# RECORD a483774defcbadf7676aaa742f594af28562b13a
# TITLE: Predictability of Belgian residential real estate rents using tree-based ML models and IML techniques
# YEAR: 2023.0  VENUE: International Journal of Housing Markets and Analysis  DOI: 10.1108/ijhma-11-2022-0172
# AUTHORS: Ian Lenaers; K. Boudt; L. De Moor
# PAGES: 27  CANDIDATE TABLE PAGES (1-based): [10]
# ABSTRACT: 
Purpose
The purpose is twofold. First, this study aims to establish that black box tree-based machine learning (ML) models have better predictive performance than a standard linear regression (LR) hedonic model for rent prediction. Second, it shows the added value of analyzing tree-based ML models with interpretable machine learning (IML) techniques.


Design/methodology/approach
Data on Belgian residential rental properties were collected. Tree-based ML models, random forest regression and eXtreme gradient boosting regression were applied to derive rent prediction models to compare predictive performance with a LR model. Interpretations of the tree-based models regarding important factors in predicting rent were made using SHapley Additive exPlanations (SHAP) feature importance (FI) plots and SHAP summary plots.


Findings
Results indicate that tree-based models perform better than a LR model for Belgian residential rent prediction. The SHAP FI plots agree that asking price, cadastral income, surface livable, number of bedrooms, number of bathrooms and variables measuring the proximity to points of interest are dominant predictors. The direction of relationships between rent and its factors is determined with SHAP summary plots. In addition to linear relationships, it emerges that nonlinear relationships exist.


Originality/value
Rent prediction using ML is relatively less studied than house price prediction. In addition, studying prediction models using IML techniques is relatively new in real estate economics. Moreover, to the best of the authors’ knowledge, this study is the first to derive insights of driving determinants of predicted rents from SHAP FI and SHAP summary plots.



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Vrije Universiteit Brussel
Predictability of Belgian residential real estate rents using tree-based ML models and IML
techniques
Lenaers, Ian; Boudt, Kris; De Moor, Lieven
Published in:
International Journal of Housing Markets and Analysis
DOI:
10.1108/IJHMA-11-2022-0172
Publication date:
2023
License:
CC BY-NC
Document Version:
Accepted author manuscript
Link to publication
Citation for published version (APA):
Lenaers, I., Boudt, K., & De Moor, L. (2023). Predictability of Belgian residential real estate rents using tree-
based ML models and IML techniques. International Journal of Housing Markets and Analysis.
https://doi.org/10.1108/IJHMA-11-2022-0172
Copyright
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Download date: 15. Dec. 2023


