1# RECORD 53d1b6d48e64b056e88ebabd287c3f06ec3b559d2# TITLE: Comparing automated valuation models for real estate assessment in the Santiago Metropolitan Region: A study on machine learning algorithms and hedonic pricing with spatial adjustments.3# YEAR: 2025.0 VENUE: PLoS ONE DOI: 10.1371/journal.pone.03187014# AUTHORS: Jocelyn Tapia; Nicolas Chavez-Garzon; R. Pezoa; Paulina Suarez-Aldunate; M. Pilleux5# PAGES: 27 CANDIDATE TABLE PAGES (1-based): [11, 20]6# ABSTRACT: This study compares the precision and interpretability of two automated valuation models for evaluating the real estate market in the Santiago Metropolitan Region of Chile: machine learning algorithms, specifically LightGBM, and hedonic prices with spatial adjustments (SAR). Traditional residence attributes, such as housing amenities and proximity to services, were considered alongside visual information extracted from images using Convolutional Neural Networks (CNN). The research evaluates the influence of each model characteristic on performance metrics and identifies the relative importance of attributes using the SHapley Additive exPlanations (SHAP) algorithm. The results demonstrate the positive impact of image-based variables on performance metrics, showing that the introduction of visual information can considerably reduce error margins when estimating housing prices. In addition, the SHAP algorithm reveals complex non-linear interactions between price and crucial variables such as total surface area and neighborhood attributes, highlighting the importance of using methods that can capture these effects. Likewise, both LightGBM and SAR models indicate that variables that have the most significant impact on the value of properties are total surface area, municipality quality index, average academic level of nearby schools, and the number of bathrooms.789===== PAGE 1 (score 11, numeric-paren 0, table-words 0, var-words 11) =====1011PLOS ONE12OPEN ACCESS13Citation: Tapia J, Chavez-Garzon N, Pezoa R,14Suarez-Aldunate P, Pilleux M (2025)15Comparing automated valuation models for real16estate assessment in the Santiago Metropolitan17Region: A study on machine learning algorithms18and hedonic pricing with spatial adjustments.19PLoS ONE 20(3): e0318701. https://doi.org/10.201371/journal.pone.031870121Editor: Marco Civera, Politecnico di Torino,22ITALY23Received: March 27, 202424Accepted: January 20, 202525Published: March 25, 202526Copyright: © 2025 Tapia et al. This is an open27access article distributed under the terms of the28Creative Commons Attribution License, which29permits unrestricted use, distribution, and30reproduction in any medium, provided the31original author and source are credited.32Data availability statement: All relevant data33and code are included in our submission,34available on Mendeley Data.35Funding: The author(s) received no specific36funding for this work.37Competing interests: The authors have38declared that no competing interests exist.39RESEARCH ARTICLE40Comparing automated valuation models41for real estate assessment in the Santiago42Metropolitan Region: A study on machine43learning algorithms and hedonic pricing44with spatial adjustments45Jocelyn Tapia46 47 481☯∗, Nicolas Chavez-Garzon1☯, Raúl Pezoa2☯,49Paulina Suarez-Aldunate3¤, Mauricio Pilleux3501 Department of Business Engineering, Universidad Técnica Federico Santa María, Santiago, Chile,512 School of Industrial Engineering, Faculty of Engineering and Sciences, Universidad Diego Portales,52Santiago, Chile, 3 Coderhub SpA, Santiago, Chile53¤ PS-A and MP also contributed equally to this work.54☯These authors contributed equally to this work.55∗jocelyn.tapias@usm.cl56Abstract57This study compares the precision and interpretability of two automated valuation mod-58els for evaluating the real estate market in the Santiago Metropolitan Region of Chile:59machine learning algorithms, specifically LightGBM, and hedonic prices with spatial60adjustments (SAR). Traditional residence attributes, such as housing amenities and prox-61imity to services, were considered alongside visual information extracted from images62using Convolutional Neural Networks (CNN). The research evaluates the influence of63each model characteristic on performance metrics and identifies the relative importance64of attributes using the SHapley Additive exPlanations (SHAP) algorithm. The results65demonstrate the positive impact of image-based variables on performance metrics,66showing that the introduction of visual information can considerably reduce error mar-67gins when estimating housing prices. In addition, the SHAP algorithm reveals complex68non-linear interactions between price and crucial variables such as total surface area and69neighborhood attributes, highlighting the importance of using methods that can capture70these effects. Likewise, both LightGBM and SAR models indicate that variables that have71the most significant impact on the value of properties are total surface area, municipality72quality index, average academic level of nearby schools, and