1# RECORD 33b79cf36579ae3f85aa1db50b2d2c31cb4ba23a2# TITLE: Predicting the rental value of houses in household surveys in Tanzania, Uganda and Malawi: Evaluations of hedonic pricing and machine learning approaches3# YEAR: 2021.0 VENUE: PLoS ONE DOI: 10.1371/journal.pone.02449534# AUTHORS: Weldensie T. Embaye; Yacob A. Zereyesus; Bowen Chen5# PAGES: 20 CANDIDATE TABLE PAGES (1-based): [10, 11, 12, 14, 15, 17]6# 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.789===== PAGE 1 (score 4, numeric-paren 0, table-words 0, var-words 4) =====1011RESEARCH ARTICLE12Predicting the rental value of houses in13household surveys in Tanzania, Uganda and14Malawi: Evaluations of hedonic pricing and15machine learning approaches16Weldensie T. EmbayeID1*, Yacob Abrehe Zereyesus2, Bowen Chen3171 Department of Agricultural Economics, Kansas State University, Manhattan, Kansas, United State of18America, 2 International Trade and Development Branch, Markets and Trade Economics Division, U.S.19Department of Agriculture, Economic Research Service, Kansas City, MO, United State of America,203 Department of Agricultural and Consumer Economics, University of Illinois, Urbana, IL, United State of21America22* wembaye@ksu.edu23Abstract24Housing value is a major component of the aggregate expenditure used in the analyses of25welfare status of households in the development economics literature. Therefore, an accu-26rate estimation of housing services is important to obtain the value of housing in household27surveys. Data show that a significant proportion of households in a typical Living Standard28Measurement Survey (LSMS), adopted by the Word Bank and others, are self-owned. The29standard approach to predict the housing value for such surveys is based on the rental cost30of the house. A hedonic pricing applying an Ordinary Least Squares (OLS) method is nor-31mally used to predict rental values. The literature shows that Machine Learning (ML) meth-32ods, shown to uncover generalizable patterns based on a given data, have better predictive33power over OLS applied in other valuation exercises. We examined whether or not a class34of ML methods (e.g. Ridge, LASSO, Tree, Bagging, Random Forest, and Boosting) pro-35vided superior prediction of rental value of housing over OLS methods accounting for spatial36autocorrelations using household level survey data from Uganda, Tanzania, and Malawi,37across multiple years. Our results showed that the Machine Learning methods (Boosting,38Bagging, Forest, Ridge and LASSO) are the best models in predicting house values using39out-of-sample data set for all the countries and all the years. On the other hand, Tree regres-40sion underperformed relative to the various OLS models, over the same data sets. With the41availability of abundant data and better computing power, ML methods provide viable alter-42native to predicting housing values in household surveys.43Introduction44According to World Bank [1], the number of world population in poverty had declined from451.85 billion in 1990 to 767 million in 2013. The World Bank’s Living Standards Measurement46PLOS ONE47PLOS ONE | https://doi.org/10.1371/journal.pone.024495348February 11, 2021491 / 2050a111111111151a111111111152a111111111153a111111111154a111111111155OPEN ACCESS56Citation: Embaye WT, Zereyesus YA, Chen B57(2021) Predicting the rental value of houses in58household surveys in Tanzania, Uganda and59Malawi: Evaluations of hedonic pricing and60machine learning approaches. PLoS ONE 16(2):61e0244953. https://doi.org/10.1371/journal.62pone.024495363Editor: Stefan Cristian Gherghina, The Bucharest64University of Economic Studies, ROMANIA65Received: June 5, 201966Accepted: December 18, 202067Published: February 11, 202168Copyright: © 2021 Embaye et al. This is an open69access article distributed under the terms of the70Creative Commons Attribution License, which71permits unrestricted use, distribution, and72reproduction in any medium, provided the original73author and source are credited.74Data Availability Statement: We used the data75that comes from the nationally representative76Living Standards Measurement Study (LSMS) of77household level surveys for the three countries78compiled by the World Bank. It’s freely available79data. It’s found at: http://surveys.worldbank.org/80lsms/programs/integrated-surveys-agriculture-ISA.81Funding: The author(s) received no specific82funding for this work.838485===== PAGE 10 (score 117, numeric-paren 90, table-words 2, var-words 4) =====8687Of