3603701.059371bath: more.than.one3720.286***3730.01937414.8703750.0003761.409377floor: ground.floor378-0.212***3790.020380-10.4613810.000382floor: top.floor383-0.073***3840.019385-3.9123860.0003871.070388floor: basement.floor389-0.447***3900.024391-18.3233920.000393total.floor3940.024***3950.00239615.8133970.0003981.206399age400-0.007***4010.001402-9.1384030.0004041.347405carpark.indoor: yes4060.170***4070.0184089.5704090.0004101.172411carpark.outdoor: yes412-0.035*4130.015414-2.3284150.0204161.042417gated.community: yes418-0.0104190.016420-0.6634210.5074221.016423num.views424-0.0074250.008426-0.8794270.3794281.019429dist.transportation430-0.0154310.010432-1.5184330.1294344.396435dist.school4360.210***4370.01143818.9654390.0004405.189441dist.mall442-0.160***4430.008444-19.6144450.0004464.018447dist.hospital448-0.091***4490.011450-8.6194510.0004524.832453dist.university454-0.049***4550.008456-6.3954570.0004583.339459dist.police4600.060***4610.0074628.3944630.0004644.169465# of Observations4662784467Global Moran I for regression residuals468R24690.6974470Moran’s I Index4710.149472Adj. R24730.6953474Expected Index475-0.001476RSS477350.0301478Variance4790.000480F-statistic481335.2482p-value4830.000484p-value4850.000486Note: ***, **, and * represent significance at 1%, 5% and 10% respectively487TABLE 2 | Summary Statistics488Variables489N490Mean491Std. Dev.492Min493Q1494Median495Q3496Max497price 4982784499647650500525446501880005023250005034900005047750005055820000506net.area 5072784508135.8550948.6651040511105512120513150514430515bedroom51627845173.225180.8751915203521352245237524livingroom52527845261.025270.1452815291530153115323533total.floor53427845355.945365.29537153835394540654149542age543278454413.0554511.1854605473548125492055060551num.views55227845532.075540.8255515562557255835594560dist.transport56127845622.165633.065640.005650.445660.955672.4656824.48569dist.school57027845711.525723.165730.005740.145750.265760.4757724.62578dist.mall57927845803.195813.325820.015831.235841.975853.6358626.76587dist.hospital58827845892.315903.085910.005920.605931.075942.3559525.39596dist.university59727845982.965992.966000.006011.146021.936033.6660425.21605dist.police60627846073.286083.946090.026100.876111.576123.7361325.46614Categorical Variables615N616Percentage617floor618top.floor61968162024.50%621middle.floor622136562349.00%624ground.floor62545362616.30%627basement.floor62828562910.20%630bath631more than 1632117463342.20%634carpark.indoor635yes63675263727.00%638carpark.outdoor639yes640190664168.50%642gated.643community644yes64572464626.00%647648649===== PAGE 5 (score 53, numeric-paren 0, table-words 17, var-words 17) =====650651Spatial Heterogeneity in Housing Market: Ankara Metropolitan Area65213653Sayı: 63 | Number: 63654Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi655Erciyes University Journal of Faculty of Economics and Administrative Sciences656https://dergipark.org.tr/tr/pub/erciyesiibd657Two GWR models were estimated with a Gaussian kernel weighting 658function with adaptive bandwidth. Only difference between the two 659models is the adopted approach to find the optimal bandwidth. The 660cross-validation (CV) method in the first GWR model and the Akaike 661Information Criterion (AIC) in the second were used to obtain an 662optimum size of nearest neighbors for the adaptive kernel. The resulting 663optimal bandwidths for the first and second models were found as 45 and 66459 observations respectively. Together with the global OLS regression, 665both GWR models results are summarized in Table 5. However, the 666GWR 1 model with cross-validation approach fit the data much better 667than both GWR 2 model with AIC approach and the OLS model. As 668seen in Table 4, among the three models, the GWR 1 model has the 669lowest AIC and residual sum of squares (RSS), and the highest R2 and 670adjusted R2 values. Therefore, all evaluations are made based on the 671results of the GWR model with CV approach in the rest of the paper.672TABLE 4 | Comparison of the OLS and GWR Models673Approach674Adaptive 675Bandwidth676R2677Adj. R2678AIC679RSS680OLS6810.6976820.6956832.169.678684350.030685GWR 1686CV687456880.9016890.866690-436.021691114.824692GWR 2693AIC694596950.8896960.860697-232.054698128.918699The findings showed that the GWR model improve the adjusted R2 700values from 0.69 to 0.86. The spatial distribution of the residuals of the 701standard OLS and GWR models depicted in Figure 2 suggests that the 702GWR residuals are closer to zero compared to the OLS residuals.703The local R2 values are higher than 0.76, indicating that the selected 704variables in this study