1# RECORD b922ab81201881b47779769df9e76de174e13df72# TITLE: Comparing traditional and machine learning techniques in apartments mass appraisal in Fortaleza, Brazil3# YEAR: 2025.0 VENUE: Aestimum DOI: 10.36253/aestim-153444# AUTHORS: Antônio Augusto Ferreira de Oliveira; Fabián Reyes-Bueno; M. A. Stumpf González; Everton Nunes da Silva5# PAGES: 18 CANDIDATE TABLE PAGES (1-based): [7, 16, 17, 18]6# ABSTRACT: Mass appraisal has significant applications, such as urban planning, real estate appraisal, and property tax. Due to the challenges of analyzing massive models, they are often developed using semi-automatic assessment methods and machine learning techniques. This article explores different appraisal model methods that utilize statistics and machine learning. It also looks at incorporating spatial information to see if the chosen method can effectively capture the typical spatial dependency of the real estate market. This can help reduce the spatial autocorrelation observed in the residuals. The study compared nine machine learning methods with traditional statistical approaches using a dataset of over 43,000 apartments in Fortaleza, Brazil. The results of the machine learning algorithms were similar. The XGBoost minimized spatial autocorrelation. The easiest interpretations were with MRA, M5P, and MARS techniques. Although, these techniques had the greatest residual spatial autocorrelations. There is a trade-off between the methods, depending on whether the aim is to improve accuracy or provide a clear explanation for property taxation.789===== PAGE 1 (score 5, numeric-paren 0, table-words 0, var-words 5) =====1011Aestimum 85: 21-38, 202412Firenze University Press 13www.fupress.com/ceset14ISSN 1592-6117 (print) | ISSN 1724-2118 (online) | DOI: 10.36253/aestim-15344 15A E S T I M U M16CENTRO STUDI DI ESTIMO E DI ECONOMIA TERRITORIALE - Ce.S.E.T.17Citation: Oliveira, A. A. F., Reyes-18Bueno, F., González, M. A. S. & 19Silva, E. (2024). Comparing traditional 20and machine learning techniques in 21apartments mass appraisal in For-22taleza, Brazil. Aestimum 85: 21-38. doi: 2310.36253/aestim-15344 24Received: November 15, 202325Accepted: July 2, 202426Published: February 14, 202527© 2024 Author(s). This is an open 28access, peer-reviewed article pub-29lished by Firenze University Press 30(https://www.fupress.com) and distrib-31uted, except where otherwise noted, 32under the terms of the CC BY 4.0 33License for content and CC0 1.0 Uni-34versal for metadata.35Data Availability Statement: The 36datasets used and/or analyzed during 37the current study are available from 38the corresponding author on reason-39able request.40Conflicts of Interest: The authors 41declare no conflict of interest. The 42funders had no role in the design of 43the study; in the collection, analyses, 44or interpretation of data; in the writing 45of the manuscript, or in the decision to 46publish the results.47ORCID:48AAFO: 0000-0003-3890-421949FRB: 0000-0002-5646-026350MASG: 0000-0002-1975-002651EdS: 0000-0001-9724-838452Comparing traditional and machine learning 53techniques in apartments mass appraisal in 54Fortaleza, Brazil55Antônio Augusto Ferreira de Oliveira1, Fabián Reyes-Bueno2, Marco 56Aurelio Stumpf González3,*, Everton da Silva4571 Municipal treasury auditor of Fortaleza, Brazil 582 Facultad de Ciencias Exactas y Naturales, Universidad Técnica Particular de Loja, Loja, 59Ecuador603 Polytechnic School, Universidade do Vale do Rio dos Sinos, São Leopoldo, Brazil614 Geosciences Department, Universidade Federal de Santa Catarina, Florianópolis, Brazil62E-mail: augusto.oliveira@sefin.fortaleza.ce.gov.br; frreyes@utpl.edu.ec; mgonzalez@63unisinos.br; everton.silva@ufsc.br64*Corresponding author65Abstract. Mass appraisal has significant applications, such as urban planning, real 66estate appraisal, and property tax. Due to the challenges of analyzing massive mod-67els, they are often developed using semi-automatic assessment methods and machine 68learning techniques. This article explores different appraisal model methods that utilize 69statistics and machine learning. It also looks at incorporating spatial information to see 70if the chosen method can effectively capture the typical spatial dependency of the real 71estate market. This can help reduce the spatial autocorrelation observed in the resid-72uals. The study compared nine machine learning methods with traditional statistical 73approaches using a dataset of over 43,000 apartments in Fortaleza, Brazil. The results 74of the machine learning algorithms were similar. The XGBoost minimized spatial auto-75correlation. The easiest interpretations were with MRA, M5P, and MARS techniques. 