1# RECORD 03ae226b461f39ce77988b8e944f5ba8259156d32# TITLE: Modelling hedonic residential rents for land use and transport simulation while considering spatial effects3# YEAR: 2010.0 VENUE: nan DOI: 10.5198/jtlu.v3i2.1174# AUTHORS: Michael Löchl; K. Axhausen5# PAGES: 25 CANDIDATE TABLE PAGES (1-based): [14, 15, 16, 25]6# 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.789===== PAGE 1 (score 5, numeric-paren 0, table-words 0, var-words 5) =====101112http://jtlu.org13. 3 . 2 [Summer 2010] pp. 39–6314doi: 10.1598/jtlu.v3i2.11715Modeling hedonic residential rents for land use and transport16simulation while considering spatial effects17Michael Löchl18ETH Zürich a19Kay W. Axhausen20ETH Zürich b21Abstract:22ăe application of UrbanSim requires land or real estate price data for the study area. ăese23can be difficult to obtain, particularly when tax assessor data and data from commercial sources are un-24available. ăe article discusses an alternative method of data acquisition and applies hedonic modeling25techniques in order to generate the required data. Many studies have highlighted that ordinary least26square (OLS) regression approaches lack the ability to consider spatial dependency and spatial hetero-27geneity, consequently leading to biased and inefficient estimations. ăerefore, a comprehensive data set28is used for modeling residential asking rents by applying and comparing OLS, spatial autoregressive, and29geographically weighted regression (GWR) techniques. ăe latter technique performed best with re-30gard to model đt, but the issue of correlated coefficients favored a spatial simultaneous autoregressive31model. Overall, the article reveals that when housing markets are a particular concern in UrbanSim ap-32plications, signiđcanteffortsareneededforthepricedatagenerationandmodeling. ăestudyconcludes33with further development potentials for UrbanSim.34Keywords:35Hedonic technique; UrbanSim; asking rents; spatial effects; Switzerland36137Introduction38One of the key components of UrbanSim is the use of land or real estate price data. ăese39are applied in the model system as an indicator of the relative market valuations for attributes40of housing, non-residential space, and location (Waddell and Ulfarsson 2003, 63). However,41đnding suitable data sources for real estate transaction prices and rents can be a challenge while42setting up an UrbanSim application when transaction and rent price data from data suppliers43are unavailable to researchers. As a minimum prerequisite for modeling purposes, sufficient in-44formation about a decent amount of properties is needed, including price (transaction cost or45rent) and some explanatory spatial variables to which the model system should be sensitive in46the application. ăese typically include at least some kind of regional accessibility, proximities,47and neighborhood characteristics. ăe hedonic approach is a suitable method to model price48values for every cell or parcel in the UrbanSim application based on such a sample. Moreover,49the analysis exposes the implicit prices of housing and location characteristics. In the case of the50UrbanSim application for Zürich (Löchl et al. 2007), tax assessor data and data from commer-51cial sources were unavailable. ăerefore, an alternative method of data acquisition was needed.52aloechl@ivt.baug.ethz.ch53baxhausen@ivt.baug.ethz.ch54Copyright 2010 Michael Löchl and Kay W. Axhausen.55Licensed under the Creative Commons Attribution – NonCommercial License 3.0.565758===== PAGE 14 (score 93, numeric-paren 61, table-words 11, var-words 10) =====596061()62Table 2: Estimated OLS parameters (N = 8592).63Y = Ln(RENT)64Model 165Model 266Explanatory Variable67Estimate68SE69sig.70VIF71Estimate72SE73sig.74VIF75(Constant)765.214773.63878Ln(SQM)790.777800.005 ***811.392820.776830.005 ***841.39485LIFT860.026870.004 ***881.160890.024900.005 ***911.15992FIREPLACE930.108940.010 ***951.167960.118970.011 ***981.16799BALCONY1000.0331010.004 ***1021.1861030.0331040.004 ***1051.186106GTERRACE1070.1051080.015 ***1091.0131100.1071110.016 ***1121.013113ISHOUSE1140.1331150.013 ***1161.1531170.1251180.013 ***1191.153120BUILTBEF211210.0771220.006 ***1231.2301240.1091250.006 ***1261.209127BUILT21TO301280.0861290.011 ***1301.0621310.0941320.011 ***1331.061134BUILT81TO901350.0181360.005 ***1371.1991380.0181390.005 ***1401.199141BUILT91TO051420.0671430.005 ***1441.3051450.0671460.005 ***1471.306148Ln(CARTT_CBD)149−0.2941500.007 ***1512.089152CARACC1530.1191540.005 ***1552.471156PTACC1570.0061580.001 ***1591.4721600.0111610.001 ***1621.493163Ln(RAILSTATION)164−0.0121650.002 ***1661.184167−0.0121680.003 ***1691.232170AUTOBAHN171−0.0601720.013 ***1731.033174−0.0671750.013 ***1761.033177AIRNOISE178−0.0391790.006 ***1801.281181−0.0961820.006 ***1831.276184Ln(HOTREST_JOBS)1850.0201860.002 ***1872.3391880.0321890.002 ***1902.447191Ln(POP_DENS)192−0.0281930.002 ***1941.242195−0.0261960.002 ***1971.243198FOREIGNERS (logit)199−0.0182000.002 ***2011.340202−0.0232030.002 ***2041.338205Ln(TAXLEVEL)206−0.1302070.014 ***2081.326209−0.2232100.015 ***2111.292212SLOPE (logit)2130.0162140.002 ***2151.2852160.0262170.002 ***2181.255219Ln(VIEW_LAKE)2200.0082210.001 ***2221.7592230.0122240.001 ***2251.944226Ln(VIEW_ALL)2270.0052280.002229**2301.450231−0.0012320.0022331.528234Ln(SOLAR_EVE)2350.0372360.003 ***2371.1072380.0182390.003 ***2401.0892411Q_042420.0802430.013 ***2441.1952450.0792460.014 ***2471.1952482Q_042490.0382500.012 ***2511.2282520.0322530.013254**2551.2282563Q_042570.0592580.009 ***2591.6182600.0572610.009 ***2621.6182634Q_052640.0322650.007 ***2662.6122670.0332680.007 ***2692.6132701Q_052710.0452720.007 ***2732.6162740.0442750.007 ***2762.6162772Q_052780.0262790.007 ***2802.0352810.0242820.008 ***2832.0352843Q_052850.0372860.007 ***2872.5262880.0342890.007 ***2902.526291Adjusted R-square2920.8542930.836294F -test2951677.000296***2971460.000298***299Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1300301302===== PAGE 15 (score 26, numeric-paren 10, table-words 5, var-words 6) =====303304Modeling hedonic residential rents305306Table 3: OLS diagnostics (N = 8592).307Model 1308Model 2309Measure310Value311sig.312Value313sig.314LogLik3153685.6533163183.261317AIC318−7307.306319−6302.522320Global Moran’s I3210.213322***3230.287324***325LMerr3262164.867327***3283918.393329***330LMlag331454.444332***333977.235334***335Robust LMerr3361722.903337***3382981.065339***340Robust LMlag34112.480342***34339.907344***345Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1346plots of the model indicated a problem with heteroscedasticity, as very low and very high ob-347served asking rents tended to be overestimated. ăe problem may have been caused by missing348and unavailable crucial structural variables, such as information about building conditions or349the landlord. However, the standard error of the OLS model was compared to the results based350on the heteroscedasticity consistent covariance matrix and did not show any signiđcant differ-351ence (for the procedure in R, see Bivand 2008, 290). ăerefore, heteroscedasticity was not352considered to be a serious problem in this case.353Since the data points were not randomly located and sometimes spaced widely about (see354Figure 1), an adaptive kernel was used for the GWR approach. As there was no prior justiđca-355tion for supplying a particular bandwidth, the two available options for đnding the most appro-356priate bandwidth were tested: 1) minimization of the cross-validation (CV) score and 2) min-357imization of the AIC measure (Fotheringham et al. 2002, 212). Both methods suggested the358same bandwidth. In Table 4, the results of the OLS, SARerr, SARmix, and GWR estimations,359based on the variable selection in Model 2, are shown. For the GWR model, the mean and the360standard deviations of the parameter values are presented. ăe parameter estimates do not vary361dramatically among the models (exceptions are CARACC, AIRNOISE, and VIEW_ALL, for362which the GWR model indicates