the significantly associated variables, for example, house rent increases with the increase88of number of rooms. If the number of rooms is increased by one, average monthly aggregate89house rent increases by about $0.36–6.43 in Uganda, $0.66–0.80 in Tanzania, and $0.41–0.5090in Malawi. The effect of electricity on house rent is also positive. Rental values of houses with91access to electricity are higher by $0.50–0.60 per month in Uganda, $0.54–0.64 in Tanzania,92and $0.71–0.82 in Malawi. These results imply the essence of electricity for household purposes93(e.g. lighting, cooking, etc.), mechanizations (farming and non-farming), and communication94and other purposes [50]. Private tap water is also positively associated with the value of house95rent in all the three countries. On average, a house rent in dwellings with a private water tap96are higher by $2.36 in the year 2010 in Uganda, by $0.15 in the year 2014 in Tanzania, and by97$0.58 in the year 2014 in Malawi. North and Griffin [51] found that households value in-house98piped water sources higher than any other house characteristics which is in agreement with99the results of the current work. Rental houses increase with access to clean water because more100households want to stay closer to clean water [52].101Mullainathan and Spiess [14] noted that machine learning algorithms are not built for102parameter estimation and hence the estimated regression coefficients are rarely consistent.103The results of the estimated coefficients from the ML approaches are estimated with this caveat104in mind. However, in general, results from the Ridge ML regression models show that most of105the estimated coefficients of the explanatory variables are smaller in magnitude compared to106the OLS coefficients (Tables 2–4). This is consistent with the literature [41] in that Ridge107regression shrinks the estimated coefficients and reduces the variance resulting in increased108predictive power of the covariates. Similarly, the LASSO regression approach shrinks the vari-109able estimates, and, in some cases, the coefficients are reduced to zero. When the estimated110variable coefficients are zero, then the variables may not play a role in predicting the value of111Table 1. Summary statistics of variables used in the house rental value predictions.112Variable113Definitions114Mean values (standard deviations)115Uganda116Tanzania117Malawi118201011920121202014121201612220141232016124Annual rent125Rent paid per month in dollar12622.18 (25.25)12723.46 (36.20)12817.89 (21.30)12922.65 (24.20)13020.34 (23.37)13117.39 (19.96)132Dwelling1331 if the room is located within a house, 0 otherwise1340.65 (0.46)1350.66 (0.46)1360.30 (0.40)1370.37 (0.48)1380.92 (0.28)1390.92 (0.27)140Roof1411 if roof type is mud, 0 otherwise1420.92 (0.27)1430.95 (0.26)1440.95 (0.25)1450.96 (0.25)1460.86 (0.35)1470.89 (0.31)148Floor1491 if floor is mud, 0 otherwise1500.68 (0.46)1510.34 (0.46)1520.22 (0.41)1530.91 (0.41)1540.80 (0.41)1550.77 (0.41)156External wall1571 if external wall is in mud, 0 otherwise1580.70 (0.45)1590.68 (0.45)1600.54 (0.45)1610.63 (0.48)1620.95 (0.21)1630.97 (0.18)164Number of rooms165Number of rooms rented1661.86 (1.12)1671.84 (1.16)1681.68 (0.91)1691.61 (0.92)1702.09 (0.97)1712.25 (0.98)172Electricity1731 if the house has electricity, 0 otherwise1740.35 (0.48)1750.37 (0.49)1760.53 (0.50)1770.59 (0.49)1780.42 (0.50)1790.44 (0.49)180Water sources181Private tap water1821 if private tap water source, 0 otherwise1830.03 (0.16)1840.07 (0.25)1850.12 (0.32)1860.56 (0.50)1870.14 (0.35)1880.43 (0.49)189Public tap water1901 if public tap water source, 0 otherwise1910.07 (0.26)1920.47 (0.49)1930.12 (0.33)1940.26 (0.44)1950.27 (0.44)1960.28 (0.45)197Bore hole water1981 if bore hole water source, 0 otherwise1990.47 (0.50)2000.19 (0.39)2010.07 (0.25)202-2030.31 (0.46)2040.23 (0.42)205Protected well water2061 if protected well water source, 0 otherwise2070.18 (0.39)2080.13 (0.34)2090.25 (0.43)2100.09 (0.29)2110.04 (0.28)2120.04 (0.20)213Unprotected water2141 if unprotected well water, 0 otherwise2150.14 (0.35)2160.10 (0.25)2170.13 (0.34)2180.08 (0.28)2190.20 (0.40)2200.01 (0.11)221Covered private toilet2221 if covered private toilet, 0 otherwise2230.16 (0.37)2240.17 (0.37)2250.04 (0.19)226-2270.16 (0.37)228-229Cover shared toilet2301 if covered shared toilet, 0 otherwise2310.61 (0.49)2320.62 (0.48)2330.25 (0.43)234-2350.05 (0.22)236-237VIP latrine private toilet2381 if VIP private toilet, 0 otherwise2390.02 (0.13)2400.08 (0.26)2410.05 (0.22)2420.06 (0.23)2430.64 (0.48)2440.09 (0.29)245Pit latrine2461 if pit latrine, 0 otherwise247-248-2490.48 (0.31)2500.76 (0.42)251Flush toilet2521 if flush toilet, 0 otherwise2530.12 (0.19)2540.42 (0.38)2550.13 (0.34)256Observations25724225826325987326013632616622621,479263https://doi.org/10.1371/journal.pone.0244953.t001264PLOS ONE265Evaluation of hedonic pricing and machine learning approaches266PLOS ONE | https://doi.org/10.1371/journal.pone.0244953267February 11, 202126810 / 20269270271===== PAGE 11 (score 90, numeric-paren 57, table-words 4, var-words 3) =====272273Table 2. