# RECORD 33b79cf36579ae3f85aa1db50b2d2c31cb4ba23a
# TITLE: Predicting the rental value of houses in household surveys in Tanzania, Uganda and Malawi: Evaluations of hedonic pricing and machine learning approaches
# YEAR: 2021.0  VENUE: PLoS ONE  DOI: 10.1371/journal.pone.0244953
# AUTHORS: Weldensie T. Embaye; Yacob A. Zereyesus; Bowen Chen
# PAGES: 20  CANDIDATE TABLE PAGES (1-based): [10, 11, 12, 14, 15, 17]
# ABSTRACT: Housing value is a major component of the aggregate expenditure used in the analyses of welfare status of households in the development economics literature. Therefore, an accurate estimation of housing services is important to obtain the value of housing in household surveys. Data show that a significant proportion of households in a typical Living Standard Measurement Survey (LSMS), adopted by the Word Bank and others, are self-owned. The standard approach to predict the housing value for such surveys is based on the rental cost of the house. A hedonic pricing applying an Ordinary Least Squares (OLS) method is normally used to predict rental values. The literature shows that Machine Learning (ML) methods, shown to uncover generalizable patterns based on a given data, have better predictive power over OLS applied in other valuation exercises. We examined whether or not a class of ML methods (e.g. Ridge, LASSO, Tree, Bagging, Random Forest, and Boosting) provided superior prediction of rental value of housing over OLS methods accounting for spatial autocorrelations using household level survey data from Uganda, Tanzania, and Malawi, across multiple years. Our results showed that the Machine Learning methods (Boosting, Bagging, Forest, Ridge and LASSO) are the best models in predicting house values using out-of-sample data set for all the countries and all the years. On the other hand, Tree regression underperformed relative to the various OLS models, over the same data sets. With the availability of abundant data and better computing power, ML methods provide viable alternative to predicting housing values in household surveys.


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RESEARCH ARTICLE
Predicting the rental value of houses in
household surveys in Tanzania, Uganda and
Malawi: Evaluations of hedonic pricing and
machine learning approaches
Weldensie T. EmbayeID1*, Yacob Abrehe Zereyesus2, Bowen Chen3
1 Department of Agricultural Economics, Kansas State University, Manhattan, Kansas, United State of
America, 2 International Trade and Development Branch, Markets and Trade Economics Division, U.S.
Department of Agriculture, Economic Research Service, Kansas City, MO, United State of America,
3 Department of Agricultural and Consumer Economics, University of Illinois, Urbana, IL, United State of
America
* wembaye@ksu.edu
Abstract
Housing value is a major component of the aggregate expenditure used in the analyses of
welfare status of households in the development economics literature. Therefore, an accu-
rate estimation of housing services is important to obtain the value of housing in household
surveys. Data show that a significant proportion of households in a typical Living Standard
Measurement Survey (LSMS), adopted by the Word Bank and others, are self-owned. The
standard approach to predict the housing value for such surveys is based on the rental cost
of the house. A hedonic pricing applying an Ordinary Least Squares (OLS) method is nor-
mally used to predict rental values. The literature shows that Machine Learning (ML) meth-
ods, shown to uncover generalizable patterns based on a given data, have better predictive
power over OLS applied in other valuation exercises. We examined whether or not a class
of ML methods (e.g. Ridge, LASSO, Tree, Bagging, Random Forest, and Boosting) pro-
vided superior prediction of rental value of housing over OLS methods accounting for spatial
autocorrelations using household level survey data from Uganda, Tanzania, and Malawi,
across multiple years. Our results showed that the Machine Learning methods (Boosting,
Bagging, Forest, Ridge and LASSO) are the best models in predicting house values using
out-of-sample data set for all the countries and all the years. On the other hand, Tree regres-
sion underperformed relative to the various OLS models, over the same data sets. With the
availability of abundant data and better computing power, ML methods provide viable alter-
native to predicting housing values in household surveys.