the number of bathrooms.73Introduction74The traditional property valuation method is based on the visual and comparative charac-75teristics that an appraiser can gather, where variables such as the year of construction, total76surface area, number of bathrooms and number of bedrooms, among others, are analyzed.77Then, a detailed report is created that indicates the estimated value of the property based on78PLOS ONE https://doi.org/10.1371/journal.pone.031870179March 25, 2025801/ 27818283===== PAGE 11 (score 39, numeric-paren 0, table-words 11, var-words 13) =====8485PLOS ONE86A comparative analysis of automated valuation models: Machine learning and spatially-adjusted hedonic pricing87Table 2. Metrics to measure the performance of the model.88Metric89Abbreviation90Formula91Mean absolute percentage error92MAPE9310094N ∑N95i=1 | yi– ̂yi96yi |97Median absolute percentage error98MdAPE99med| yi– ̂yi100yi | ⋅100101Mean absolute error102MAE1031104N ∑N105i=1 |yi – ̂yi|106Root mean squared error107RMSE108√109∑Ni=1(yi– ̂yi)2110N111Coefficient of determination112R21131 – ∑Ni=1(yi– ̂yi)2114∑Ni=1(yi– ̄y)2115https://doi.org/10.1371/journal.pone.0318701.t0021162. Results1172.1. Performance of AVMs118To evaluate the increase in performance due to the addition of different variables, we train119multiple AVMs using the variables presented in Table 1. First, we train a model using only the120BV. Then, we sequentially add the rest of the variables. The idea is to add as many variables121of each type as possible until there is no significant improvement in the model performance,122discarding the characteristics that do not improve at least 3 of the 5 performance metrics123presented in Table 2, compared to the previous model in the sequence.124For each model’s performance evaluation, we used 5-fold cross-validation, implying that125five iterations were made, and in each one, 80% of the dataset was used as training and the126remaining 20% as validation.127Table 3 summarizes the validation results of each model of the sequence. We only present128the variables that increased the previous model’s performance in at least 3 of the 5 perfor-129mance metrics presented in Table 2, see S3 Table for more details. The column Variables130describes the variables used to train each model. In this case, some similar variables were131grouped to ease the interpretation. For example, the group “amenities” contains the variables132parking_lots, swimpool, terrace and storage_units, while the group “distances” contains the133distances to services that improved the performance of the model.134Table 4 shows that the AVM that presents the best performance contains the seven base135variables, five structural variables obtained from the property description, 10 location vari-136ables, two neighborhood variables, and 10 image variables linked to the photos of property137features (bathroom, bedroom, living room, dining room, interior, exterior, balcony, laundry138room, floor plans and swimming pool), for a total of 34 predictor variables.139Table 3. Summary of the performances of AVMs in 5-fold cross-validation with different sets of variables.140Models141Variables142MAPE143MdAPE144MAE145RMSE146R2147Base Model148Base Variables (BV)14911.59%1507.87%151906.661521513.441530.9412154Model 1155Base Model +156quality_municipality15711.46%1587.81%159898.401601501.931610.9421162Model 2163Model 1 + amenities16410.94%1657.46%166863.401671448.801680.9461169Model 3170Model 2 + new_house17110.88%1727.44%173860.921741446.021750.9463176Model 4177Model 3 + simce_4b17810.72%1797.30%180849.601811430.321820.9475183Model 5184Model 4 +185nearby_schools_3km18610.63%1877.23%188844.361891424.251900.9479191Model 6192Model 5 + 9 distances19310.24%1946.88%195816.991961391.431970.9503198Final Model199Model 6 + 10 features20010.07%2016.84%202807.532031373.232040.9516205https://doi.org/10.1371/journal.pone.0318701.t003206PLOS ONE https://doi.org/10.1371/journal.pone.0318701207March 25, 202520811/ 27209210211===== PAGE 12 (score 30, numeric-paren 0, table-words 4, var-words 22) =====212213PLOS ONE214A comparative analysis of automated valuation models: Machine learning and spatially-adjusted hedonic pricing215Table 4. Independent variables used in the final model.216Final Model217Dependent variable: ln(price)218Independent variables used:2191. bathrooms2202. bedrooms2213. latitude2224. longitude2235. building_type2246. seller_type2257. total_surface2268. quality_municipality2279. parking_lots22810. swimpool22911. terrace23012. storage_units23113. new_house23214. simce_4b23315. nearby_schools_3km23416. dist_subway23517. dist_park23618. dist_hospital23719. dist_police23820. dist_university23921. dist_mall24022. dist_penitentiary24123. dist_industry24224. dist_dump24325. photo_bathroom24426. photo_bedroom24527. photo_livingroom24628. photo_diningroom24729. photo_interior24830. photo_exterior24931. photo_balcony25032. photo_laundryroom25133. photo_floorplans25234. photo_swimpool253Unused independent