1# RECORD 3d555b719dcd66f5b773ee480ecb47ce9229f3fe2# TITLE: Estimation of Residential Property Market Price: Comparison of Artificial Neural Networks and Hedonic Pricing Model3# YEAR: 2020.0 VENUE: Emerging Science Journal DOI: 10.28991/esj-2020-012504# AUTHORS: Michaela Štubňová; Marta Urbaníková; J. Hudáková; V. Papcunová5# PAGES: 9 CANDIDATE TABLE PAGES (1-based): [4, 7]6# ABSTRACT: The correct real estate property price estimation is significant not only in the real estate market but also in the banking sector for collateral loans and the insurance sector for property insurance. The paper focuses on both traditional and advanced methods for real estate property valuation. Attention is paid to the analysis of the accuracy of valuation models. From traditional methods, a regression model is used for residential property price estimation, which represents the hedonic approach. Modern advanced valuation methods are represented by the artificial neural network, which is one of the soft computing techniques. The results of both methods in residential property market price estimation are compared. The analysis is performed using data on residential properties sold on the real estate market in the city of Nitra in the Slovak Republic. To estimate the residential property prices, artificial neural networks trained with the Levenberg-Marquart learning algorithm, the Bayesian Regularization learning algorithm, and the Scaled Conjugate Gradient learning algorithm, and the regression pricing model are used. Among the constructed neural networks, the best results are achieved with networks trained with the Regularization learning algorithm with two hidden layers. Its performance is compared with the performance of the regression pricing model, and it can state that artificial neural networks can considerably improve prediction accuracy in the estimation of residential property market price. Doi: 10.28991/esj-2020-01250 Full Text: PDF789===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) =====1011 12Available online at www.ijournalse.org 13Emerging Science Journal 14Vol. 4, No. 6, December, 2020 15 16 17 18Page | 530 19 20Estimation of Residential Property Market Price: Comparison of 21Artificial Neural Networks and Hedonic Pricing Model 22Michaela Štubňová a, Marta Urbaníková a*, Jarmila Hudáková a, Viera Papcunová a 23a Institute of Economics and Management, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda Andreja 24Hlinku 1, 949 01 Nitra, Slovak Republic 25 26Abstract 27The correct real estate property price estimation is significant not only in the real estate market but 28also in the banking sector for collateral loans and the insurance sector for property insurance. The 29paper focuses on both traditional and advanced methods for real estate property valuation. Attention 30is paid to the analysis of the accuracy of valuation models. From traditional methods, a regression 31model is used for residential property price estimation, which represents the hedonic approach. 32Modern advanced valuation methods are represented by the artificial neural network, which is one of 33the soft computing techniques. The results of both methods in residential property market price 34estimation are compared. The analysis is performed using data on residential properties sold on the 35real estate market in the city of Nitra in the Slovak Republic. To estimate the residential property 36prices, artificial neural networks trained with the Levenberg-Marquart learning algorithm, the 37Bayesian Regularization learning algorithm, and the Scaled Conjugate Gradient learning algorithm, 38and the regression pricing model are used. Among the constructed neural networks, the best results 39are achieved with networks trained with the Regularization learning algorithm with two hidden layers. 40Its performance is compared with the performance of the regression pricing model, and it can state 41that artificial neural networks can considerably improve prediction accuracy in the estimation of 42residential property market price. 43Keywords: 44Artificial Neural Network; 45Hedonic Regression Model; 46Price Estimation; 47Residential Property; 48Market Price. 