Introduction
According to World Bank [1], the number of world population in poverty had declined from
1.85 billion in 1990 to 767 million in 2013. The World Bank’s Living Standards Measurement
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OPEN ACCESS
Citation: Embaye WT, Zereyesus YA, Chen B
(2021) Predicting the rental value of houses in
household surveys in Tanzania, Uganda and
Malawi: Evaluations of hedonic pricing and
machine learning approaches. PLoS ONE 16(2):
e0244953. https://doi.org/10.1371/journal.
pone.0244953
Editor: Stefan Cristian Gherghina, The Bucharest
University of Economic Studies, ROMANIA
Received: June 5, 2019
Accepted: December 18, 2020
Published: February 11, 2021
Copyright: © 2021 Embaye et al. This is an open
access article distributed under the terms of the
Creative Commons Attribution License, which
permits unrestricted use, distribution, and
reproduction in any medium, provided the original
author and source are credited.
Data Availability Statement: We used the data
that comes from the nationally representative
Living Standards Measurement Study (LSMS) of
household level surveys for the three countries
compiled by the World Bank. It’s freely available
data. It’s found at: http://surveys.worldbank.org/
lsms/programs/integrated-surveys-agriculture-ISA.
Funding: The author(s) received no specific
funding for this work.


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Of the significantly associated variables, for example, house rent increases with the increase
of number of rooms. If the number of rooms is increased by one, average monthly aggregate
house rent increases by about $0.36–6.43 in Uganda, $0.66–0.80 in Tanzania, and $0.41–0.50
in Malawi. The effect of electricity on house rent is also positive. Rental values of houses with
access to electricity are higher by $0.50–0.60 per month in Uganda, $0.54–0.64 in Tanzania,
and $0.71–0.82 in Malawi. These results imply the essence of electricity for household purposes
(e.g. lighting, cooking, etc.), mechanizations (farming and non-farming), and communication
and other purposes [50]. Private tap water is also positively associated with the value of house
rent in all the three countries. On average, a house rent in dwellings with a private water tap
are higher by $2.36 in the year 2010 in Uganda, by $0.15 in the year 2014 in Tanzania, and by
$0.58 in the year 2014 in Malawi. North and Griffin [51] found that households value in-house
piped water sources higher than any other house characteristics which is in agreement with
the results of the current work. Rental houses increase with access to clean water because more
households want to stay closer to clean water [52].
Mullainathan and Spiess [14] noted that machine learning algorithms are not built for
parameter estimation and hence the estimated regression coefficients are rarely consistent.
The results of the estimated coefficients from the ML approaches are estimated with this caveat
in mind. However, in general, results from the Ridge ML regression models show that most of
the estimated coefficients of the explanatory variables are smaller in magnitude compared to
the OLS coefficients (Tables 2–4). This is consistent with the literature [41] in that Ridge
regression shrinks the estimated coefficients and reduces the variance resulting in increased
predictive power of the covariates. Similarly, the LASSO regression approach shrinks the vari-
able estimates, and, in some cases, the coefficients are reduced to zero. When the estimated
variable coefficients are zero, then the variables may not play a role in predicting the value of
Table 1. Summary statistics of variables used in the house rental value predictions.
