1# RECORD 7b29c36e620db272e042f7b9f343c676a20386782# TITLE: Interpretable Machine Learning for Real Estate Market Analysis3# YEAR: 2022.0 VENUE: Social Science Research Network DOI: 10.2139/ssrn.38359314# AUTHORS: Felix Lorenz; Jonas Willwersch; Marcelo Cajias; F. Fuerst5# PAGES: 31 CANDIDATE TABLE PAGES (1-based): [11]6# ABSTRACT: Machine Learning (ML) excels at most predictive tasks but its complex nonparametric structure renders it less useful for inference and out-of sample predictions. This article aims to elucidate and enhance the analytical capabilities of ML in real estate through Interpretable ML (IML). Specifically, we compare a hedonic ML approach to a set of model-agnostic interpretation meth-ods. Our results suggest that IML methods permit a peek into the black box of algorithmic decision making by showing the web of associative relationships between variables in greater resolution. In our empirical applications, we confirm that size and age are the most important rent drivers. Further analysis reveals that certain bundles of hedonic characteristics, such as large apartments in historic buildings with balconies located in affluent neighborhoods, attract higher rents than adding up the contributions of each hedonic characteristic. Building age is shown to exhibit a U-shaped pattern in that both the youngest and oldest buildings attract the highest rents. Besides revealing valuable distance decay functions for spatial variables, IML methods789===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) =====1011DOI: 10.1111/1540-6229.1239712O R I G I NA L A RT I C L E13Interpretable machine learning for real estate14market analysis15Felix Lorenz116Jonas Willwersch117Marcelo Cajias1,218Franz Fuerst3191International Real Estate Business20School (IRE|BS), University of21Regensburg, Regensburg, Germany222PATRIZIA AG, Augsburg, Germany233Department of Land Economy and24Trinity Hall, University of Cambridge,25Cambridge, UK26Correspondence27Jonas Willwersch, University of28Regensburg, International Real Estate29Business School (IRE|BS),30Universitaetsstrasse 31, 93053 Regensburg,31Germany.32Email:33jonas.willwersch@wiwi.uni-regensburg.de34Abstract35Machine Learning (ML) excels at most predictive tasks36but its complex nonparametric structure renders it less37useful for inference and out-of sample predictions. This38article aims to elucidate and enhance the analytical39capabilities of ML in real estate through Interpretable40ML (IML). Specifically, we compare a hedonic ML41approach to a set of model-agnostic interpretation meth-42ods. Our results suggest that IML methods permit a43peek into the black box of algorithmic decision mak-44ing by showing the web of associative relationships45between variables in greater resolution. In our empiri-46cal applications, we confirm that size and age are the47most important rent drivers. Further analysis reveals48that certain bundles of hedonic characteristics, such as49large apartments in historic buildings with balconies50located in affluent neighborhoods, attract higher rents51than adding up the contributions of each hedonic char-52acteristic. Building age is shown to exhibit a U-shaped53pattern in that both the youngest and oldest buildings54attract the highest rents. Besides revealing valuable dis-55tance decay functions for spatial variables, IML methods56This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits57use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or58adaptations are made.59© 2022 The Authors. Real Estate Economics published by Wiley Periodicals LLC on behalf of American Real Estate and Urban Economics60Association.61Real Estate Econ. 2022;1–31.62wileyonlinelibrary.com/journal/reec631646566===== PAGE 11 (score 144, numeric-paren 117, table-words 6, var-words 15) =====6768LORENZ et al.691170TA B L E 271Results of the OLS, GAM, and SAR estimation72Dependent variable: log Rent per month73OLS74GAM75SAR76log size in sq.m.770.939***78(0.002)790.900***800.928 ***81(0,008)82Floors830.002***84(0.0004)850.003***86(0.0003)870.003 ***88(0,002)89Age (relative to 2017)90−0.0002***91(0.00003)92s 8.000***93−0.000 ***94(0,0001)95Bathtub96−0.032***97(0.002)98−0.016***99(0.001)100−0.032 ***101(0,006)102Refurbished103−0.015***104(0.002)1050.005***106(0.002)107−0.013 ***108(0,007)109Built-in kitchen1100.084***111(0.002)1120.077***113(0.002)1140.077 ***115(0,007)116Balcony1170.011***118(0.002)1190.025***120(0.002)1210.012 ***122(0,007)123Parking1240.053***125(0.002)1260.032***127(0.002)1280.048 ***129(0,008)130Elevator1310.053***132(0.002)1330.020***134(0.002)1350.048 ***136(0,009)137Terrace1380.041***139(0.002)1400.020***141(0.002)1420.041 ***143(0,009)144log Purchasing Power1450.406***146(0.011)1470.069***148(0.002)1490.313 ***150(0,040)151CBD_distance152−0.019***153(0.001)154s 8.692***155−0.014 ***156(0,002)157Bar_distance158−0.031***159(0.002)160s 8.579***161−0.024 ***162(0,008)163Beergarden_distance164−0.020***165(0.002)166s 8.631***167−0.015 ***168(0,005)169Cafe_distance170−0.014***171(0.003)172s 8.700***173−0.011 ***174(0,010)175Bakery_distance176−0.011***177(0.003)178s 8.842***179−0.016 ***180(0,009)181Convenience store_distance182−0.036***183(0.002)184s 8.144***185−0.035 ***186(0,007)187Department store_distance188−0.006***189(0.001)190s 8.580***191−0.008 ***192(0,005)193Supermarket_distance194−0.018***195(0.006)196s 6.487***197−0.029 ***198(0,020)199Bus station_distance200−0.028***201(0.001)202s 8.794***203−0.017 ***204(0,004)205Railway station_distance206−0.020***207(0.002)208s 8.757***209−0.020 ***210(0,007)211Traffic signals_distance2120.086***213(0.007)214s 8.243***2150.075 ***216(0,024)217Car wash_distance2180.012***219(0.002)220s 8.763***2210.007***222(0.006)223Park_distance224−0.024***225(0.006)226s 8.343***227−0.019***228(0.020)229School_distance230−0.003***231(0.005)232s 8.412***2330.008 ***234(0,006)235Constant236−34.043***237(3.087)2382.405***239(0.100)240−22.860***241(11,359)242rho2430.131***244Time controls245Yes246Yes247Yes248Locational controls249Yes250Yes251Yes252Observations25352,96625452,96625552,966256R22570.8802580.885259adjusted R22600.8802610.898262UBRE2630.028264Note: *p < 0.1; **p < 0.05; ***p < 0.01, standard errors are displayed in parentheses. The GAM column reports the estimated265degrees of freedom of the smooth terms (s) as well as their joint significance. Time controls (year and month) as well as location266controls (apartment coordinates) are included in all models.267shows the results of the OLS, GAM, and spatial autoregressive regression (SAR) models. OLS and268SAR display similar coefficients for all variables.269Variables that exhibit nonlinear behavior are included as splines in the GAM with the esti-270mated degrees of freedom of smoothing terms being provided (denoted with “s”). Regarding the271goodness of fit, OLS shows an adjusted R2 of 0.880 and the SAR a R2 of 0.885. The GAM has a272273274===== PAGE 12 (score 14, numeric-paren 0, table-words 1, var-words 12) =====27527612277LORENZ et al.278F I G U R E 2279Hyperparameter tuning and model accuracy280Note: The figure displays the root mean square error (RMSE) decline per iteration step. The stacked bars represent boxplots with281the black line indicating the median RMSE value.282Source: Own depiction.283marginally better fit of 0.898, which is likely due to its capability of handling nonlinear relation-284ships. The structural hedonic variables, such as size, floor, and age, are highly significant and285show expected signs. Similar findings are reported by Dumm et al. (2016, 2018) and Seo (2018) for286property prices. The same holds true for the binary variables (kitchen, balcony, parking, elevator,287and terrace). Gröbel and Thomschke (2018) or Stamou et al. (2017) provide analogous results for288rents and prices, respectively. The location variables are also highly significant and show mostly289negative signs, indicating that the smaller the distance to a certain amenity, the higher the rent.290Only distance to car wash facilities and distance to traffic signals are positive, with greater distance291resulting in higher rental values confirming that negative externalities associated with these fea-292tures such as noise and air pollution result in a desire to not live in their immediate vicinity. In293summary, the results presented in Table 2 show that the hedonic approach seems to work, and294thus, justifies a more in-depth ML analysis.2955.2296Nonparametric models and machine learning297To set up a functional ML framework, we first train the XGB algorithm on our dataset of rental298prices described in the data section. We apply random cross-validation with five folds and five rep-299etitions. Appendix B provides additional information on parameter tuning. The final XGB model300