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regressions models in Uganda.274Variables+27520102762012277OLS278Ridge279LASSO280OLS281Ridge282LASSO283Constant2841.662851.782861.772871.09 (55.60)2881.982891.70290Dwelling2910.40 (0.18)2920.162930.112940.22 (0.14)2950.082960.13297Roof298-0.38 (0.33)2990.01300-3010.23 (0.73)302-0.27303-0.09304Floor3050.64 (0.24)3060.283070.293080.01 (0.09)309-0.08310-311External wall3120.32 (0.22)3130.283140.293150.40 (0.18)3160.293170.37318Number of rooms3190.36 (0.18)3200.223210.123226.43 (2.34)3230.393240.53325Electricity3260.60 (0.16)3270.383280.493290.50 (0.11)3300.423310.49332Private tap water3332.36 (0.85)3340.943351.153360.29 (0.30)3370.313380.20339Public tap water340-0.15 (0.41)3410.22342-3430.05 (0.24)3440.07345-346Bore hole water347-0.13 (0.30)3480.04349-350-0.58 (0.33)351-0.42352-0.56353Protected well water3540.02 (0.39)355-0.05356-3570.25 (0.26)3580.203590.13360Unprotected water361-0.04 (0.33)362-0.01363-364-0.87 (0.36)365-0.54366-0.74367Covered private toilet3680.42 (0.79)369-0.13370-3710.63 (0.32)3720.173730.21374Cover shared toilet3750.53 (0.75)376-0.02377-3780.40 (0.28)3790.023800.04381VIP latrine toilet3820.22 (1.01)3830.09384-385-0.14 (0.45)386-0.34387-0.38388Flush toilet3890.62 (0.75)3900.06391-3921.29 (0.49)3930.863940.87395R23960.753970.41398+ 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.399There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.400https://doi.org/10.1371/journal.pone.0244953.t002401Table 3. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regressions models in Tanzania.40220144032016404Variables+405OLS406Ridge407LASSO408OLS409Ridge410LASSO411Constant4121.65 (0.13)4131.824141.684151.34 (0.24)4161.774171.33418Roof419-0.63 (0.11)420-0.53421-0.52422-0.73 (0.14)423-0.66424-0.72425Floor426-0.16 (0.07)427-0.21428-0.21429-0.28 (0.08)430-0.32431-0.28432External wall4330.42 (0.05)4340.404350.44436-4370.11438-0.00439Number of rooms4400.66 (0.05)4410.604420.614430.80 (0.05)4440.724450.80446Electricity4470.64 (0.05)4480.624490.704500.54 (0.05)4510.504520.50453Private tap water4540.15 (0.09)4550.144560.104570.10 (0.05)4580.05459-460Public tap water461-0.15 (0.11)462-0.19463-4640.31 (0.09)465-0.15466-0.20467Protected well water468-0.27 (0.18)469-0.29470-0.13471-0.04 (0.12)4720.124730.05474Unprotected water475-0.15 (0.12)476-0.16477-0.05478-4790.124800.09481VIP latrine toilet482-0.18 (0.11)483-0.17484-0.044850.89 (0.24)4860.324870.80488Flush toilet4890.03 (0.11)4900.054910.014920.72 (0.22)4930.194940.63495Pit latrine4960.14 (0.10)4970.154980.104990.49 (0.22)500-0.015010.40502Private toilet503-0.16 (0.13)504-0.19505-0.07506-507-508-509Shared toilet510-0.31 (0.07)511-0.30512-0.22513-514-515-516R25170.755180.58519+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.520There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.521https://doi.org/10.1371/journal.pone.0244953.t003522PLOS ONE523Evaluation of hedonic pricing and machine learning approaches524PLOS ONE | https://doi.org/10.1371/journal.pone.0244953525February 11, 202152611 / 20527528529===== PAGE 12 (score 47, numeric-paren 26, table-words 3, var-words 4) =====530531the dependent variables. In Uganda, the variable estimates that were reduced to zero under532LASSO regression are roof (in the year 2010), floor (in the year 2012), public tap water, bore533hole water, protected well water, covered private toilet, covered shared toilet, VIP latrine, and534flush toilet (in the year 2010). In Tanzania, the estimated coefficient values of public tap water535(in the year 2014) and private tap water (in the year 2016) are reduced to zero. For Malawi, the536variables with zero estimated coefficients in the year 2014 under LASSO regression are exter-537nal wall, borehole water, protected water well, VIP and pit latrine type of toilet. Variables that538are reduced to zero in the year 2016 under LASSO estimation are