Variable
Definitions
Mean values (standard deviations)
Uganda
Tanzania
Malawi
2010
2012
2014
2016
2014
2016
Annual rent
Rent paid per month in dollar
22.18 (25.25)
23.46 (36.20)
17.89 (21.30)
22.65 (24.20)
20.34 (23.37)
17.39 (19.96)
Dwelling
1 if the room is located within a house, 0 otherwise
0.65 (0.46)
0.66 (0.46)
0.30 (0.40)
0.37 (0.48)
0.92 (0.28)
0.92 (0.27)
Roof
1 if roof type is mud, 0 otherwise
0.92 (0.27)
0.95 (0.26)
0.95 (0.25)
0.96 (0.25)
0.86 (0.35)
0.89 (0.31)
Floor
1 if floor is mud, 0 otherwise
0.68 (0.46)
0.34 (0.46)
0.22 (0.41)
0.91 (0.41)
0.80 (0.41)
0.77 (0.41)
External wall
1 if external wall is in mud, 0 otherwise
0.70 (0.45)
0.68 (0.45)
0.54 (0.45)
0.63 (0.48)
0.95 (0.21)
0.97 (0.18)
Number of rooms
Number of rooms rented
1.86 (1.12)
1.84 (1.16)
1.68 (0.91)
1.61 (0.92)
2.09 (0.97)
2.25 (0.98)
Electricity
1 if the house has electricity, 0 otherwise
0.35 (0.48)
0.37 (0.49)
0.53 (0.50)
0.59 (0.49)
0.42 (0.50)
0.44 (0.49)
Water sources
Private tap water
1 if private tap water source, 0 otherwise
0.03 (0.16)
0.07 (0.25)
0.12 (0.32)
0.56 (0.50)
0.14 (0.35)
0.43 (0.49)
Public tap water
1 if public tap water source, 0 otherwise
0.07 (0.26)
0.47 (0.49)
0.12 (0.33)
0.26 (0.44)
0.27 (0.44)
0.28 (0.45)
Bore hole water
1 if bore hole water source, 0 otherwise
0.47 (0.50)
0.19 (0.39)
0.07 (0.25)
-
0.31 (0.46)
0.23 (0.42)
Protected well water
1 if protected well water source, 0 otherwise
0.18 (0.39)
0.13 (0.34)
0.25 (0.43)
0.09 (0.29)
0.04 (0.28)
0.04 (0.20)
Unprotected water
1 if unprotected well water, 0 otherwise
0.14 (0.35)
0.10 (0.25)
0.13 (0.34)
0.08 (0.28)
0.20 (0.40)
0.01 (0.11)
Covered private toilet
1 if covered private toilet, 0 otherwise
0.16 (0.37)
0.17 (0.37)
0.04 (0.19)
-
0.16 (0.37)
-
Cover shared toilet
1 if covered shared toilet, 0 otherwise
0.61 (0.49)
0.62 (0.48)
0.25 (0.43)
-
0.05 (0.22)
-
VIP latrine private toilet
1 if VIP private toilet, 0 otherwise
0.02 (0.13)
0.08 (0.26)
0.05 (0.22)
0.06 (0.23)
0.64 (0.48)
0.09 (0.29)
Pit latrine
1 if pit latrine, 0 otherwise
-
-
0.48 (0.31)
0.76 (0.42)
Flush toilet
1 if flush toilet, 0 otherwise
0.12 (0.19)
0.42 (0.38)
0.13 (0.34)
Observations
242
263
873
1363
662
1,479
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Table 2. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regressions models in Uganda.
Variables+
2010
2012
OLS
Ridge
LASSO
OLS
Ridge
LASSO
Constant
1.66
1.78
1.77
1.09 (55.60)
1.98
1.70
Dwelling
0.40 (0.18)
0.16
0.11
0.22 (0.14)
0.08
0.13
Roof
-0.38 (0.33)
0.01
-
0.23 (0.73)
-0.27
-0.09
Floor
0.64 (0.24)
0.28
0.29
0.01 (0.09)
-0.08
-
External wall
0.32 (0.22)
0.28
0.29
0.40 (0.18)
0.29
0.37
Number of rooms
0.36 (0.18)
0.22
0.12
6.43 (2.34)
0.39
0.53
Electricity
0.60 (0.16)
0.38
0.49
0.50 (0.11)
0.42
0.49
Private tap water
2.36 (0.85)
0.94
1.15
0.29 (0.30)
0.31
0.20
Public tap water
-0.15 (0.41)
0.22
-
0.05 (0.24)
0.07
-
Bore hole water
-0.13 (0.30)
0.04
-
-0.58 (0.33)
-0.42
-0.56
Protected well water
0.02 (0.39)
-0.05
-
0.25 (0.26)
0.20
0.13
Unprotected water
-0.04 (0.33)
-0.01
-
-0.87 (0.36)
-0.54
-0.74
Covered private toilet
0.42 (0.79)
-0.13
-
0.63 (0.32)
0.17
0.21
Cover shared toilet
0.53 (0.75)
-0.02
-
0.40 (0.28)
0.02
0.04
VIP latrine toilet
0.22 (1.01)
0.09
-
-0.14 (0.45)
-0.34
-0.38
Flush toilet
0.62 (0.75)
0.06
-
1.29 (0.49)
0.86
0.87
R2
0.75
0.41
+ District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
https://doi.org/10.1371/journal.pone.0244953.t002
Table 3. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regressions models in Tanzania.