49 50 51 52Article History: 53Received: 5427 55August 562020 57Accepted: 5828 59November 602020 61Published: 6201 63December 642020 65 66 67 68 691- Introduction 70The estimation of the right price of residential property is essential not only in the real estate market but also for 71collateral loans and property insurance. It is also significant in business practice for the estimation of the value of a 72company's real estate property [1]. Legal persons and institutions can estimate the market price of residential property 73using traditional or advanced appraisal methods. Pagourtzi et al. (2003) ranked the comparative method, the profits 74method, the contractor's/cost method, and the regression models among the traditional methods [2]. By the comparative 75method, the price is estimated by comparison with selling prices of recently sold similar properties in the same market 76location. However, this is only possible in areas with a developed real estate market. The profit method for estimating 77the market price of a property can be applied to a property that generates revenue and the market value of the property 78is estimated by the potential cash flow from the property ownership. The contractor's/cost method is based on the 79principle of estimating how much it would cost at the time of sale to construct a property similar to that valued, taking 80into account its obsolescence and depreciation. The method is based on the assumption that the buyer will not pay more 81for the property than he would pay for the construction of a new building relative to the existing one. Regression models 82are often used as evaluation methods [3]. The regression models represent the hedonic approach to property appraisal in 83academic research studies [4-6]. It is a quantitative method of the comparable approach. “The methodology of hedonic 84prices allows us to estimate the value contributed by each of the attributes (physical or otherwise) to a property, and to 85make predictions about the behavior of the rest of the properties when any of these elements vary” [7]. Doumpos et al. 86 87* CONTACT: murbanikova@ukf.sk 88DOI: http://dx.doi.org/10.28991/esj-2020-01250 89© 2020 by the authors. Licensee ESJ, Italy. This is an open access article under the terms and conditions of the Creative 90Commons Attribution (CC-BY) license (https://creativecommons.org/licenses/by/4.0/). 919293===== PAGE 4 (score 29, numeric-paren 0, table-words 5, var-words 17) =====9495Emerging Science Journal | Vol. 4, No. 696 97Page | 533 98Where 𝛼 and 𝛽 are parameters to optimize, 𝐸𝑤 is the sum of squares of network weights, 𝑛 is a number of data 99points,𝑒𝑖= 𝑦𝑖 −𝑦𝑖̂, where 𝑦𝑖 are target values, 𝑦𝑖̂ are output values [26, 27, 28]. 1002-3- Scaled Conjugate Gradient learning algorithm 101The SCG learning algorithm is based on the conjugate gradient method, which is suitable for large-scale problems. 102The step size scaling method is used to avoid line-search at each iteration, which makes the training process time-103consuming. The calculations used in the algorithm are described in detail by Møller (1993) [29]. 1043- Methodology and Data 105The data were obtained from the internet real estate portal TopReality (2019) in the period from Sept. 9, 2019, to 106Sept. 13, 2019 [30]. The search criteria for published properties were: property type = apartment, locations = city of 107Nitra, bid category = sale. Based on these search criteria, 711 properties were selected from which mislabeled properties 108that did not meet some of the criteria, duplicate properties, and properties that did not include all monitored parameters 109were excluded. 256 properties were obtained after the selection. Table 1 shows the monitored property parameters. The 110categorical parameters were converted to dummy variables. Table 2 shows their descriptive statistics for categorical 111parameters. Table 3 shows descriptive statistics for quantitative variables. 112Table 1. Property parameters. 