public water tap, and VIP539latrine type of toilet.540Unlike OLS, Ridge, and LASSO, the other ML approaches (i.e. the Regression Tree, Bag-541ging, Random Forest, and Boosting) do not provide the estimated coefficients. With the542Regression Tree method, the prediction of the house rental values is done by using the mean543of the group at each node of the tree. For example, in Uganda, variables selected in the Regres-544sion Tree by rank are availability of electricity, and number of rooms (Fig 2). The figures of the545results for the rest of the Regression Trees for other countries and years are not presented here546in the interest of space. For Uganda, the variables selected in the Regression Tree in the year5472010 by rank are availability of electricity, floor, and number of rooms. Regression Tree is548highly criticized in that changing the data slightly brings substantial change in tree construc-549tion [41]. The variables used in the Regression Tree in Tanzania are electricity, number of550rooms, and external wall in the year 2014; and number of rooms, electricity, and dwelling in551the year 2016. In Malawi, variables such as electricity, private water tap and district 16 in 2014;552and electricity, flush toilet, and roof in 2016 are used in the Tree Regression.553As previously stated, the Bagging method is an extension of the Regression Tree. We con-554struct numerous trees through resampling multiple times from the same data (i.e. bootstrap-555ping) and then we average the entire prediction. In each Bagging, 500 trees are created using556all of the variables. Results from the Bagging are presented in Tables 5–7 for the three557Table 4. Determinants of housing rental values based on Ordinary Least Squares (OLS), LASSO, and ridge regression models in Malawi.558Variables+55920145602016561OLS562Ridge563LASSO564OLS565Ridge566LASSO567Constant5681.29 (0.21)5691.445701.365711.57 (0.25)5721.575731.43574Dwelling575-5760.305770.30578-0.01 (0.12)5790.065800.01581Roof5821.115830.185840.125850.34 (0.10)5860.295870.30588Floor589-590-0.15591-0.11592-0.15 (0.06)593-0.15594-0.14595External wall5960.14 (0.13)5970.11598-5990.17 (0.12)6000.156010.09602Number of rooms6030.50 (0.07)6040.426050.426060.41 (0.05)6070.406080.40609Electricity6100.82 (0.08)6110.586120.696130.71 (0.05)6140.676150.72616Private tap water6170.58 (0.18)6180.496190.476200.14 (0.20)6210.176220.15623Public tap water6240.24 (0.09)6250.176260.096270.01 (0.20)6280.02629-630Bore hole water631-0.12 (0.19)6320.03633-634-0.22 (0.20)635-0.18636-0.18637Protected well water6380.06 (0.14)6390.05640-641-0.07 (0.22)642-0.08643-0.04644Unprotected water6450.55 (0.41)6460.416470.09648-0.21 (0.28)649-0.17650-0.10651VIP latrine toilet6520.13 (0.13)6530.04654-6550.24 (0.15)656-0.07657-658Flush toilet6590.26 (0.17)6600.266610.206620.86 (0.16)6630.526640.61665Pit latrine666-667-0.05668-6690.14 (0.14)670-0.18671-0.07672R26730.756740.65675+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.676There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.677https://doi.org/10.1371/journal.pone.0244953.t004678PLOS ONE679Evaluation of hedonic pricing and machine learning approaches680PLOS ONE | https://doi.org/10.1371/journal.pone.0244953681February 11, 202168212 / 20683684685===== PAGE 13 (score 19, numeric-paren 0, table-words 8, var-words 3) =====686687countries. The results from the Bagging regression are ordered according to their importance688in the prediction process. For example, in the year 2010 in Uganda, the four top most variables689used during the Bagging regression by rank are electricity, external wall, floor and number of690rooms (Table 5). The arrangement of variables varies by year and by country of analysis (see691Tables A1 and A2 in S1 Appendix).692Random Forest is similar to Bagging, but instead of averaging all the predictors, the693approach selects some of the predictors via random selection to perform the prediction.694Results of the Random Forest regressions for Uganda are shown in Table 6. The top four vari-695ables randomly selected under Random Forest in Uganda are electricity, external wall, floor696and district 20 in the year 2010 (Table 6); and are electricity, district 20, number of rooms and697flush type of toilet in the year 2012 (Table 6). Results of the Random Forest regressions for698Tanzania (Table A3 in S1 Appendix) and Malawi (Table A4 in S1 Appendix) are reported in699the S1 Appendix in the interest of space.700The results from the Boosting Regression, which