2014
2016
Variables+
OLS
Ridge
LASSO
OLS
Ridge
LASSO
Constant
1.65 (0.13)
1.82
1.68
1.34 (0.24)
1.77
1.33
Roof
-0.63 (0.11)
-0.53
-0.52
-0.73 (0.14)
-0.66
-0.72
Floor
-0.16 (0.07)
-0.21
-0.21
-0.28 (0.08)
-0.32
-0.28
External wall
0.42 (0.05)
0.40
0.44
-
0.11
-0.00
Number of rooms
0.66 (0.05)
0.60
0.61
0.80 (0.05)
0.72
0.80
Electricity
0.64 (0.05)
0.62
0.70
0.54 (0.05)
0.50
0.50
Private tap water
0.15 (0.09)
0.14
0.10
0.10 (0.05)
0.05
-
Public tap water
-0.15 (0.11)
-0.19
-
0.31 (0.09)
-0.15
-0.20
Protected well water
-0.27 (0.18)
-0.29
-0.13
-0.04 (0.12)
0.12
0.05
Unprotected water
-0.15 (0.12)
-0.16
-0.05
-
0.12
0.09
VIP latrine toilet
-0.18 (0.11)
-0.17
-0.04
0.89 (0.24)
0.32
0.80
Flush toilet
0.03 (0.11)
0.05
0.01
0.72 (0.22)
0.19
0.63
Pit latrine
0.14 (0.10)
0.15
0.10
0.49 (0.22)
-0.01
0.40
Private toilet
-0.16 (0.13)
-0.19
-0.07
-
-
-
Shared toilet
-0.31 (0.07)
-0.30
-0.22
-
-
-
R2
0.75
0.58
+District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
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the dependent variables. In Uganda, the variable estimates that were reduced to zero under
LASSO regression are roof (in the year 2010), floor (in the year 2012), public tap water, bore
hole water, protected well water, covered private toilet, covered shared toilet, VIP latrine, and
flush toilet (in the year 2010). In Tanzania, the estimated coefficient values of public tap water
(in the year 2014) and private tap water (in the year 2016) are reduced to zero. For Malawi, the
variables with zero estimated coefficients in the year 2014 under LASSO regression are exter-
nal wall, borehole water, protected water well, VIP and pit latrine type of toilet. Variables that
are reduced to zero in the year 2016 under LASSO estimation are public water tap, and VIP
latrine type of toilet.
Unlike OLS, Ridge, and LASSO, the other ML approaches (i.e. the Regression Tree, Bag-
ging, Random Forest, and Boosting) do not provide the estimated coefficients. With the
Regression Tree method, the prediction of the house rental values is done by using the mean
of the group at each node of the tree. For example, in Uganda, variables selected in the Regres-
sion Tree by rank are availability of electricity, and number of rooms (Fig 2). The figures of the
results for the rest of the Regression Trees for other countries and years are not presented here
in the interest of space. For Uganda, the variables selected in the Regression Tree in the year
2010 by rank are availability of electricity, floor, and number of rooms. Regression Tree is
highly criticized in that changing the data slightly brings substantial change in tree construc-
tion [41]. The variables used in the Regression Tree in Tanzania are electricity, number of
rooms, and external wall in the year 2014; and number of rooms, electricity, and dwelling in
the year 2016. In Malawi, variables such as electricity, private water tap and district 16 in 2014;
and electricity, flush toilet, and roof in 2016 are used in the Tree Regression.
As previously stated, the Bagging method is an extension of the Regression Tree. We con-
struct numerous trees through resampling multiple times from the same data (i.e. bootstrap-
ping) and then we average the entire prediction. In each Bagging, 500 trees are created using
all of the variables. Results from the Bagging are presented in Tables 5–7 for the three
Table 4. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regression models in Malawi.