76Although, these techniques had the greatest residual spatial autocorrelations. There is a 77trade-off between the methods, depending on whether the aim is to improve accuracy 78or provide a clear explanation for property taxation.79Keywords: semi-automatic assessment methods, mass appraisal techniques, machine 80learning.81JEL codes: O18, R33.821. INTRODUCTION83The real estate market is a segment of the economy, and as such, the 84importance of traded goods is measured through the sales prices reached 85because of buyer and seller agreements. This market presents macro and 86microeconomic aspects. Macroeconomic aspects are related to government 87decisions, the conduct of the economy, international influences, interest rates, 888990===== PAGE 7 (score 33, numeric-paren 0, table-words 2, var-words 25) =====91922793Comparing traditional and machine learning techniques in apartments mass appraisal in Fortaleza, Brazil94sion Splines (MARS) and M5 pruned (M5P); Deep 95Learning; Ensemble Decision Trees, like Random Forest 96(RF); Quantile Random Forest (QRF); Gradient Boosting 97Machine (GBM) and its optimized implementations such 98as XGBoost, CATBoost, and LightGBM. All of them are 99essential alternatives. 100In general, ML models provide better accuracy in 101their predictions than hedonic pricing models and their 102variants, as long as they are trained with a large vol-103ume of high-quality data that is representative of the 104population under study. They are capable of identifying 105complex non-linear patterns that traditional methods 106may not capture. They have high scalability for deploy-107ment in environments that require quick and accurate 108responses, such as those in governmental property taxa-109tion departments. On the other hand, such models are 110known as “black boxes” because they are difficult to 111interpret, making it impossible in some cases to directly 112extract the marginal contribution of each explanatory 113variable to the observed price under “ceteris paribus” 114conditions. Additionally, ML models can overfit the 115training data, losing the ability to generalize to new data 116(overfitting).1173.3.3. Decision trees118In direct words, a Decision Tree (DT) is a non-119parametric supervised learning approach used in sta-120tistics and machine learning to develop classification 121and regression as a predictive model to conclude a set 122of observations by partitioning the feature space (if-else 123conditions). Tree models in which the target variable 124can assume a discrete set of values are called classifica-125tion trees. In these structures, leaves are class labels, 126and branches represent connections of features that 127lead to those class labels. Decision trees where the tar-128get variable can be continuous (usually real numbers) 129Table 2. Description and descriptive statistics of the predictor variables assessed in the models.130Variable131Description132Min133Median134Mean135Max136age137Age in years13801395.7414010.6014166.76142distpv143Nearest distance to main urban amenities in m1441145272.47146363.461472,795.92148distassp149Distance to the nearest precarious settlement1501151224.15152282.461531,379.06154distsh155Distance to the nearest shopping center in m15611571,136.341581,367.981596,231.17160distbm161Distance to the beach (north of the city) in m1621.791634,144.861645,185.5916516,442.75166income167The mean income of the head of the family in Brazilian minimum wage1680.631695.741707.1317129.96172landarea173The total area of the land parcel in m²1741431754,580.521766,286.201775,7718178maxind179Maximum allowed floor area ratio (FAR)1800.471812.51822.321833184parcelarea185The proportional area of a land plot in m² related to the apartment1864.518743.4618877.8018940,012.5190privarea191Private property size in m²1923019376.6619496.58195883.32196test197Length in m of the front of the land parcel.1985.51996120073.60201379.32202totalarea203Total area in m²20432.16205126.97206152.562072,278.95208vertdens209Verticalization density measure. Indicates the concentration of unities in 210the neighborhood2110.012120.15872130.242140.9982215xcen216X coordinates in