is another extension to the Tree Regres-701sion, are presented in Table 7. The estimation output from the Boosting Regression are702arranged in order of their importance to the prediction process. For instance, in Uganda in the703year 2010, the top three variables used in Boosting by order of importance are private tap704water, electricity, and number of rooms; whereas the four variables that are not used for pre-705diction in the Boosting regression are VIP private latrine, flush toilet, and a district informa-706tion (Table 7). A number of variables are not used in the Boosting Regression of different707countries and in different years as shown in Tables A5 and A6 in the S1 Appendix.708In-sample prediction709The main strength of ML approaches is their predictive capability. Machine Learning710approaches outperform OLS regression, especially when the number of determinants is large711[53]. The Mean Squared Error and R Squared are two of the methods used to compare the pre-712diction performance between the ML approaches and the standard OLS regression. The Mean713Squared Error is used to compare the results of the ML approaches and the standard OLS714regression. The model with minimum average MSE of the predictions is considered as the best715Fig 2. Tree regression in Uganda for 2012.716https://doi.org/10.1371/journal.pone.0244953.g002717PLOS ONE718Evaluation of hedonic pricing and machine learning approaches719PLOS ONE | https://doi.org/10.1371/journal.pone.0244953720February 11, 202172113 / 20722723724===== PAGE 14 (score 15, numeric-paren 0, table-words 2, var-words 4) =====725726Table 5. List of explanatory variables by importance in predicting housing rental values using bagging regression in Uganda.727Variable+728Relative information729Variable730Relative information73120107322012733Electricity73422.68735Electricity73628.51737External wall73812.20739Number of rooms74013.34741Floor74210.98743District 2074413.09745Number of rooms74610.09747Flush toilet7487.49749Private water tap7507.09751External wall7525.56753District 207546.67755Floor7565.32757Dwelling7586.12759Dwelling7604.83761District 647622.86763District 647643.55765Public tap water7662.60767Unprotected well7683.53769Flush toilet7702.31771Private water tap7723.44773Borehole water7742.14775Borehole water7762.93777District 277782.07779Public water tap7802.71781District 337821.79783Shared toilet7842.65785Unprotected well7861.75787Private toilet7882.01789Private toilet7901.66791Protected well7922.00793Protected well7941.66795District 417961.90797District 327981.54799District 378001.74801Shared toilet8021.54803VIP toilet8041.64805District 378061.52807District 518081.36809Roof8101.22811District 48121.04813+ 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.814There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.815https://doi.org/10.1371/journal.pone.0244953.t005816Table 6. List of explanatory variables by importance in predicting housing rental values using random forest regression in Uganda.817Variable+818Relative information819Variable820Relative information82120108222012823Electricity82411.20825Electricity8267.89827External wall8288.46829District 208304.43831Floor8326.83833Number of rooms8343.63835District 208365.44837Flush toilet8383.08839Private tap water8403.87841Private water tap8422.63843Number of rooms8443.62845External wall8462.25847Dwelling8482.97849Floor8502.06851Public tap water8522.70853Unprotected water8541.99855Borehole water8561.93857Borehole water8581.58859Protected well8601.49861Public tap water8621.20863Private toilet8641.34865District 48661.09867Roof8681.22869District 378700.99871District 378721.13873District 418740.82875District 648761.08877dwelling8780.72879District 378801.00881Private toilet8820.49883District 558840.91885Shared toilet8860.47887Flush toilet8880.79889Protected well8900.45891+ 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.892There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.893https://doi.org/10.1371/journal.pone.0244953.t006894PLOS ONE895Evaluation of hedonic pricing and machine learning approaches896PLOS ONE | https://doi.org/10.1371/journal.pone.0244953897February 11, 202189814 / 20899900901===== PAGE 15 (score 14, numeric-paren 0, table-words 3, var-words 4) =====902903model for prediction. The MSE results for the ML approaches are presented as a proportion of904the MSE of the OLS model such that the MSE of the OLS model will be equal to 1. The results905of the in-sample prediction comparisons of these models