Variables+
2014
2016
OLS
Ridge
LASSO
OLS
Ridge
LASSO
Constant
1.29 (0.21)
1.44
1.36
1.57 (0.25)
1.57
1.43
Dwelling
-
0.30
0.30
-0.01 (0.12)
0.06
0.01
Roof
1.11
0.18
0.12
0.34 (0.10)
0.29
0.30
Floor
-
-0.15
-0.11
-0.15 (0.06)
-0.15
-0.14
External wall
0.14 (0.13)
0.11
-
0.17 (0.12)
0.15
0.09
Number of rooms
0.50 (0.07)
0.42
0.42
0.41 (0.05)
0.40
0.40
Electricity
0.82 (0.08)
0.58
0.69
0.71 (0.05)
0.67
0.72
Private tap water
0.58 (0.18)
0.49
0.47
0.14 (0.20)
0.17
0.15
Public tap water
0.24 (0.09)
0.17
0.09
0.01 (0.20)
0.02
-
Bore hole water
-0.12 (0.19)
0.03
-
-0.22 (0.20)
-0.18
-0.18
Protected well water
0.06 (0.14)
0.05
-
-0.07 (0.22)
-0.08
-0.04
Unprotected water
0.55 (0.41)
0.41
0.09
-0.21 (0.28)
-0.17
-0.10
VIP latrine toilet
0.13 (0.13)
0.04
-
0.24 (0.15)
-0.07
-
Flush toilet
0.26 (0.17)
0.26
0.20
0.86 (0.16)
0.52
0.61
Pit latrine
-
-0.05
-
0.14 (0.14)
-0.18
-0.07
R2
0.75
0.65
+District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
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countries. The results from the Bagging regression are ordered according to their importance
in the prediction process. For example, in the year 2010 in Uganda, the four top most variables
used during the Bagging regression by rank are electricity, external wall, floor and number of
rooms (Table 5). The arrangement of variables varies by year and by country of analysis (see
Tables A1 and A2 in S1 Appendix).
Random Forest is similar to Bagging, but instead of averaging all the predictors, the
approach selects some of the predictors via random selection to perform the prediction.
Results of the Random Forest regressions for Uganda are shown in Table 6. The top four vari-
ables randomly selected under Random Forest in Uganda are electricity, external wall, floor
and district 20 in the year 2010 (Table 6); and are electricity, district 20, number of rooms and
flush type of toilet in the year 2012 (Table 6). Results of the Random Forest regressions for
Tanzania (Table A3 in S1 Appendix) and Malawi (Table A4 in S1 Appendix) are reported in
the S1 Appendix in the interest of space.
The results from the Boosting Regression, which is another extension to the Tree Regres-
sion, are presented in Table 7. The estimation output from the Boosting Regression are
arranged in order of their importance to the prediction process. For instance, in Uganda in the
year 2010, the top three variables used in Boosting by order of importance are private tap
water, electricity, and number of rooms; whereas the four variables that are not used for pre-
diction in the Boosting regression are VIP private latrine, flush toilet, and a district informa-
tion (Table 7). A number of variables are not used in the Boosting Regression of different
countries and in different years as shown in Tables A5 and A6 in the S1 Appendix.
In-sample prediction
The main strength of ML approaches is their predictive capability. Machine Learning
approaches outperform OLS regression, especially when the number of determinants is large
[53]. The Mean Squared Error and R Squared are two of the methods used to compare the pre-
diction performance between the ML approaches and the standard OLS regression. The Mean
Squared Error is used to compare the results of the ML approaches and the standard OLS
regression. The model with minimum average MSE of the predictions is considered as the best
Fig 2. Tree regression in Uganda for 2012.
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Table 5. List of explanatory variables by importance in predicting housing rental values using bagging regression in Uganda.