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nternational Journal of Housing Markets and Analysis
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Table I: Summary statistics for the target variable and features
Feature name
Data type
Nr. of 
observations
Mean
Standard 
deviation
Skewness
Correlation 
with target
Monthly rent (indexed to 2019) in EUR
Continuous
18935
887.384
430.668
4.270
/
Asking price (indexed to 2019) in EUR
Continuous
18831
295106.971
155702.016
3.409
0.812
Cadastral income (in base year 1975) in EUR
Continuous
6270
941.815
745.955
5.579
0.614
Energy Prestation Certificate (EPC; A = 0, B = 
1, C = 2, D = 3, E = 4, F = 5)
Ordinal
8302
/
/
/
/
Furnished (0 = no, 1 = yes)
Binary
5896
0.120
0.325
2.341
-0.019
Garage (0 = no, 1 = yes)
Binary
16067
0.264
0.441
1.066
0.079
Garden (0 = no, 1 = yes)
Binary
14052
0.320
0.467
0.771
0.098
Land area in m2
Continuous
11054
478.771
1088.858
7.319
0.087
Min. distance to doctor (in degrees)
Continuous
18935
0.023
0.029
1.843
-0.126
Min. distance to hospital (in degrees)
Continuous
18935
0.160
0.113
0.965
-0.058
Min. distance to mall (in degrees)
Continuous
18935
0.196
0.155
0.795
-0.172
Min. distance to park (in degrees)
Continuous
18935
0.133
0.080
0.748
-0.040
Min. distance to restaurant (in degrees)
Continuous
18935
0.008
0.010
2.238
-0.050
Min. distance to school (in degrees)
Continuous
18935
0.023
0.025
1.916
-0.101
Min. distance to station (in degrees)
Continuous
18935
0.024
0.027
2.315
-0.057
Min. distance to supermarket (in degrees)
Continuous
18935
0.017
0.020
1.718
-0.057
Min. distance to university (in degrees)
Continuous
18935
0.256
0.153
-0.126
-0.0127
Nr. of bathrooms
Integer
16924
1.149
0.451
3.905
0.506
Nr. of bedrooms
Integer
15817
2.349
1.012
0.689
0.434
Nr. of doctors in 5.5km range
Integer
18935
18.669
26.950
1.461
0.226
Nr. of hospitals in 5.5km range
Integer
18935
0.388
1.062
3.600
0.094
Nr. of malls in 5.5km range
Integer
18935
0.293
0.552
1.736
0.191
Nr. of parks in 5.5km range
Integer
18935
0.231
0.522
2.213
0.020
Nr. of restaurants in 5.5km range
Integer
18935
136.421
208.078
2.291
0.253
Nr. of schools in 5.5km range
Integer
18935
11.213
13.706
1.296
0.244
Nr. of stations in 5.5km range
Integer
18935
5.234
9.899
4.720
0.184
Nr. of supermarkets in 5.5km range
Integer
18935
41.407
68.017
2.201
0.253
Nr. of universities in 5.5km range
Integer
18935
0.368
1.358
7.967
0.089
Number of toilets
Integer
11296
1.246
0.745
1.074
0.395
Property type (0 = house, 1 = apartment)
Binary
18935
0.694
0.461
-0.844
-0.202
Surface livable in m2
Continuous
17263
122.999
70.087
3.884
0.616
Surface of garden in m2
Continuous
6827
28.857
163.532
15.004
0.093
Terrace (0 = no, 1 = yes)
Binary
14698
0.775
0.418
-1.317
-0.012
Zip code
Nominal
18935
/
/
/
/
Source: own elaboration of the provided data
ML models
Tree-based (ensemble) models seem to have a slight edge in the literature considered, therefore RFR and 
XGBR were selected as ML models for this study. Both are compared on predictive performance to a LR 
model, estimated with OLS, which serves as a baseline model.
Tree-based regression techniques are based on individual Regression Trees (RT), which can identify 
complex patterns such as non-linear relationships and interactions (Antipov & Pokryshevskaya, 2012). 
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nternational Journal of Housing Markets and Analysis
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However, individual RTs are prone to misspecification, overfitting and there is as such little generalization 
(Provost & Fawcett, 2013). Therefore, tree-based ensemble techniques are used, which address these 
drawbacks while still being able to capture the complex relationships. These ensemble models create several 
sub models based on RTs. With the predictions of the sub models, the ensemble models combine the different 
predictions, of rent in this study, to obtain a final prediction (Hastie et al., 2009). RFR and XGBR both 
belong to different groups of ensemble models, which are called bagging and boosting, respectively.
RFR is a bagging ensemble method that combines predictions from several individual RTs into a final 
prediction. In parallel RTs are constructed. Random variation is introduced by selecting a subset of the data 
along one side for constructing the RT and along the other side by randomly selecting features for 
constructing branches of the RT (Hastie et al., 2009). From the predictions of different RTs, the average is 
taken to provide a final prediction. For more technical information on RFR, see Hastie et al. (2009).
Unlike RFR, which builds the forest of RTs in parallel, XGBR will build a sequence of trees where the next 
RT tries to improve the errors of the previous RTs. In its core concept, GBR builds an initial RT, calculates 
the errors of predictions with the initial RT and then builds a new RT to incrementally lower the prediction 
error and thus improve the final prediction model (Hastie et al., 2009). Several frameworks have been 
developed for implementing the boosting algorithm, including XGBR. For more technical details on XGBR, 
see Chen & Guestrin (2016). 
Hyperparameter tuning is done with the Tree-structured Parzen Estimator (TPE), a Bayesian optimizer. This 
method is chosen since the tuning process is considerably faster and more efficient than a grid search. 
Furthermore, the outcome is superior to a random search of hyperparameters (Yang & Shami, 2020). Models 
are then trained via 10-fold cross-validation (CV) on the train set.
The evaluation metrics are calculated on both train and test set, so that an impression can be obtained about 
the degree of overfitting of the models. Considering there are many evaluation metrics (Steurer et al., 2021), 
a selection of metrics, which were also considered in the studied literature, is chosen. These metrics are 
Mean Absolute Error (MAE), Root Mean Square Error (RMSE) and Mean Average Percentage Error 
(MAPE) and are defined according to the following formulas:
𝑀𝐴𝐸=
1
𝑛∑
𝑛
𝑖= 1
|𝑦𝑖― 𝑓𝑖|,
(1)
𝑅𝑀𝑆𝐸=
1
𝑛∑
𝑛
𝑖= 1
(𝑦𝑖― 𝑓𝑖)2,
(2)
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