UTM of the normalized geographic position217-1.062180.282190.172200.98221ycen222Y coordinate in UTM of the normalized geographic position223-0.982240.42250.252260.91227bedroom228Number of bedrooms2291230323132327233floor234Apartment’ floor23502365237723831239garage240Number of garages24102422243224415245nfloors246Total number of floors in the building2472248142491325032251elev252Presence of one or more elevators - dummy253025412550 or 12561257pool258Presence of swimming pool - dummy259026012610 or 12621263lastfloor264Property is on top floor position - dummy265026602670 or 12681269standardi270Finishing standard - set of dummies (1-rustic, 2-proletarian, 2713-economical, 4-simple, 5-medium, 6-superior, 7-fine, 8-luxury).272 273 2741-8275 276yeari277Real estate transaction year - set of dummies for 2017-2021278 279 2800 or 1281 282sale283Effective sale – dummy284 285 2860 or 1287 288listing289List price – dummy: 0 = sale’s price; 1 = asking price290 291 2920 or 1293 294Source: Authors.295296297===== PAGE 8 (score 4, numeric-paren 0, table-words 0, var-words 4) =====29829928300Antônio Augusto Ferreira de Oliveira et al.301are called regression trees. DT has the advantage of 302being more intuitive and easier to interpret than other 303machine learning models. Depending on the number of 304nodes and depth, each decision criterion chosen by the 305algorithm can be easily visualized graphically, facilitat-306ing the understanding of the entire decision-making 307process. However, they can easily overfit the training 308data, capturing noise and leading to poor performance 309on new data. Pruning and ensemble decision trees (e.g., 310Random Forest and XGBoost) are techniques necessary 311to mitigate this problem. The more robust algorithms 312described below were used in this research instead of 313this approach.3143.3.4. Multiple adaptive regression splines315Multiple Adaptive Regression Splines (MARS) is a 316decision tree that combines recursive partitioning with 317spline fitting to model the relationship between a set 318of input (predictive) variables and dependent variables 319(Friedman, 1991; Friedman and Roosen, 1995). Data is 320modeled by separate piecewise linear segments (splines) 321of differing slopes known as essential functions. MARS 322generates basis functions by searching stepwise, where 323an adaptive regression algorithm selects the locations of 324the knot (endpoints of the segment) (Reyes-Bueno et al., 3252018). The regions between submarkets are continuous. 326Some recent studies using MARS include Al-Qawas-327mi (2022), Reyes-Bueno et al. (2018), and Wang and Li 328(2019). For the model used in MARS, the best combina-329tion of hyperparameters was obtained using the “Rand-330omizedSearchCV” method with ten folds for cross-vali-331dation, with a maximum degree of interaction (degree) 332from 1 to 3, and a maximum number of terms in the 333pruned model (“nprune”) from 1 to 100. The strategy to 334evaluate the performance was the lowest RMSE. The best 335results were obtained with a “nprune” of 21 and a degree 336of 1. Although MARS can capture non-linear relation-337ships more flexibly than M5P, the resulting model still 338lacks the ability to capture complex interactions com-339pared to ensemble techniques due to its reliance on local 340linear fits.3413.3.5. M5 pruned342M5 pruned (M5P) is a model tree algorithm devel-343oped to predict continuous variables by applying regres-344sion that can exploit the local linearity of the data. For 345this purpose, model trees generate subsets by choos-346ing attributes to minimize the intra-subset variation in 347the class values down each branch and maximize the 348expected error reduction (Zurada et al., 2011). There are 349three significant steps when applying the M5P meth-350odology: (1) tree construction, (2) tree pruning, and (3) 351tree smoothing (Reyes-Bueno et al., 2018). The regions 352between submarkets are often discrete. For the model 353used in this research, the best combination of hyperpa-354rameters was obtained using the “RandomizedSearch-355CV” method with ten folds for cross-validation, with a 356range of minimum number of instances from 0 to 1000. 