Variable+
Relative information
Variable
Relative information
2010
2012
Electricity
22.68
Electricity
28.51
External wall
12.20
Number of rooms
13.34
Floor
10.98
District 20
13.09
Number of rooms
10.09
Flush toilet
7.49
Private water tap
7.09
External wall
5.56
District 20
6.67
Floor
5.32
Dwelling
6.12
Dwelling
4.83
District 64
2.86
District 64
3.55
Public tap water
2.60
Unprotected well
3.53
Flush toilet
2.31
Private water tap
3.44
Borehole water
2.14
Borehole water
2.93
District 27
2.07
Public water tap
2.71
District 33
1.79
Shared toilet
2.65
Unprotected well
1.75
Private toilet
2.01
Private toilet
1.66
Protected well
2.00
Protected well
1.66
District 41
1.90
District 32
1.54
District 37
1.74
Shared toilet
1.54
VIP toilet
1.64
District 37
1.52
District 51
1.36
Roof
1.22
District 4
1.04
+ District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
https://doi.org/10.1371/journal.pone.0244953.t005
Table 6. List of explanatory variables by importance in predicting housing rental values using random forest regression in Uganda.
Variable+
Relative information
Variable
Relative information
2010
2012
Electricity
11.20
Electricity
7.89
External wall
8.46
District 20
4.43
Floor
6.83
Number of rooms
3.63
District 20
5.44
Flush toilet
3.08
Private tap water
3.87
Private water tap
2.63
Number of rooms
3.62
External wall
2.25
Dwelling
2.97
Floor
2.06
Public tap water
2.70
Unprotected water
1.99
Borehole water
1.93
Borehole water
1.58
Protected well
1.49
Public tap water
1.20
Private toilet
1.34
District 4
1.09
Roof
1.22
District 37
0.99
District 37
1.13
District 41
0.82
District 64
1.08
dwelling
0.72
District 37
1.00
Private toilet
0.49
District 55
0.91
Shared toilet
0.47
Flush toilet
0.79
Protected well
0.45
+ District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
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model for prediction. The MSE results for the ML approaches are presented as a proportion of
the MSE of the OLS model such that the MSE of the OLS model will be equal to 1. The results
of the in-sample prediction comparisons of these models is presented in Table 8.
An overall performance score is developed to rank the ML approaches in relation to the
OLS approach. The score is developed by adding the number of instances the MSE in each
year of analysis is lower than the MSE of the OLS model. Then, this number is divided by 6
(for a total of 6 comparisons with 3 countries and 2 years) and then multiplied by 100. The
score ranges from 0 to 100% and the higher the percentage, the better the performance. A 50%
threshold is used to determine whether a particular model outperformed the OLS predictions.
A score of 50% indicates that the model outperformed the OLS model in 3 out of the 6 datasets,
indicating that both models are equally preferred. The overall performance score is shown in
the last column of Table 8. Based on this score, Boosting, Bagging, Random Forest Regression
outperformed all other ML and OLS approaches for all the data sets. Ridge, LASSO and Tree
Regressions have been outperformed by the OLS in-sample predictions in all countries and all
years.
Out-of-sample prediction
As previously mentioned, ML approaches are believed to provide better out-of-sample predic-
tive values considering higher dimensionality of data structures. The results of out-of-sample
prediction performance of the models are presented in Tables 9–11.
Table 7. List of explanatory variables by importance in predicting housing rental values using boosting regression in Uganda.
Variable+
Relative information
Variable
Relative information
2010
2012
Private water tap
25.78
Electricity
24.00
Electricity
21.56
Private water
23.85
Number of rooms
18.45
Number of rooms
19.87
District 20
9.41
District 22
9.77
Public water tap
8.15
Public water tap
6.27
Protected well
5.72
Protected well
5.57
Dwelling
4.18
Dwelling
4.17
Floor
2.41
Floor
2.78
Shared toilet
1.82
External wall
1.70
External wall
1.36
Shared toilet
1.45
District 64
0.66
District 68
0.33
Private toilet
0.18
Private toilet
0.16
Borehole water
0.16
Uncovered latrine
0.05
Roof
0.09
Bore hole
0.02
Uncovered latrine
0.04
VIP shared latrine
0.01
VIP shared latrine
0.02
Unprotected well
0.01
Unprotected well
0.01
roof
0.00
VIP private latrine
0.00
VIP private latrine
0.00
Flush toilet
0.00
Flush toilet
0.00
District 1
0.00
District 1
0.00
District 2
0.00
+District fixed effect variables are used in the estimation of the models and the specific results for these variables are not reported in the Tables in the interest of space.