have quite able to explain the housing prices in 705the study area. Figure 3 shows the spatial distribution of the goodness 706to fit between the housing attributes and prices based on the results 707obtained from the GWR model. The local explanatory powers are 708relatively higher in the west areas far from the city center. These results 709might present that the selected variables can explain the variation in 710the housing prices on the west side while in the central business area 711further determinants might also impact the house prices. For instance, 712majority of the buildings in the central business district are older than 713those on the west side, where the city tends to grow towards, and gated 714communities are more popular. Another example is that rising oil prices 715might be a significant driver in people’s housing choices, and thus on 716the house prices, as commuting has become a significant component 717of household expenditures recently (Akkoç, Akçağlayan, & Kargın 718Akkoç, 2021). The variation in the local R2 values is an indicator of the 719existence of spatial heterogeneity in the study area.720FIGURE 2 | Model Residuals721(OLS)722(GWR)723FIGURE 3 | Local R2 values derived from the GWR model724Estimated coefficients from the GWR model are generated for 725each point differently as the influence of independent variables on 726dwelling prices is varied over the space. Minimum, maximum and 727quartile values of these estimations are shown in Table 5 together 728with the OLS regression results. In addition to that the distribution of 729selected regression coefficients obtained from the GWR model, and by 730following Morali and Yilmaz (2020), Spearman Correlations between 731the logarithm of house prices and these variables are depicted on Figure 7324. The geographically weighted Spearman Correlations were computed 733by using the same bandwidth specification in the GWR Model. 734As illustrated in Figure 4, that the spatial patterns of the parameter 735estimations for each variable and the correlations differ over the space 736suggest the spatial heterogeneity in the study area.737As seen in Table 5, there are variabilities in coefficient estimations for 738all variables in terms of their impact of both magnitude and direction. 739For instance, coefficient estimations for the net area of the dwellings 740vary from -0.001 to 0.012; similarly, this variation range is between 741-0.036 and 0.003 for the building age variable and -0.069 and 0.104 742for the number of views of the dwellings. The GWR coefficients being 743positive and negative reveals the fact that drivers of the housing prices 744have an obvious spatial heterogeneity and instability over the study 745area. Furthermore, many of the median coefficients differ from the OLS 746coefficients, and even the signs of the three out of coefficients in the 747OLS regression are not the same as the GWR’s. 748Majority of parameter values for the distance measures have negative 749signs, which means that the house prices decrease as the points of 750interests are getting further away them. On the other hand, their effect 751on the house prices is larger in the west areas where are far away from 752the central business area. Consistent with the related literature (e.g. 753Wang and Chen (2020), Morali and Yilmaz (2020), and Soltani et al. 754(2021)), this result supports the significant impact of accessibility to 755various points of interests such as hospitals and schools on residential 756property prices. 757Similarly, there is a negative correlation between the building age and 758house prices. As seen on Figure 4 (b), the effect of the building age is 759less notable in the older neighborhoods where are closer to the central 760business area than it is in those areas on the far western and north-761eastern side of the city.762By contrast, the dwelling size variables (i.e., number of bedrooms, 763net surface area, and extra bathroom) and existence of a car park have 764positive impacts on the house prices. Compared to the overall picture, 765it is noteworthy that the effects of the number of bedrooms and the net 766surface area seem stronger in a particular micro area in the district of 767Çankaya, as seen on Figure 4 (a and c).768769770===== PAGE 6 (score 46, numeric-paren 0, table-words 6, var-words 11) =====771772Güneş, T. & Apaydın A.77314774Sayı: 63 | Number: 63775Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi776Erciyes University Journal of Faculty of Economics and Administrative Sciences777https://dergipark.org.tr/tr/pub/erciyesiibd778TABLE 5 | GWR Models and Global OLS779GWR 1 (CV approach)780GWR 2 (AIC approach)781Global OLS782Min.7831st Qu.784Median7853rd Qu.786Max.787Min.7881st Qu.789Median7903rd Qu.791Max.792(Intercept)7932.11979412.55179512.82879613.16079778.08879811.04779912.62480012.83280113.18480232.08880313.015804net.area805-0.0018060.0028070.0038080.0048090.0128100.0008110.0028120.0038130.0048140.0098150.004816bedroom817-0.4018180.0078190.0608200.0938210.205822-0.2348230.0058240.0538250.0948260.192827-0.013828livingroom829-14.027830-0.1408310.0398320.1848330.969834-0.999835-0.1118360.0408370.1658380.431839-0.048840bath: more.than.one841-0.0708420.0948430.1478440.2108450.400846-0.0278470.1048480.1558490.2078500.3968510.286852floor: ground.floor853-0.472854-0.348855-0.271856-0.2058570.225858-0.444859-0.347860-0.270861-0.2098620.093863-0.212864floor: top.floor865-0.278866-0.105867-0.073868-0.0348690.119870-0.199871-0.106872-0.075873-0.0408740.060875-0.073876floor: basement.floor877-0.856878-0.566879-0.481880-0.4108810.679882-0.774883-0.564884-0.476885-0.413886-0.097887-0.447888total.floor889-0.0238900.0188910.0258920.0318930.053894-0.0058950.0208960.0258970.0308980.0508990.024900age901-0.036902-0.016903-0.011904-0.0089050.003906-0.034907-0.015908-0.011909-0.0089100.002911-0.007912carpark.indoor: yes913-0.1059140.0269150.0719160.1259170.384918-0.0689190.0359200.0759210.1239220.3609230.170924carpark.outdoor: yes925-0.195926-0.0199270.0059280.0369290.175930-0.177931-0.0169320.0049330.0329340.137935-0.035936gated.community: yes937-0.141938-0.047939-0.0219400.0099410.112942-0.096943-0.043944-0.0199450.0069460.052947-0.010948num.views949-0.069950-0.021951-0.0029520.0139530.104954-0.061955-0.019956-0.0029570.0129580.058959-0.007960dist.transportation961-76.786962-0.141963-0.0339640.0689652.473966-1.223967-0.109968-0.0209690.0709701.890971-0.015972dist.school973-552.540974-0.1129750.0839760.2629773.246978-1.420979-0.0769800.1279810.3019822.5459830.210984dist.mall985-2.735986-0.208987-0.096988-0.019989304.215990-2.140991-0.213992-0.118993-0.0459941.430995-0.160996dist.hospital997-1.741998-0.139999-0.05610000.0541001409.4461002-1.4481003-0.1381004-0.07110050.01410060.8501007-0.0911008dist.university1009-2.0221010-0.1581011-0.02110120.068101338.3151014-1.6661015-0.1351016-0.02410170.05510183.6731019-0.0491020dist.police1021-170.9001022-0.1031023-0.00710240.08910253.6121026-5.6371027-0.0841028-0.01310290.07410301.92310310.0601032GWR 11033GWR 21034Global OLS1035# of Observations1036278410372784103827841039R2 & Adj. R210400.900 & 0.86610410.889 & 0.86010420.697 & 0.6951043Adaptive Bandwidth1044451045591046Effective # of Parameters1047715.6151048565.5731049Residual Sum of Squares1050114.8241051128.9181052350.0301053FIGURE 4 | Spatial Distribution of GWR Coefficients and Spearman Correlations (1/2)1054Coefficient1055Spearman Correlation1056(a) Number of Bedrooms (bedroom)1057(b) Building Age (age)105810591060===== PAGE 7 (score 16, numeric-paren 0, table-words 3, var-words 10) =====10611062Spatial Heterogeneity in Housing Market: Ankara Metropolitan Area1063151064Sayı: 63 | Number: 631065Erciyes Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi1066Erciyes University Journal of Faculty of Economics and Administrative Sciences1067https://dergipark.org.tr/tr/pub/erciyesiibd1068CONCLUSIONS1069It is well known that real estate markets are characterized by 1070both spatial heterogeneity and spatial autocorrelation. This paper 1071accounts for the spatial heterogeneity in the housing market in Ankara 1072metropolitan area by using geographically weighted regression. Taking 1073several explanatory variables representing the structural and locational 1074attributes of dwellings, the GWR model with a Gaussian kernel 1075weighting function with adaptive bandwidth based on cross-validation 1076approach fit the data much better than the traditional OLS in explaining 1077the housing prices and raised the adjusted R2 significantly from 0.695 1078to 0.866. Spatial variations in parameter estimations and R2 values 1079confirmed the spatial heterogeneity in the market, which was also 1080supported by the spatial correlations depicted on the map.1081Hedonic models are still the most prominent approach in automated 1082valuations of real estates due to their simplicity and easy interpretability 1083(Matysiak, 2017). However, as seen in the previous studies in the 1084literature summarized in Section I, and suggested in this study as well, 1085the models considering spatial dependence and spatial heterogeneity 1086can give more accurate estimations in real estate market analysis. 