# RECORD 7f206890031d1d54ba82515e526e51ef8c34c412
# TITLE: A Parsimonious Hedonic Distributional Regression Model for Large Data with Heterogeneous Covariate Effects
# YEAR: 2025.0  VENUE: Austrian Journal of Statistics  DOI: 10.17713/ajs.v54i2.1904
# AUTHORS: Julian Granna; Wolfgang A. Brunauer; Stefan Lang; Nikolaus Umlauf
# PAGES: 25  CANDIDATE TABLE PAGES (1-based): [22]
# 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.


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AJS
Austrian Journal of Statistics
2025, Volume 54, 44–68.
http://www.ajs.or.at/
doi:10.17713/ajs.v54i2.1904
A Parsimonious Hedonic Distributional Regression
Model for Large Data with Heterogeneous
Covariate Effects
Julian Granna
University of Innsbruck
Innsbruck, Austria
Wolfgang Brunauer
DataScience Service GmbH
Vienna, Austria
Stefan Lang
University of Innsbruck
Innsbruck, Austria
Nikolaus Umlauf
University of Innsbruck
Innsbruck, Austria
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 re-
gressed 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 ma-
chines. 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 addi-
tive 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.
Keywords: generalized additive models for location scale and shape, hedonic regression, re-
gional cluster, real estate prices.
1. Introduction
Rosen (1974) interprets hedonic prices as the sum of implicit prices of attributes of a good.
These directly unobservable prices, hence often referred to as "shadow prices", are estimated


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Austrian Journal of Statistics
65
A. Descriptive tables
Table 2: Summary statistics of variables considered for modeling. Arithmetic mean is pro-
vided for metric covariates, relative frequency for discrete variables (Part 1).
variable
description
mean / rel. frequency
std. deviation
min
max
ppqm
Price per square meter
2.070
0.080
1.360
2.420
log.ppqm
log(Price per square meter)
7.930
0.600
3.910
11.260
age
Age of flat in years
37.680
30.230
-4.000
119.000
area
Area of flat in square meters
80.080
32.380
21.000
240.000
quarter
Quarter of last offer
2019.200
2.010
2016.000
2022.500
KGS
county ID
balcony
Whether object has balcony
0 = no
0.435
1 = yes
0.565
built.in.kitchen
Whether object has built-in kitchen
0 = no
0.993
1 = yes
0.007
cellar
Whether object has a cellar
0 = no
0.461
1 = yes
0.539
condition
condition of object
1 = other
0.634
2 = first-time occupancy
0.161
3 = renovated
0.173
4 = in need of renovation
0.031
cul.de.sac
Whether object is located in cul de sac
0 = no
0.998
1 = yes
0.002
district.heating
Whether object features district heating
0 = no
0.946
1 = yes
0.054
electric.heating
Whether object has electric heating
0 = no
0.997
1 = yes
0.003
elevated.ground.floor
Whether object is on elevated ground floor
0 = no
0.994
1 = yes
0.006
floor.boards
Whether object has floorboards
0 = no
0.995
1 = yes
0.005
floor.heating
Whether object has floor heating
0 = no
0.909
1 = yes
0.091
furnished
Whether object is furnished
0 = no
0.967
1 = yes
0.033
garage
Whether object has a garage
0 = no
0.882
1 = yes
0.118
garden
Whether object features a garden
0 = no
0.924
1 = yes
0.076
garden.share
Whether object inlcudes share of a garden
0 = no
0.990
1 = yes
0.010
garden.use
Whether object inlcudes a shared garden
0 = no
0.997
1 = yes
0.003
geothermal.heating
Whether object features geothermal heating
0 = no
0.998
1 = yes
0.002


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66
Hedonic Distributional Regression for Large Data with Heterogeneous Effects
Table 3: Summary statistics of variables considered for modeling. Arithmetic mean is pro-
vided for metric covariates, relative frequency for discrete variables (Part 2).
variable
description
mean / rel. frequency
std. deviation
min
max
heating.type
Type of heating in dwelling
1 = other
0.079
2 = unknown
0.661
3 = district_heating
0.052
4 = gas
0.189
5 = oil
0.019
hereditary.lease
Whether dwelling is hereditary lease type
0 = no
0.984
1 = yes
0.016
historic.preservation
Whether dwelling is historically preserved
0 = no
0.978
1 = yes
0.022
laminated.flooring
Whether object features laminated flooring
0 = no
0.954
1 = yes
0.046
lift
Whether object features a lift
0 = no
0.710
1 = yes
0.290
maisonette
Whether object has multiple floors
0 = no
0.944
1 = yes
0.056
no..of.rooms
Number of rooms in the flat
1
0.092
2
0.310
3
0.389
4
0.160
> 5
0.049
north.facing
Whether object is facing north
0 = no
0.999
1 = yes
0.001
refurbished.flat
Whether object is refurbished
0 = no
0.809
1 = yes
0.191
rented
Whether object is rented
0 = no
0.719
1 = yes
0.281
skyscraper
Whether object is located in skyscraper
0 = no
0.999
1 = yes
0.001
solar.power
Whether object features solar power
0 = no
0.997
1 = yes
0.003
south.facing
Whether object is facing south
0 = no
0.997
1 = yes
0.003
storage.room
Whether object has a storage room
0 = no
0.993
1 = yes
0.007
underground.parking
Whether object has underground parking
0 = no
0.871
1 = yes
0.129
wellness
Whether object has a wellness area
0 = no
0.996
1 = yes
0.004
winter.garden
Whether object has a winter garden
0 = no
0.994
1 = yes
0.006