is presented in Table 8.906An overall performance score is developed to rank the ML approaches in relation to the907OLS approach. The score is developed by adding the number of instances the MSE in each908year of analysis is lower than the MSE of the OLS model. Then, this number is divided by 6909(for a total of 6 comparisons with 3 countries and 2 years) and then multiplied by 100. The910score ranges from 0 to 100% and the higher the percentage, the better the performance. A 50%911threshold is used to determine whether a particular model outperformed the OLS predictions.912A score of 50% indicates that the model outperformed the OLS model in 3 out of the 6 datasets,913indicating that both models are equally preferred. The overall performance score is shown in914the last column of Table 8. Based on this score, Boosting, Bagging, Random Forest Regression915outperformed all other ML and OLS approaches for all the data sets. Ridge, LASSO and Tree916Regressions have been outperformed by the OLS in-sample predictions in all countries and all917years.918Out-of-sample prediction919As previously mentioned, ML approaches are believed to provide better out-of-sample predic-920tive values considering higher dimensionality of data structures. The results of out-of-sample921prediction performance of the models are presented in Tables 9–11.922Table 7. List of explanatory variables by importance in predicting housing rental values using boosting regression in Uganda.923Variable+924Relative information925Variable926Relative information92720109282012929Private water tap93025.78931Electricity93224.00933Electricity93421.56935Private water93623.85937Number of rooms93818.45939Number of rooms94019.87941District 209429.41943District 229449.77945Public water tap9468.15947Public water tap9486.27949Protected well9505.72951Protected well9525.57953Dwelling9544.18955Dwelling9564.17957Floor9582.41959Floor9602.78961Shared toilet9621.82963External wall9641.70965External wall9661.36967Shared toilet9681.45969District 649700.66971District 689720.33973Private toilet9740.18975Private toilet9760.16977Borehole water9780.16979Uncovered latrine9800.05981Roof9820.09983Bore hole9840.02985Uncovered latrine9860.04987VIP shared latrine9880.01989VIP shared latrine9900.02991Unprotected well9920.01993Unprotected well9940.01995roof9960.00997VIP private latrine9980.00999VIP private latrine10000.001001Flush toilet10020.001003Flush toilet10040.001005District 110060.001007District 110080.001009District 210100.001011+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.1012There are 66 districts, 9 districts, and 32 districts included in the data from Uganda, Tanzania, and Malawi, respectively.1013https://doi.org/10.1371/journal.pone.0244953.t0071014PLOS ONE1015Evaluation of hedonic pricing and machine learning approaches1016PLOS ONE | https://doi.org/10.1371/journal.pone.02449531017February 11, 2021101815 / 20101910201021===== PAGE 16 (score 13, numeric-paren 0, table-words 2, var-words 1) =====10221023Tables 9 and 10 contain results of the spatial lag model (SAR) and the spatial error model1024(SEM) respectively. These tables present the standardized MSE values of the OLS and the ML1025approaches. Overall, except Tree Regression, all ML methods are preferred to the OLS model1026in predicting house rental values using an out-of-sample data set for all of the countries and1027years. Boosting Regression is superior to OLS in terms of out-of-sample predictions in all of1028the datasets. Ridge, LASSO, Bagging, and Forest Regression outperformed OLS in most of the1029datasets.1030An overall performance score is also developed for the out-of-sample predictions. The1031results of such overall performance score comparisons are presented in the final columns of1032Tables 9–11. Based on this score, Boosting is the top performer in terms of out-of-sample pre-1033dictions, followed by Bagging, Random Forest and Ridge and LASSO Regressions. Unlike in1034the in-sample predictions, Ridge and LASSO regressions performed better than OLS in the1035out-of-sample predictions. Tree Regression is again the least performer in the group.1036Conclusion and recommendation1037Housing value is a major component of the household’s aggregate expenditure, a commonly1038used metric for welfare analysis. Data shows that a significant proportion of households in a1039typical household survey, adopted by the Word Bank are self-owned, and predicting the true1040market price of housing service are crucial to obtain