113Parameter 114Type 115Values 116Variable name 117Price 118quantitative 119real number 120Price 121Location 122qualitative 123Old Town, Chrenová, Klokočina, Diely, Čermáň, Zobor 124Loc_1, Loc_2, Loc_3, Loc_4, Loc_5 125Number of rooms 126quantitative 127integer 128Num_rooms 129Living area (m2) 130quantitative 131real number 132Area 133Floor 134qualitative 135ground floor, middle floor, upper floor 136Floor_1, Floor_2 137Number of storeys 138qualitative 1391 to 4 storeys building, 5 or more storeys building 140Num_storeys 141Elevator 142qualitative 143yes, no 144Elevator 145Balcony 146qualitative 147yes, no 148Balcony 149Cellar 150qualitative 151yes, no 152Cellar 153Apartment condition 154qualitative 155new building, complete reconstruction, partial 156reconstruction, original condition 157Cond_1, Cond_2, Cond_3 158Storage room 159qualitative 160yes, no 161Storage 162Insulated building 163qualitative 164yes, no 165Insulation 166Parking space 167qualitative 168yes, no, can be purchased 169Parking_1, Parking_2 170Table 2. Descriptive statistics for qualitative variables. 171Variable 172N 173% 174Variable 175N 176% 177Location 178Old Town 17973 18028.52% 181Balcony 182180 18370.31% 184Chrenová 18558 18622.66% 187Cellar 188183 18971.48% 190Klokočina 19180 19231.25% 193Apartment condition 194new building 19521 1968.20% 197Diely 19825 1999.77% 200complete reconstruction 201106 20241.41% 203Čermáň 20415 2055.86% 206partial reconstruction 20792 20835.94% 209Zobor 2105 2111.95% 212Floor 213ground floor 21426 21510.16% 216original condition 21737 21814.45% 219middle floor 220182 22171.09% 222Storage room 22364 22425.00% 225upper floor 22648 22718.75% 228Insulated building 229209 23081.64% 231Number of storeys 2321 to 4 storeys building 23373 23428.52% 235Parking space 236yes 23722 2388.59% 2395 or more storeys building 240183 24171.48% 242no 243227 24488.67% 245Elevator 246190 24774.22% 248can be purchased 2497 2502.73% 251 252253254===== PAGE 5 (score 12, numeric-paren 0, table-words 3, var-words 6) =====255256Emerging Science Journal | Vol. 4, No. 6257 258Page | 534 259Table 3. Descriptive statistics for quantitative variables. 260Variable 261Min 262Max 263Average 264Median 265Transformation 266Price 26747 000 268219 000 269101 471.5 27097 800 271log 272Number of rooms 2730 2744 2752.519531 2763 277square root 278Living area [m2] 27919 280134 28167.95703 28267 283log 284Figure 2 shows the flowchart of the research methodology. The pricing models were developed using the MATLAB 285R2019b program. The performance of the hedonic pricing model and ANNs train with the LM learning algorithm, the 286BR learning algorithm, and the SCG learning algorithm were compared. In the paper, the regression model represents 287hedonic pricing models: 288𝑌𝑖= 𝛽0 + 𝛽1𝑋𝑖1 + 𝛽2𝑋𝑖2 + ⋯+ 𝛽𝑝𝑋𝑖𝑝+ 𝜀𝑖, 289(5) 290Where 𝑌𝑖 is the 𝑖 th observation of the dependent variable, 𝑋𝑖 is the 𝑖 th observation of the 1 × 𝑝 vector of the 291independent variables, 𝛽 is the (𝑝+ 1) × 1 vector of the parameters, where 𝛽0 is the intercept, and 𝜀𝑖 is the random 292error for the 𝑖th observation. 293The data were divided into a training and test set at a ratio of 85:15 for the regression model. 𝑝+ 1 parameters 𝛽𝑗, 294𝑗= 0, ⋯, 𝑝 were estimated using the least square method of estimation. The stepwise regression method with backward 295elimination was used to decide which variables to include in the regression model. It starts with a full model containing 296all independent variables and eliminates one variable at each step. It chooses to eliminate the variable, which elimination 297will cause the least increase of the residual sum of square. It calculates 𝐹-test value (significance level to stay) for each 298variable and eliminates the variable with the smallest 𝐹 value. The backward elimination terminates when none of the 299𝐹 values is less than the critical value for elimination, therefore, all remaining variables in the model meet the criterion 300to stay [31]. 301The data were divided into a training, validation, and test set at a ratio of 70:15:15 for ANNs trained with the LM 302and the SCG learning algorithms. The data were divided into a training and test set at a ratio of 85:15 for ANNs trained 303with the BR learning algorithm and for the regression model. 