variables:2541. simce_8b2552. simce_2m2563. nearby_schools_1km2574. nearby_schools_2km2585. dist_school2596. photo_kitchen2607. photo_patio2618. photo_gym2629. photo_gameroom26310. photo_street26411. photo_parkinglot265https://doi.org/10.1371/journal.pone.0318701.t004266As Table 3 shows, there was a significant impact on the performance metrics when the267variables obtained from the description were used, since they determine the extra value of268properties with parking lots, terraces, swimming pools, and storage units, which are ameni-269ties that undoubtedly affect the price of a property. Also, using the variable new_house helped270to differentiate the used properties from the new ones, which is a relevant aspect when selling271a property. Another set of variables that also significantly reduced the error when estimating272the value of the properties were the distances to services, since they provided details related to273the added value of the property, and the externalities of unwanted services, and it also allowed274to differentiate properties within the same municipality. Finally, the image variables reduced275the error even when the model already incorporated a wide range of information about the276dwelling and its surroundings. This can be explained since these variables provided details277that were not contained in the property description, such as the presence of balconies and278laundry rooms. These variables also allowed prices to be differentiated when the properties279did not include critical photos such as those of bathrooms, living rooms, dining rooms, and280bedrooms, which may be related to the omission of information given the quality and visual281appeal of these settings.282Regarding the variables that were not used in the final model, the simce_8b and simce_2m283attributes were discarded because while they improved the model’s performance, they had284a lower impact than simce_4b. The same occurred with the variables related to the number285of nearby schools. The variables calculated within a one and two kilometer radius did not286enter the final model because the variable with a three-kilometer radius achieved a greater287improvement in performance. On the other hand, the image variables that did not pro-288vide relevant information to the model were the kitchen, patio, game room, gym, street,289and parking lot features, which failed to improve the model’s performance in at least three290metrics.2912.1.1. Relative importance of variables To use the TreeSHAP algorithm, a model was fit-292ted with simple validation. Therefore, the dataset was randomly divided, using 80% to fit the293PLOS ONE https://doi.org/10.1371/journal.pone.0318701294March 25, 202529512/ 27296297298===== PAGE 20 (score 54, numeric-paren 0, table-words 11, var-words 18) =====299300PLOS ONE301A comparative analysis of automated valuation models: Machine learning and spatially-adjusted hedonic pricing302As expected, Table 7 shows that the SAR model handles the spatial dependence better303than the traditional OLS model by reporting a Moran’s I close to 0. The non-standardized304coefficients of the OLS and SAR models are presented in Table 8.305From Table 8, it can be seen that the number of bathrooms, number of bedrooms, and the306quality of the municipality had overestimated coefficients in the OLS model, which was cor-307rected in the SAR model. On the other hand, some distance variables drastically changed their308behavior, such as the distance to a park, which changed from having a statistically significant309negative coefficient to a statistically significant positive one. In contrast, the distance to an310industry stopped to have a statistically significant impact in the SAR model. In addition, the311Table 7. Moran’s I for the residuals of the OLS and SAR models.312Model313Statistic I314OLS3150.1337316SAR3170.0751318https://doi.org/10.1371/journal.pone.0318701.t007319Table 8. Non-standardized coefficients of the OLS and SAR models (∗∗p-value<0.01.)320OLS (R2 = 0.8654)321SAR (R2 = 0.8774)322Coefficient323Std Error324Coefficient325Std Error326constant3273.7782∗∗3280.04163291.9507∗∗3300.0515331bathrooms3320.1798∗∗3330.00243340.1712∗∗3350.0023336bedrooms3370.0814∗∗3380.00213390.0752∗∗3400.0021341building_type3420.0874∗∗3430.00573440.0957∗∗3450.0055346seller_type347-0.0662∗∗3480.0044349-0.0649∗∗3500.0043351total_surface3520.0008∗∗3530.00003540.0007∗∗3550.0000356quality_municipality3570.0273∗∗3580.00033590.0178∗∗3600.0003361parking_lots3620.0159∗∗3630.00133640.0139∗∗3650.0012366swimpool3670.00023680.00343690.00213700.0033371terrace3720.0582∗∗3730.00323740.0465∗∗3750.0031376storage_units3770.0304∗∗3780.00163790.0289∗∗3800.0015381new_house3820.0753∗∗3830.00733840.0668∗∗3850.0070386simce_4b3870.0082∗∗3880.00013890.0036∗∗3900.0001391nearby_schools_3km392-0.0008∗∗3930.00003940.0014∗∗3950.0000396dist_subway3970.0045∗∗3980.00113990.0054∗∗4000.0010401dist_park402-0.00194030.00174040.0087∗∗4050.0016406dist_hospital4070.0038∗∗4080.0010409-0.0084∗∗4100.0009411dist_police4120.0263∗∗4130.00204140.0194∗∗4150.0019416dist_university417-0.0176∗∗4180