1# RECORD 7f206890031d1d54ba82515e526e51ef8c34c4122# TITLE: A Parsimonious Hedonic Distributional Regression Model for Large Data with Heterogeneous Covariate Effects3# YEAR: 2025.0 VENUE: Austrian Journal of Statistics DOI: 10.17713/ajs.v54i2.19044# AUTHORS: Julian Granna; Wolfgang A. Brunauer; Stefan Lang; Nikolaus Umlauf5# PAGES: 25 CANDIDATE TABLE PAGES (1-based): [22]6# ABSTRACT: Modeling real estate prices in the context of hedonic models often involves fitting a Generalized Additive Model, where only the mean of a (lognormal) distribution is regressed on a set of variables without taking other parameters of the distribution into account. Thus far, the application of regression models that model the full conditional distribution of the prices, has been infeasible for large data sets, even on powerful machines. Moreover, accounting for heterogeneity of effects regarding time and locale, is often achieved by naive stratification of the data rather than on a model basis. A novel batchwise backfitting algorithm is applied in the context of a structured additive distributional regression model, which enables us to efficiently model all distributional parameters of the price distribution. Using a large German dataset of apartment asking prices with over one million observations, we employ a model-based clustering algorithm to capture the heterogeneity of covariate effects on the parameters with respect to dwelling locale. We thus identify clusters that are homogeneous with respect to the influence of dwelling locale on price. A boosting type algorithm of the batchwise backfitting algorithm is then used to automatically determine the variables relevant for modelling the location and scale parameters in each regional cluster. This allows for a different influence of variables on the distribution of prices depending on the locale and price segment of the dwelling.789===== PAGE 1 (score 5, numeric-paren 0, table-words 1, var-words 3) =====1011AJS12Austrian Journal of Statistics132025, Volume 54, 44–68.14http://www.ajs.or.at/15doi:10.17713/ajs.v54i2.190416A Parsimonious Hedonic Distributional Regression17Model for Large Data with Heterogeneous18Covariate Effects19Julian Granna20University of Innsbruck21Innsbruck, Austria22Wolfgang Brunauer23DataScience Service GmbH24Vienna, Austria25Stefan Lang26University of Innsbruck27Innsbruck, Austria28Nikolaus Umlauf29University of Innsbruck30Innsbruck, Austria31Abstract32Modeling real estate prices in the context of hedonic models often involves fitting a33Generalized Additive Model, where only the mean of a (lognormal) distribution is re-34gressed on a set of variables without taking other parameters of the distribution into35account. Thus far, the application of regression models that model the full conditional36distribution of the prices, has been infeasible for large data sets, even on powerful ma-37chines. Moreover, accounting for heterogeneity of effects regarding time and locale, is38often achieved by naive stratification of the data rather than on a model basis.39A novel batchwise backfitting algorithm is applied in the context of a structured addi-40tive distributional regression model, which enables us to efficiently model all distributional41parameters of the price distribution. Using a large German dataset of apartment asking42prices with over one million observations, we employ a model-based clustering algorithm43to capture the heterogeneity of covariate effects on the parameters with respect to dwelling44locale. We thus identify clusters that are homogeneous with respect to the influence of45dwelling locale on price. A boosting type algorithm of the batchwise backfitting algorithm46is then used to automatically determine the variables relevant for modelling the location47and scale parameters in each regional cluster.48This allows for a different influence of49variables on the distribution of prices depending on the locale and price segment of the50dwelling.51Keywords: generalized additive models for location scale and shape, hedonic regression, re-52gional cluster, real estate prices.531. Introduction54Rosen (1974) interprets hedonic prices as the sum of implicit prices of attributes of a good.55These directly unobservable