357The strategy to evaluate the performance was the lowest 358RAE. The best results were 50 as the minimum num-359ber of cases per leaf. Inside subM5P generates segments 360and exploits the local linearity of the data within those 361segments, which can be a limitation in situations where 362the relationships between variables are not locally lin-363ear, as it does not adequately capture the true nature of 364the interactions between variables. Within each submar-365ket, M5P exploits the local linearity of the data, which 366can be a limitation in situations where the relationships 367between variables are not locally linear, as it does not 368adequately capture the true nature of the interactions 369among variables.3703.3.6. Random Forests371Random forests (RF) or random decision forests are 372an ensemble learning method for classification, regres-373sion, and other tasks that operate by building several 374decision trees at training time. For classification tasks, 375the output of the RF is the class selected by most trees. 376For regression tasks, the mean or average prediction of 377the individual trees is returned. Random decision for-378ests correct for decision trees’ habit of overfitting to their 379training set. RF outperforms regular decision trees, but 380their accuracy is lower than gradient-boosted trees. Data 381characteristics, however, can affect their performance. 382Random Forests, like other machine learning and deep 383learning algorithms, are often named “black box” mod-384els because they generate reasonable predictions for 385a wide range of data while requiring little configura-386tion. However, the analyst cannot understand the logic 387behind them.388RF is a combination of predictor trees such that each 389tree depends on the values of a random vector assessed 390independently and with the same distribution for each 391of these. It is a substantial modification of bagging that 392builds a vast collection of uncorrelated trees and aver-393ages them. The method combined the idea of applying 394the general technique of bootstrap aggregating (bag-395ging) technique to develop trees and the random subset 396of attributes to build a collection of decision trees with 397controlled bias and variance. The selection of a random 398399400===== PAGE 16 (score 80, numeric-paren 53, table-words 5, var-words 6) =====40140236403Antônio Augusto Ferreira de Oliveira et al.404APPENDIX A. RESULTS OF MRA, SER, AND MARS MODELS.405Table A1. Regression Results for MRA and SER models406Variable407Coefficients408Variable409Coefficients410MRA (OLS)411SER (GMM)412MRA (OLS)413SER (GMM)414intercept4158.8663 *4168.8529 *417bedroom4180.0084 (0.0015)4190.0163 *420parcelarea421-1.24E-05 *422-1.26E-05 *423garage4240.0317 *4250.0305 *426income4270.0120 *4280.0118 *429ln_privarea4300.3680 *4310.3670 *432vertdens4330.1830 *4340.1919 *435ln_totalarea4360.3021 *4370.3061 *438distpv439-8.40E-06 (0.0137)440-1.09E-05 (0.1556)441lastfloor4420.0689 *4430.0799 *444distassp4454.88E-05 *4463.93E-05 *447floor4480.0065 *4490.0065 *450distbm451-1.34E-05 *452-1.49E-05 *453age454-0.0097 *455-0.0098 *456elev4570.0372 *4580.0488 *459a20184600.0095 *4610.0026 (0.3697)462pool4630.1085 *4640.0938 *465a20194660.0075 (0.0335)4670.0003 (0.9242)468nfloors4690.0104 *4700.0103 *471a20204720.0230 *4730.0187 *474standard34750.0989 *4760.1833 *477a20214780.0792 *4790.0719 *480standard44810.3631 *4820.3979 *483sale484-0.0626 *485-0.0759 *486standard54870.5058 *4880.5163 *489listing4900.0528 *4910.0407 *492standard64930.6890 *4940.6667 *495Lambda (λ)496n/a4970.6389 *498standard74990.8583 *5000.8574 *501R-squared5020.93865030.9380504standard85051.1789 *5061.1219 *507Observations50832,68850932,688510Source: Authors. Notes: The dependent variable is the natural logarithm from price. *Shows P-values < 0.01; otherwise, values in parenthe-511ses are the P-values.512Table A2. Regression Results for MARS model513Variable514Coefficients515Variable516Coefficients517Variable518Coefficients519Intercept5207.7533639521h(14.68-income)522-0.0090807523h(1-floor)524-0.0329661525districtPAPICU526-0.1488743527h(income-14.68)5280.0087215529h(floor-1)5300.0058125531pool5320.1010973533h(0.0908-vertdens)534-1.8229510535h(27.56-age)5360.0175039537of5380.1154500539h(vertdens-0.0908)5400.1308400541h(age-27.56)542-0.0016117543h(2020-year)544-0.0081761545h(distbm-125.04)5460.0032095547h(4.8820-ln_privarea)548-0.4324477549h(year-2020)5500.0691490551h(1708.96-distbm)5520.0033438553h(ln_privarea-4.8820)5540.6268375555h(0.38-ycen)556-0.1600824557h(distbm-1708.96)558-0.0032261559h(4.40769-ln_areaed)560-0.2502487561h(ycen-0.38)562-0.4244964563h(18-pvtp)564-0.0235340565h(ln_areaed-4.40769)5660.2851514567h(53.31-cotat)568-0.0051410569h(2-garage)570-0.0236326571h(cotat-53.31)572-0.0000217573h(garage-2)5740.0693027575Source: Authors.576577578===== PAGE 17 (score 26, numeric-paren 11, table-words 1, var-words 1) =====57958037581Comparing traditional and machine learning techniques in apartments mass appraisal in Fortaleza, Brazil582APPENDIX B. PRELIMINARY RESULTS OF DEVELOPED MODELS IN THE TEST SET583Table B. Regression Results for MRA and SER models (p-values between parentheses)584#585Model586Median 587Ratio588COD (%)589PRD590PRD Status591PRB592PRB Status593RMSE594RMSLE595MAE596MAPE 597(%)598R²599Global600Moran’s 601I* (P)6021603MRA6041.0060513.896061.038607Regressivity608-0.019609Regressivity 610between 611+/- 5%612197,400.286130.1861477,416.8661513,906160.886170.37474618(0.001)6192620SER6211.0062211.016231.025624Normal625-0.011626Regressivity 627between 628+/- 5%629137,965.356300.1563160,292.5363211.026330.946340.38433635(0.001)6363637MARS6381.0063914.196401.045641Regressivity642-0.022643Regressivity 644between 645+/- 5%646177,807.976470.1964875,590.8264914.206500.906510.32921652(0.001)6534654M5P6550.9965613.786571.026658Normal659-0.007660Regressivity 661between 662+/- 5%663164,919.996640.2066571,138.1966613.676670.926680.28474669(0.001)6705671RF6721.016738.986741.019675Normal676-0.011677Regressivity 678between 679+/- 5%680121,314.746810.1368248,558.116839.056840.96685-0.0097686(0.010)6876688QRF6891.006909.186911.018692Normal693-0.009694Regressivity 695between 696+/- 5%697129,928.756980.1469949,908.677009.187010.95702-0.01903703(0.001)7047705GBM7061.007079.247081.018709Normal710-0.011711Regressivity 712between 713+/- 5%714113,640.607150.1371650,229.937179.257180.96719-0.01252720(0.001)7218722LightGBM7231.0172410.527251.022726Normal727-0.016728Regressivity 729between 730+/- 5%731114,551.807320.1473354,026.6573410.607350.967360.00919737(0.006)7389739CatBoost7401.017419.157421.020743Normal744-0.013745Regressivity 746between 747+/- 5%748127,548.827490.1375048,832.367519.217520.95753-0.02712754(0.001)75510 XGBoost7561.007578.987581.020759Normal760-0.013761Regressivity 762between 763+/- 5%764116,633.777650.1376648,542.727678.967680.96769-0.001770(0.404)77111772Deep 773Learning7741.0177512.097761.051777Regressivity778-0.045779Regressivity 780between 781+/- 5%782138,462.947830.1778461,889.1778512.257860.947870.15635788(0.001)789Source: Authors. Notes: *Global Moran’s I was performed over the training sample; values in parentheses show P-values.790791792===== PAGE 18 (score 64, numeric-paren 55, table-words 2, var-words 0) =====79379438795Antônio Augusto Ferreira de Oliveira et al.796APPENDIX C – WILCOXON TEST797Table C. Wilcoxon signed-rank test on residuals (p-values in parentheses).798 799MRA800SER801MARS802M5P803RF804QRF805GBM806LightGBM CatBoost807XGBoost808Deep 809Learning810MRA811 81228654871813(0.002)81429287516.5815(0.222)81610764694817(0.000)81828273101819(0.000)82029387804821(0.359)82229621056823(0.836)82428776431.5825(0.005)82628924854827(0.020)82828080357829(0.000)83029606772.5831(0.802)832SER833 834 83529152309836(0.102) 8378112396838(0.000)83926330696840(0.000)84128932765842(0.021)84329264854844(0.197) 84526362893846(0.000) 84726818224848(0.000)84928868465850(0.012)85128811277852(0.008)853MARS854 855 856 85712006409.5858(0.000)85929140611860(0.095)86129377956862(0.344)86329292579.5864(0.228)86529551878.5866(0.677)86729140611868(0.095)86928617181.5870(0.000)87129509893872(0.586)873M5P874 875 876 877 8784378069879(0.000) 8806370087.5881(0.000)8826920394883(0.000)8845432615885(0.000)8864378069887(0.000)8885506569.5889(0.000)8908206475891(0.000)892RF893 894 895 896 897 89824311550899(0.000)90028713742901(0.003)90228938424903(0.022)90428360664905(0.0000)90619623564.5907(0.000)90827151928909(0.0000)910QRF911 912 913 914 915 916 91729681109.5918(0.981)9192779046920(0.000)92127826249922(0.000)92327070630.5924(0.000)92529682344926(0.984)927GBM928 929 930 931 932 933 934 93529051187.5936(0.052)93729067581938(0.056)93928791992940(0.006)94129447044.5942(0.4619)943LightGBM944 945 946 947 948 949 950 951 95229497222953(0.559)95424482096.5955(0.000)95626983269.5957(0.000)958CatBoost959 960 961 962 963 964 965 966 967 9681644228969(0.000)9705852011971(0.000)972XGBoost973 974 975 976 977 978 979 980 981 982 98328031575984(0.000)985Deep 986Learning987Note: Bolded values represent significance with p-value < 0.01.988