.0013419-0.0121∗∗4200.0011421dist_mall422-0.0039∗∗4230.00144240.0052∗∗4250.0013426dist_penitentiary427-0.0050∗∗4280.0006429-0.0035∗∗4300.0006431dist_industry4320.0096∗∗4330.0009434-0.00064350.0009436dist_dump4370.0019∗∗4380.0005439-0.0045∗∗4400.0005441photo_bathroom442-0.0506∗∗4430.0035444-0.0450∗∗4450.0034446photo_bedroom447-0.00154480.0038449-0.00154500.0037451photo_livingroom4520.0492∗∗4530.00394540.0438∗∗4550.0037456photo_diningroom4570.0488∗∗4580.00324590.0441∗∗4600.0030461photo_interior4620.00174630.00304640.00364650.0029466photo_exterior467-0.00114680.0031469-0.00044700.0030471photo_balcony4720.0249∗∗4730.00304740.0209∗∗4750.0029476photo_laundryroom477-0.0326∗∗4780.0039479-0.0249∗∗4800.0037481photo_floorplans4820.0445∗∗4830.00544840.0422∗∗4850.0052486photo_swimpool487-0.0092∗∗4880.0034489-0.0115∗∗4900.0032491W_ln_price492-493-4940.4271∗∗4950.0080496https://doi.org/10.1371/journal.pone.0318701.t008497PLOS ONE https://doi.org/10.1371/journal.pone.0318701498March 25, 202549920/ 27500501502===== PAGE 21 (score 23, numeric-paren 0, table-words 7, var-words 8) =====503504PLOS ONE505A comparative analysis of automated valuation models: Machine learning and spatially-adjusted hedonic pricing506distance to a hospital and the distance to a dump changed from positive to negative param-507eters. The opposite occurred with the distance to a mall, which underwent a coefficient sign508change from negative to positive. Regarding the neighborhood variables, the average SIMCE509score of elementary schools reduced the positive impact on the price in the SAR model. In510contrast, the number of nearby schools within a 3-kilometer radius went from having a neg-511ative coefficient to a positive one, maintaining a statistically significant impact on the price.512Note that this effect is the opposite to the one obtained with the IML approach. In other513words, the insight obtained from the IML approach, regarding the effect of schools, only coin-514cides with that of the OLS model, i.e., the model with no spatial corrections. Moreover, note515that the spatial autoregressive parameter (𝜌) had a value of 0.4271, confirming a positive516spatial dependence on the price of residences, thus suggesting a biased result from the IML517approach. Additionally, although the OLS and SAR models were fitted primarily for quali-518tative comparisons with the AVM approach, we report their performance results in Table 9.519As expected, both models show significantly worse prediction performance than the AVMs520(Table 3), a result that is consistent with previous literature [21,44].521Finally, we compared the relative importance that the three models assigned to the vari-522ables. To do this, we standardized the attributes of the OLS and SAR models, so their unit of523measurement was the number of standard deviations. The standardization formula or Z-score524is shown in Eq 8.525Z = x – 𝜇526𝜎527(8)528In Eq 8, x is the variable’s value, 𝜇is the mean, and 𝜎is the standard deviation. Perform-529ing this transformation allows the coefficients of the models to be standardized, so the abso-530lute value of the coefficients can be analyzed to see which characteristics have a more signif-531icant effect on the price of homes. On the other hand, the relative importance of the Light-532GBM model variables is assigned by the SHAP algorithm. For comparative purposes, we533excluded the latitude and longitude variables from the ranking since they were used in the534spatial weights matrix in the SAR model.535Table 10 shows a close relationship between the importance assigned to the variables in536each model, even though the methods and approaches were different. In the five most impor-537tant variables of each model, four attributes stand out: total surface area, quality of the munic-538ipality, average SIMCE score of elementary schools, and the number of bathrooms. Although539the rankings assigned for these attributes are not the same, the three models agree that these540variables are the ones that have the most significant impact on the price. Due to the spa-541tial correction made by the SAR model, the quality of the municipality decreased its effect542on the price, causing the number of bathrooms to be the most important variable. A simi-543lar change occurred with the average SIMCE score of elementary schools, which reduced its544impact on property values, relegating it to fifth place and moving the number of bathrooms545to fourth place in the ranking. On the other hand, the distance variables lost importance546in econometric models because their interactions with the prices are not linear, which is a547characteristic that the LightGBM model can capture.548Table 9. Performance summary of OLS and SAR models in 5-fold cross-validation.549Model550MAPE551MdAPE552MAE553RMSE554R2555OLS55621.13%55716.86%5581887.855593356.505600.7103561SAR56220.92%56317.13%5641893.095653115.855660.7405567https://doi.org/10.1371/journal.pone.0318701.t009568PLOS ONE https://doi.org/10.1371/journal.pone.0318701569March 25, 202557021/ 27571