true assessment of economic well-being.1041Table 8. In-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and years of analysis.1042Uganda1043Tanzania1044Malawi1045Overall performance score1046201010472012104820141049201610502014105120161052OLS+10531.0010541.0010551.0010561.0010571.0010581.001059-1060Ridge10611.0310621.0110631.0110641.0110651.0110661.0110670%1068LASSO+ +10691.0310701.0110711.0110721.0110731.0110741.0110750%1076Tree10770.9510780.9810791.0610801.5910811.1310821.07108333%1084Bagging10850.9410860.9310870.9710880.6810890.9110900.981091100%1092Forest10930.7110940.8910950.9410960.5110970.7710980.901099100%1100Boosting11010.8611020.9011030.8811040.4811050.7611060.891107100%1108+ OLS = Ordinary Least Squares1109+ +LASSO = Least Absolute Shrinkage and Selection Operator.1110https://doi.org/10.1371/journal.pone.0244953.t0081111Table 9. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year, account-1112ing spatial lag autocorrelation (SAR).1113Uganda1114Tanzania1115Malawi1116Overall performance score1117201011182012111920141120201611212014112220161123OLS+11241.0011251.0011261.0011271.0011281.0011291.001130-1131Ridge11320.9411330.9811340.9911350.9611360.9511371.01113883%1139LASSO+ +11400.8811410.9611420.9911430.8811440.9511451.01114683%1147Tree11480.8311490.8611501.1111511.5911521.1211531.06115433%1155Bagging11560.7811570.8311580.9711591.2811600.8711610.91116283%1163Forest11640.8211650.9111661.0011670.8011680.8411690.89117083%1171Boosting11720.8711730.8811740.9611750.9511760.8611770.911178100%1179+OLS = Ordinary Least Squares1180+ +LASSO = Least Absolute Shrinkage and Selection Operator.1181https://doi.org/10.1371/journal.pone.0244953.t0091182PLOS ONE1183Evaluation of hedonic pricing and machine learning approaches1184PLOS ONE | https://doi.org/10.1371/journal.pone.02449531185February 11, 2021118616 / 20118711881189===== PAGE 17 (score 15, numeric-paren 0, table-words 2, var-words 3) =====11901191Several Machine Learning approaches (Ridge, LASSO, Tree, Random Forest, Bagging, and1192Boosting), in reference to hedonic pricing approach, are evaluated in this article for the pur-1193pose of predicting the rental values of housing in household level survey data from three sub-1194Saharan countries (Uganda, Tanzania, and Malawi).1195Results from the OLS specifications and various machine-learning approaches used to esti-1196mate the determinants of house rental values in Uganda, Tanzania, and Malawi are presented.1197The significance of the explanatory variables in the OLS models are consistent across all the1198data sets providing robust estimates for the determinants of house rental values in these coun-1199tries. Most variables selected by all the ML approaches are similar with what the OLS regres-1200sion identified as determinants of rental values: the number of rooms, availability of electricity,1201private tap water, and toilet characteristics.1202The Mean Squared Error (MSE) is used to compare the prediction performance of the ML1203approaches and the OLS regressions. The model with minimum average MSE of the predic-1204tions is considered as the best model for prediction. In general, Boosting is the best model in1205predicting house values using out-of-sample data set for all the countries and all the years.1206Tree is the least performer in the group. Although hedonic pricing models using OLS regres-1207sion provide consistent and reliable predictions of house rental values, especially when the sta-1208tistically properties (e.g. consistency and unbiasedness of estimated coefficients) of the1209Table 10. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year, account-1210ing for spatial error autocorrelation (SEM).1211Uganda1212Tanzania1213Malawi1214Overall performance score1215201012162012121720141218201612192014122020161221OLS+12221.0012231.0012241.0012251.0012261.0012271.001228-1229Ridge12300.9312310.9212321.0112330.8912340.9612351.01123666%1237LASSO+ +12380.9212390.9312401.0112410.9612420.9512431.01124466%1245Tree12460.8812470.8612481.1312491.3012501.1312511.05125233%1253Bagging12540.8612550.7612560.9912570.8912580.8812590.921260100%1261Forest12620.8312630.8212641.0012650.8812660.8312670.89126883%1269Boosting12700.9112710.8412720.9712730.9912740.8812750.921276100%1277+OLS = Ordinary Least Squares1278+ +LASSO = Least Absolute Shrinkage and Selection Operator.1279https://doi.org/10.1371/journal.pone.0244953.t0101280Table 11. Out-of-sample prediction performances based on standardized mean squared errors of