There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.
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Tables 9 and 10 contain results of the spatial lag model (SAR) and the spatial error model
(SEM) respectively. These tables present the standardized MSE values of the OLS and the ML
approaches. Overall, except Tree Regression, all ML methods are preferred to the OLS model
in predicting house rental values using an out-of-sample data set for all of the countries and
years. Boosting Regression is superior to OLS in terms of out-of-sample predictions in all of
the datasets. Ridge, LASSO, Bagging, and Forest Regression outperformed OLS in most of the
datasets.
An overall performance score is also developed for the out-of-sample predictions. The
results of such overall performance score comparisons are presented in the final columns of
Tables 9–11. Based on this score, Boosting is the top performer in terms of out-of-sample pre-
dictions, followed by Bagging, Random Forest and Ridge and LASSO Regressions. Unlike in
the in-sample predictions, Ridge and LASSO regressions performed better than OLS in the
out-of-sample predictions. Tree Regression is again the least performer in the group.
Conclusion and recommendation
Housing value is a major component of the household’s aggregate expenditure, a commonly
used metric for welfare analysis. Data shows that a significant proportion of households in a
typical household survey, adopted by the Word Bank are self-owned, and predicting the true
market price of housing service are crucial to obtain true assessment of economic well-being.
Table 8. In-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and years of analysis.
Uganda
Tanzania
Malawi
Overall performance score
2010
2012
2014
2016
2014
2016
OLS+
1.00
1.00
1.00
1.00
1.00
1.00
-
Ridge
1.03
1.01
1.01
1.01
1.01
1.01
0%
LASSO+ +
1.03
1.01
1.01
1.01
1.01
1.01
0%
Tree
0.95
0.98
1.06
1.59
1.13
1.07
33%
Bagging
0.94
0.93
0.97
0.68
0.91
0.98
100%
Forest
0.71
0.89
0.94
0.51
0.77
0.90
100%
Boosting
0.86
0.90
0.88
0.48
0.76
0.89
100%
+ OLS = Ordinary Least Squares
+ +LASSO = Least Absolute Shrinkage and Selection Operator.
https://doi.org/10.1371/journal.pone.0244953.t008
Table 9. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year, account-
ing spatial lag autocorrelation (SAR).
Uganda
Tanzania
Malawi
Overall performance score
2010
2012
2014
2016
2014
2016
OLS+
1.00
1.00
1.00
1.00
1.00
1.00
-
Ridge
0.94
0.98
0.99
0.96
0.95
1.01
83%
LASSO+ +
0.88
0.96
0.99
0.88
0.95
1.01
83%
Tree
0.83
0.86
1.11
1.59
1.12
1.06
33%
Bagging
0.78
0.83
0.97
1.28
0.87
0.91
83%
Forest
0.82
0.91
1.00
0.80
0.84
0.89
83%
Boosting
0.87
0.88
0.96
0.95
0.86
0.91
100%
+OLS = Ordinary Least Squares
+ +LASSO = Least Absolute Shrinkage and Selection Operator.
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Several Machine Learning approaches (Ridge, LASSO, Tree, Random Forest, Bagging, and
Boosting), in reference to hedonic pricing approach, are evaluated in this article for the pur-
pose of predicting the rental values of housing in household level survey data from three sub-
Saharan countries (Uganda, Tanzania, and Malawi).
Results from the OLS specifications and various machine-learning approaches used to esti-
mate the determinants of house rental values in Uganda, Tanzania, and Malawi are presented.
The significance of the explanatory variables in the OLS models are consistent across all the
data sets providing robust estimates for the determinants of house rental values in these coun-
tries. Most variables selected by all the ML approaches are similar with what the OLS regres-
sion identified as determinants of rental values: the number of rooms, availability of electricity,
private tap water, and toilet characteristics.