a large spatial variation of those variables indicated by mul-363tiple standard deviation values compared to the mean of the estimates). For model evaluation364purposes, boththesumofsquaresoftheerrors(SSE)andtheAIChavebeencalculated. Inboth365measures, smaller values indicate better model đt. In this case, both measures identify the best366model đt for the GWR estimates; second best, the SARmix model. However, four explanatory367variables (PTACC, AIRNOISE, TAXLEVEL, and SOLAR_EVE) are not signiđcant in the368SARmix (as indicated by the values marked with a * in Table 4), whereas AIRNOISE even has369a counter-intuitive sign. Particularly with regard to the envisaged application of the hedonic370model in UrbanSim, the insigniđcance of the public transport accessibility coefficient creates a371major limitation of the model.372In order to further assess and compare the predictive accuracy of spatial autoregressive ap-373proaches and the GWR model, the predicted rents were compared with the observed values.374ăe results of this analysis (presented in Table 5), show that the OLS approach has the low-375est accuracy. Less than 66 percent of the predictions were within the range of ±2 percent of376the actual rent price and it showed the lowest accuracy within ±5 percent and ±10 percent as377378379===== PAGE 16 (score 38, numeric-paren 7, table-words 10, var-words 11) =====380381382()383Table 4: Comparison of coefficients from various modeling approaches.384Y = Ln(RENT)385GWR386Explanatory variable387OLS388Estimate389SARerr390Estimate391SARmix392Estimate393Estimate394mean395Std.dev.Ʋ396(Constant)3973.6383983.6113991.3294003.954401Ln(SQM)4020.7764030.7734040.7734050.7724060.055407LIFT4080.0244090.0264100.0254110.0224120.017413FIREPLACE4140.1184150.0854160.0884170.0964180.038419BALCONY4200.0334210.0304220.0304230.0314240.011425GTERRACE4260.1074270.0944280.0974290.0984300.073431ISHOUSE4320.1254330.1374340.1414350.1384360.047437BUILTBEF214380.1094390.0824400.0754410.0914420.026443BUILT21TO304440.0944450.0754460.0704470.0844480.042449BUILT81TO904500.0184510.0194520.0204530.0264540.024455BUILT91TO054560.0674570.0804580.0854590.0784600.023461CARACC4620.1194630.1134640.0684650.0114660.098467PTACC4680.0114690.0064700.002*4710.0394720.034473Ln(RAILSTATION)474−0.012475−0.013476−0.016477−0.0094780.016479AUTOBAHN480−0.067481−0.076482−0.079483−0.0714840.066485AIRNOISE486−0.096487−0.0834880.032*489−0.0144900.032491Ln(HOTREST_JOBS)4920.0324930.0294940.0144950.0254960.017497Ln(POP_DENS)498−0.026499−0.028500−0.028501−0.0295020.014503FOREIGNERS (logit)504−0.023505−0.014506−0.013507−0.0185080.007509Ln(TAXLEVEL)510−0.223511−0.201512−0.002*513−0.1605140.268515SLOPE (logit)5160.0265170.0165180.0075190.0105200.009521Ln(VIEW_LAKE)5220.0125230.0105240.0035250.0085260.007527Ln(VIEW_ALL)528−0.001*5290.008*5300.0175310.0065320.024533Ln(SOLAR_EVE)5340.0185350.0125360.006*5370.0245380.0275391Q_045400.0795410.0785420.0795430.0725440.0345452Q_045460.0325470.0465480.0445490.0405500.0365513Q_045520.0575530.0675540.0665550.0605560.0215574Q_055580.0335590.0385600.0365610.0325620.0205631Q_055640.0445650.0505660.0495670.0485680.0205692Q_055700.0245710.0275720.0265730.0245740.0185753Q_055760.0345770.0405780.0395790.0375800.022581Lambda5820.637583Rho5840.599585SSE586239.781587182.655588179.700589174.202590AIC591−6302.522 −8169.980 −8319.190 −8392.987592* Not signiđcant at 0.05 level593Ʋ Standard deviation of coefficient values across study area594595596===== PAGE 17 (score 8, numeric-paren 0, table-words 2, var-words 4) =====597598Modeling hedonic residential rents599600well. ăe other three models performed considerably better, whereas around 73 percent are601in the ±2 percent range and slightly above 98 percent are in the ±5 percent range. ăe GWR602approach had the best predictive accuracy in the two tighter ranges but its performance was603slightly inferior in the ±8 percent range, although the differences were only marginal among604the models. ăe SARerr model is more accurate