prices, hence often referred to as "shadow prices", are estimated565758===== PAGE 22 (score 24, numeric-paren 0, table-words 2, var-words 15) =====5960Austrian Journal of Statistics616562A. Descriptive tables63Table 2: Summary statistics of variables considered for modeling. Arithmetic mean is pro-64vided for metric covariates, relative frequency for discrete variables (Part 1).65variable66description67mean / rel. frequency68std. deviation69min70max71ppqm72Price per square meter732.070740.080751.360762.42077log.ppqm78log(Price per square meter)797.930800.600813.9108211.26083age84Age of flat in years8537.6808630.23087-4.00088119.00089area90Area of flat in square meters9180.0809232.3809321.00094240.00095quarter96Quarter of last offer972019.200982.010992016.0001002022.500101KGS102county ID103balcony104Whether object has balcony1050 = no1060.4351071 = yes1080.565109built.in.kitchen110Whether object has built-in kitchen1110 = no1120.9931131 = yes1140.007115cellar116Whether object has a cellar1170 = no1180.4611191 = yes1200.539121condition122condition of object1231 = other1240.6341252 = first-time occupancy1260.1611273 = renovated1280.1731294 = in need of renovation1300.031131cul.de.sac132Whether object is located in cul de sac1330 = no1340.9981351 = yes1360.002137district.heating138Whether object features district heating1390 = no1400.9461411 = yes1420.054143electric.heating144Whether object has electric heating1450 = no1460.9971471 = yes1480.003149elevated.ground.floor150Whether object is on elevated ground floor1510 = no1520.9941531 = yes1540.006155floor.boards156Whether object has floorboards1570 = no1580.9951591 = yes1600.005161floor.heating162Whether object has floor heating1630 = no1640.9091651 = yes1660.091167furnished168Whether object is furnished1690 = no1700.9671711 = yes1720.033173garage174Whether object has a garage1750 = no1760.8821771 = yes1780.118179garden180Whether object features a garden1810 = no1820.9241831 = yes1840.076185garden.share186Whether object inlcudes share of a garden1870 = no1880.9901891 = yes1900.010191garden.use192Whether object inlcudes a shared garden1930 = no1940.9971951 = yes1960.003197geothermal.heating198Whether object features geothermal heating1990 = no2000.9982011 = yes2020.002203204205===== PAGE 23 (score 21, numeric-paren 0, table-words 1, var-words 15) =====20620766208Hedonic Distributional Regression for Large Data with Heterogeneous Effects209Table 3: Summary statistics of variables considered for modeling. Arithmetic mean is pro-210vided for metric covariates, relative frequency for discrete variables (Part 2).211variable212description213mean / rel. frequency214std. deviation215min216max217heating.type218Type of heating in dwelling2191 = other2200.0792212 = unknown2220.6612233 = district_heating2240.0522254 = gas2260.1892275 = oil2280.019229hereditary.lease230Whether dwelling is hereditary lease type2310 = no2320.9842331 = yes2340.016235historic.preservation236Whether dwelling is historically preserved2370 = no2380.9782391 = yes2400.022241laminated.flooring242Whether object features laminated flooring2430 = no2440.9542451 = yes2460.046247lift248Whether object features a lift2490 = no2500.7102511 = yes2520.290253maisonette254Whether object has multiple floors2550 = no2560.9442571 = yes2580.056259no..of.rooms260Number of rooms in the flat26112620.09226322640.31026532660.38926742680.160269> 52700.049271north.facing272Whether object is facing north2730 = no2740.9992751 = yes2760.001277refurbished.flat278Whether object is refurbished2790 = no2800.8092811 = yes2820.191283rented284Whether object is rented2850 = no2860.7192871 = yes2880.281289skyscraper290Whether object is located in skyscraper2910 = no2920.9992931 = yes2940.001295solar.power296Whether object features solar power2970 = no2980.9972991 = yes3000.003301south.facing302Whether object is facing south3030 = no3040.9973051 = yes3060.003307storage.room308Whether object has a storage room3090 = no3100.9933111 = yes3120.007313underground.parking314Whether object has underground parking3150 = no3160.8713171 = yes3180.129319wellness320Whether object has a wellness area3210 = no3220.9963231 = yes3240.004325winter.garden326Whether object has a winter garden3270 = no3280.9943291 = yes3300.006331