The Mean Squared Error (MSE) is used to compare the prediction performance of the ML
approaches and the OLS regressions. The model with minimum average MSE of the predic-
tions is considered as the best model for prediction. In general, Boosting is the best model in
predicting house values using out-of-sample data set for all the countries and all the years.
Tree is the least performer in the group. Although hedonic pricing models using OLS regres-
sion provide consistent and reliable predictions of house rental values, especially when the sta-
tistically properties (e.g. consistency and unbiasedness of estimated coefficients) of the
Table 10. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year, account-
ing for spatial error autocorrelation (SEM).
Uganda
Tanzania
Malawi
Overall performance score
2010
2012
2014
2016
2014
2016
OLS+
1.00
1.00
1.00
1.00
1.00
1.00
-
Ridge
0.93
0.92
1.01
0.89
0.96
1.01
66%
LASSO+ +
0.92
0.93
1.01
0.96
0.95
1.01
66%
Tree
0.88
0.86
1.13
1.30
1.13
1.05
33%
Bagging
0.86
0.76
0.99
0.89
0.88
0.92
100%
Forest
0.83
0.82
1.00
0.88
0.83
0.89
83%
Boosting
0.91
0.84
0.97
0.99
0.88
0.92
100%
+OLS = Ordinary Least Squares
+ +LASSO = Least Absolute Shrinkage and Selection Operator.
https://doi.org/10.1371/journal.pone.0244953.t010
Table 11. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year without
accounting for spatial autocorrelation.
Uganda
Tanzania
Malawi
Overall performance score
2010
2012
2014
2016
2014
2016
OLS+
1.00
1.00
1.00
1.00
1.00
1.00
-
Ridge
0.94
0.96
0.99
0.97
0.95
1.01
83%
LASSO+ +
0.89
0.92
1.00
0.88
0.95
1.01
83%
Tree
0.84
0.83
1.11
1.60
1.11
1.05
33%
Bagging
0.78
0.80
0.98
1.28
0.88
0.91
83%
Forest
0.82
0.88
1.00
0.81
0.84
0.88
83%
Boosting
0.88
0.85
0.96
0.96
0.87
0.91
100%
+OLS = Ordinary Least Squares
+ +LASSO = Least Absolute Shrinkage and Selection Operator.
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explanatory variables are of interest, most of the ML approaches tend to provide alternative
predictive performances, both in in-sample and out-of-sample datasets. Therefore, while pre-
dicting the rental value non-rented houses in household surveys, the ML methods could be
used as alternative approaches. With the availability of abundant data and better computing
power, ML methods provide viable alternative to predicting housing values in household sur-
veys. Finally, whether a particular ML model is preferred to hedonic pricing model for predict-
ing rental value of housing is driven by the particular dataset, and one has to empirically test
among the range of available methods.
The current work could be extended by including data set from multiple countries and
across time. Future work should also include evaluations of consumption aggregates and wel-
fare comparisons using house values estimated by the hedonic pricing and ML approaches.
Supporting information
S1 Appendix.
(DOCX)
Acknowledgments
Disclaimer: The authors wish to thank the anonymous reviewers and the academic editor of
the PLOS ONE Journal, Dr. Stefan Cristian Gherghina, for their valuable comments during the
review process. The findings and conclusions in this article are those of the authors and should
not be construed to represent any official USDA or US Government determination or policy.
This research was conducted largely prior to Dr. Zereyesus’s employment with USDA. All
errors and omissions are the responsibility of the authors.
Author Contributions
Data curation: Weldensie T. Embaye.
Formal analysis: Weldensie T. Embaye, Yacob Abrehe Zereyesus, Bowen Chen.
Methodology: Weldensie T. Embaye, Yacob Abrehe Zereyesus.
Writing – original draft: Weldensie T. Embaye, Yacob Abrehe Zereyesus.
Writing – review & editing: Weldensie T. Embaye, Yacob Abrehe Zereyesus.
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