in the ±2 percent range than the SARmix605model, but slightly lower in the ±5 percent and ±8 percent range. Finally, the residuals of all606four models were tested for autocorrelation, measured by the Moran’s I test. Besides the OLS,607the GWR approach seems not to solve the autocorrelation, while there is essentially no auto-608correlation observable anymore in the residuals of the SARerr and the SARmix model.609Table 5: Predictive accuracy of models: Percentage of predicted rents within speciđed range of actual610asking rents (Ln(RENT)) and Moran’s I of the residuals.6112% range6125% range6138% range614Moran’s I615OLS61665.7761796.8161899.916190.287620SARerr62172.6562298.0262399.93624−0.018625SARmix62672.5962798.1462899.94629−0.016630GWR63173.7963298.4663399.926340.119635ăe fact that the GWR approach does not solve the autocorrelation in the residuals is636alarming. Wheeler and Tiefelsdorf (2005, 186) emphasize that spatially auto-correlated resid-637uals can produce severely correlated local regression coefficients. ăis is proven by a further638investigation of the correlation matrix of the regression coefficients. In the correlation matrix,639signiđcant values beyond ±0.5 can be found in almost 8 percent of the cases and values beyond640±0.6 in 4 percent. ăerefore, the issue of multicollinearity among the coefficients clearly exists641in the GWR results. ăis raised strong doubts as to whether the GWR method is the most642suitable and reliable approach here despite its good model đt. ăe SARmix model has some643limitations as well, namely that four explanatory variables, including public transport accessi-644bility, are insigniđcant. Given that the SARerr model accuracy is almost as good as the SARmix645model, it is preferred here and suggested for the next update of the UrbanSim application for646Zürich.6476648Conclusions649Setting up an UrbanSim application for a metropolitan area is a major task and includes, in650particular, a signiđcant data collection effort. ăis article focused on hedonic residential rent651modeling in order to establish a housing price surface for the UrbanSim application in Zürich.652ăe task was particularly difficult since there was no tax assessor data or data from commer-653cial sources available for the study area at the required spatial resolution. Eventually, publicly654available residential asking rents from a web-based portal were used. ăe variable selection655was found by considering signiđcant explanatory variables while strictly controlling for mul-656ticollinearity. Spatial autocorrelation later proved to be a problem and several spatial simul-657taneous autoregressive models and the GWR approach were therefore tested. Although all658goodness-of-đt measures indicated slightly better performance for the GWR model compared659to the spatial simultaneous autoregressive models, its residuals were still auto-correlated. Ad-660661662===== PAGE 25 (score 50, numeric-paren 27, table-words 9, var-words 5) =====663664Modeling hedonic residential rents665666Appendix: Additional variable data667Table 6: Estimated OLS parameters for models with spatial explanatory variables only.668Model 3669Model 4670Measure671Value672Sig.673Value674Sig.675(Constant)6769.515677***6788.366679***680Ln(CARTT_CBD)681−0.258682***683CARACC056840.064685***686PTACC05687−0.012688***689−0.004690Ln(RAILSTATION)691−0.019692***693−0.015694**695AUTOBAHN696−0.061697**698−0.064699**700AIRNOISE701−0.009702−0.053703***704Ln(HOTREST_JOBS)7050.0007060.020707***708Ln(POP_DENS)709−0.093710***711−0.091712***713FOREIGNERS (logit)714−0.087715***716−0.091717***718Ln(TAXLEVEL)719−0.289720***721−0.368722***723SLOPE (logit)7240.018725***7260.027727***728Ln(VIEW_LAKE)7290.015730***7310.018732***733Ln(VIEW_ALL)7340.0077350.005736Ln(SOLAR_EVE)7370.071738***7390.056740***741Adjusted R-square7420.2357430.215744F -test745208.800746***747182.200748***749Moran’s I7500.165751***7520.185753***754Probability of rejecting H0: *** p < 0.01; ** p < 0.05; * p < 0.1755