1087Furthermore, developing automated valuation models by applying 1088machine learning algorithms has been under the focus of both 1089professionals and academics recently to make more accurate price 1090predictions for various purposes ranging from collateral valuations 1091to portfolio assessments (e.g. Steurer et al. (2021) and Tchuente and 1092Nyawa (2021)). Thus, using machine learning methods that consider 1093spatial heterogeneity and spatial autocorrelation could be recommended 1094for further studies on housing price predictions. 1095REFERENCES10961. Akkoç, U., Akçağlayan, A., & Kargın Akkoç, G. (2021). The impacts of oil price 1097shocks in Turkey: sectoral evidence from the FAVAR approach. Economic Change and 1098Restructuring, 54(4), 1147-1171. 10992. Bidanset, P., McCord, M., Lombard, J. A., Davis, P., & McCluskey, W. (2018). 1100Accounting for locational, temporal, and physical similarity of residential sales in mass 1101appraisal modeling: the development and application of geographically, temporally, 1102and characteristically weighted regression. Journal of Property Tax Assessment and 1103Administration, 14(2), 5-13. 11043. Bidanset, P. E., & Lombard, J. R. (2014). Evaluating spatial model accuracy in mass real 1105estate appraisal: A comparison of geographically weighted regression and the spatial lag 1106model. Cityscape, 16(3), 169-182. 11074. Bidanset, P. E., Lombard, J. R., Davis, P., McCord, M., & McCluskey, W. J. (2017). 1108Further evaluating the impact of kernel and bandwidth specifications of geographically 1109weighted regression on the equity and uniformity of mass appraisal models. In Advances 1110in Automated Valuation Modeling (pp. 191-199): Springer.11115. Bitter, C., Mulligan, G. F., & Dall’erba, S. (2007). Incorporating spatial variation in 1112housing attribute prices: a comparison of geographically weighted regression and the 1113spatial expansion method. Journal of geographical systems, 9(1), 7-27. 11146. Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically weighted 1115regression: a method for exploring spatial nonstationarity. Geographical analysis, 28(4), 1116281-298. 11177. Bujanda, A., & Fullerton, T. M. (2017). Impacts of transportation infrastructure on 1118single-family property values. Applied Economics, 49(51), 5183-5199. 11198. Chica-Olmo, J. (2007). Prediction of housing location price by a multivariate spatial 1120method: Cokriging. Journal of Real Estate Research, 29(1), 91-114. 11219. Crawford, T. W. (2009). Scale Analytical. In R. Kitchin & N. Thrift (Eds.), International 1122encyclopedia of human geography (pp. 29-36): Elsevier.112310. Davis, P., Bidanset, P., McCord, M., & Cusack, M. (2019). Nationwide Mass Appraisal 1124Modeling in China: Feasibility Analysis for Scalability Given Ad Valorem Property Tax 1125Reform. Working Paper WP20PD1, Lincoln Institute of Land Policy. 112611. Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2000). Quantitative geography: 1127perspectives on spatial data analysis: Sage.112812. Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2003). Geographically weighted 1129regression: the analysis of spatially varying relationships: John Wiley & Sons.113013. Fotheringham, A. S., Charlton, M. E., & Brunsdon, C. (1998). Geographically weighted 1131regression: a natural evolution of the expansion method for spatial data analysis. 1132Environment and planning A, 30(11), 1905-1927. 113314. Fotheringham, A. S., Crespo, R., & Yao, J. (2015). Exploring, modelling and predicting 1134spatiotemporal variations in house prices. The Annals of Regional Science, 54(2), 417-1135436. 113615. Fullerton, T. M., & Bujanda, A. (2018). Commercial property values in a border 1137metropolitan economy. Asia-Pacific Journal of Regional Science, 2(2), 337-360. 113816. Gloudemans, R. J., & Almy, R. R. (2011). Fundamentals of mass appraisal: International 1139Association of Assessing Officers.114017. Grover, R. (2016). Mass valuations. Journal of Property Investment & Finance, Emerald 1141Group Publishing, Vol. 34(2), pages 191-204. 114218. Guo, L., Ma, Z., & Zhang, L. (2008). Comparison of bandwidth selection in application 1143of geographically weighted regression: a case study. Canadian Journal of Forest 1144Research, 38(9), 2526-2534. 114519. Hanink, D. M., Cromley, R. G., & Ebenstein, A. Y. (2012). Spatial variation in the 1146determinants of house prices and apartment rents in China. The Journal of Real Estate 1147Finance and Economics, 45(2), 347-363. 1148FIGURE 4 | Spatial Distribution of GWR Coefficients and Spearman Correlations (2/2)1149Coefficient1150Spearman Correlation1151(c) Net Surface Area (net.area)1152(d) Distance to Transportation (dist.transport)1153