predicting housing rental values by country and by year without1281accounting for spatial autocorrelation.1282Uganda1283Tanzania1284Malawi1285Overall performance score1286201012872012128820141289201612902014129120161292OLS+12931.0012941.0012951.0012961.0012971.0012981.001299-1300Ridge13010.9413020.9613030.9913040.9713050.9513061.01130783%1308LASSO+ +13090.8913100.9213111.0013120.8813130.9513141.01131583%1316Tree13170.8413180.8313191.1113201.6013211.1113221.05132333%1324Bagging13250.7813260.8013270.9813281.2813290.8813300.91133183%1332Forest13330.8213340.8813351.0013360.8113370.8413380.88133983%1340Boosting13410.8813420.8513430.9613440.9613450.8713460.911347100%1348+OLS = Ordinary Least Squares1349+ +LASSO = Least Absolute Shrinkage and Selection Operator.1350https://doi.org/10.1371/journal.pone.0244953.t0111351PLOS ONE1352Evaluation of hedonic pricing and machine learning approaches1353PLOS ONE | https://doi.org/10.1371/journal.pone.02449531354February 11, 2021135517 / 20135613571358===== PAGE 18 (score 3, numeric-paren 0, table-words 0, var-words 3) =====13591360explanatory variables are of interest, most of the ML approaches tend to provide alternative1361predictive performances, both in in-sample and out-of-sample datasets. Therefore, while pre-1362dicting the rental value non-rented houses in household surveys, the ML methods could be1363used as alternative approaches. With the availability of abundant data and better computing1364power, ML methods provide viable alternative to predicting housing values in household sur-1365veys. Finally, whether a particular ML model is preferred to hedonic pricing model for predict-1366ing rental value of housing is driven by the particular dataset, and one has to empirically test1367among the range of available methods.1368The current work could be extended by including data set from multiple countries and1369across time. Future work should also include evaluations of consumption aggregates and wel-1370fare comparisons using house values estimated by the hedonic pricing and ML approaches.1371Supporting information1372S1 Appendix.1373(DOCX)1374Acknowledgments1375Disclaimer: The authors wish to thank the anonymous reviewers and the academic editor of1376the PLOS ONE Journal, Dr. Stefan Cristian Gherghina, for their valuable comments during the1377review process. The findings and conclusions in this article are those of the authors and should1378not be construed to represent any official USDA or US Government determination or policy.1379This research was conducted largely prior to Dr. Zereyesus’s employment with USDA. All1380errors and omissions are the responsibility of the authors.1381Author Contributions1382Data curation: Weldensie T. Embaye.1383Formal analysis: Weldensie T. Embaye, Yacob Abrehe Zereyesus, Bowen Chen.1384Methodology: Weldensie T. Embaye, Yacob Abrehe Zereyesus.1385Writing – original draft: Weldensie T. Embaye, Yacob Abrehe Zereyesus.1386Writing – review & editing: Weldensie T. Embaye, Yacob Abrehe Zereyesus.1387References13881.1389Worldbank. Poverty: overview [Internet]. 2016 [cited 2017 Oct 14]. Available from: https://www.1390worldbank.org/en/topic/poverty/overview13912.1392Worldbank. Living Standards Measurement Study (LSMS) Generating relevant data for policy makers1393and the research community. 2009; Available from: https://microdata.worldbank.org/index.php/catalog/1394lsms/about%0D13953.1396Deaton A. Household surveys, consumption, and the measurement of poverty. Econ Syst Res. 2003;139715(2):135–59.13984.1399Deaton A, Zaidi S. Guidelines for Constructing Consumption Aggregates For Welfare Analysis. World1400Bank. 2002;1–107.14015.1402Zereyesus YA, Ross KL, Amanor-Boadu V, Dalton TJ. Baseline Feed the Future Indicators for Northern1403Ghana 2012 Monitoring, Evaluation and Technical Support Services (METSS). 2014.14046.1405Straszheim M. Hedonic Estimation of Housing Market Prices: A Further Comment Author (s): Mahlon1406Straszheim Source: The Review of Economics and Statistics, Vol. 56, No. 3 (Aug., 1974), pp. 404–4061407Published by: The MIT Press Stable URL: http://www.jstor.or. Rev Lit Arts Am. 1974;56(3):404–6.14087.1409Balca´zar CF, Ceriani L, Olivieri S, Ranzani M. Rent-Imputation for Welfare Measurement: A Review of1410Methodologies and Empirical Findings. Rev Income Wealth. 2017; 63(4):881–98.1411PLOS ONE1412Evaluation of hedonic pricing and machine learning approaches1413PLOS ONE | https://doi.org/10.1371/journal.pone.02449531414February 11, 2021141518 / 201416