304Figure 2. Research methodology. 305The determination coefficient (𝑅2), root mean square error (𝑅𝑀𝑆𝐸), mean absolute error (𝑀𝐴𝐸) and the mean 306absolute percentage error (𝑀𝐴𝑃𝐸) were used to evaluate performance of the pricing model. 307𝑅2 = 1 −308∑309(𝑦𝑖 −𝑦𝑖310̂)2311𝑛312𝑖=1313∑314(𝑦𝑖 −𝑦̅)2315𝑛316𝑖=1317, 318(6) 319𝑅𝑀𝑆𝐸= √∑320(𝑦𝑖 −𝑦𝑖321̂)2322𝑛323𝑖=1324𝑛325, 326(7) 327𝑀𝐴𝐸=3281329𝑛∑330|𝑦𝑖 −𝑦𝑖̂|331𝑛332𝑖=1333, 334(8) 335𝑀𝐴𝑃𝐸=336100337𝑛∑338|339𝑦𝑖 −𝑦𝑖340̂341𝑦𝑖 |342𝑛343𝑖=1344, 345(9) 346Where 𝑦̅ is the mean of target values. 347348349===== PAGE 7 (score 29, numeric-paren 0, table-words 6, var-words 9) =====350351Emerging Science Journal | Vol. 4, No. 6352 353Page | 536 354Table 5. 𝑭 -test values for eliminated variables. 355Step 356Variable 357𝑭-test 358𝒑-value 359First 360Parking_2 3610.00001 3620.997062 363Second 364Insulation 3650.03127 3660.859820 367Third 368Cond_3 3690.91591 3700.339724 371Fourth 372Storage 3731.62997 3740.203203 375Fifth 376Loc_5 3772.02780 3780.156010 379Sixth 380Loc_2 3811.94719 3820.164437 383Seventh 384Floor_1 3852.82345 3860.094450 387Eighth 388Balcony 3892.23348 3900.136610 391In the last ninth step, no variable was eliminated from the model because the 𝐹- test values of all variables were 392greater than the critical value for elimination. The resulting model was constructed: 393𝑃𝑟𝑖𝑐𝑒𝑖= 31722.79 −6591.80 𝐿𝑜𝑐_1𝑖−16651.07 𝐿𝑜𝑐_3𝑖−14488.27 𝐿𝑜𝑐_4𝑖+ 7993.72 𝑁𝑢𝑚_𝑟𝑜𝑜𝑚𝑠𝑖394+ 462.55 𝐴𝑟𝑒𝑎𝑖+ 4908.63 𝐹𝑙𝑜𝑜𝑟_2𝑖+ 16595.35 𝑁𝑢𝑚_𝑠𝑡𝑜𝑟𝑒𝑦𝑠𝑖+ 10900.49 𝐸𝑙𝑒𝑣𝑎𝑡𝑜𝑟𝑖395+ 3554.06 𝐶𝑒𝑙𝑙𝑎𝑟𝑖+ 17489.21 𝐶𝑜𝑛𝑑_1𝑖+ 13370.53 𝐶𝑜𝑛𝑑_2𝑖+ 8618.77 𝑃𝑎𝑟𝑘𝑖𝑛𝑔_1𝑖 396(10) 397Table 6 shows the performance index values for constructed regression model. 398Table 6. Regression pricing models results. 399𝑹𝟐 400𝑹𝑴𝑺𝑬 401𝑴𝑨𝑬 402𝑴𝑨𝑷𝑬 4030.7898 40411454.91 4058516.60 4068.41% 407The best performing ANNs trained with the BR algorithm achieved 𝑀𝐴𝑃𝐸 values 3.39% and 3.58%, on the contrary, 408the regression pricing model achieved 𝑀𝐴𝑃𝐸 value 8.41%. Table 7 shows the estimated property prices for seven 409selected real estate properties from the test set. Based on the results, it can be stated that pricing models based on ANNs 410achieved a better predictive ability than the pricing model based on the regression method. Better prediction accuracy 411of ANNs compared to regression pricing models was reported by Moreno-Izquierdo et al. (2018), Tabales et al. (2013), 412Kutasi and Badics (2016), and Abidoye and Chan (2018) [7, 14-16]. These results are also supported by the literature 413review by Valier (2020), which examined research papers analyzing the accuracy of automated valuation models [32]. 414ANNs were indicated as more effective and reliable for mass evaluation of residential properties compared to regression 415models in 29 research papers. Compared to regression models, which were indicated as more effective compared to 416ANNS only in 6 research papers. Among the constructed neural networks, ANNs trained with the BR algorithm achieved 417the best results. Kayri (2016) analyzed the predictive ability of neural networks trained with BR and LM algorithms, he 418achieved higher predictive ability using the BR training algorithm [27]. The BR algorithm can approximate the price 419function well, despite a smaller data set containing 256 observations. The ability to merge training and validation data 420sets into a training set is an advantage of the BR algorithm for small data sets [26]. Based on previous research and the 421results of our work, it can be concluded that ANN with the BR learning algorithm and two hidden layers is suitable for 422the estimation of residential property market price. 423Table 7. Estimated property prices. 424Actual market 425price EUR 426ANN pricing model BR 10_20 427ANN pricing model BR 15_15 428Regression pricing model 429Estimated price 430EUR 431Residuals 432Estimated price 433EUR 434Residuals 435Estimated price 436EUR 437Residuals 438101900.00 43995716.64 440-6183.36 44195484.04 442-6415.96 44399432.76 4442467.24 44588400.00 446103351.84 44714951.84 448104905.06 44916505.06 450102164.72 451-13764.72 452115000.00 453116713.36 4541713.36 455115946.06 456946.06 457109295.56 4585704.44 45990000.00 46085782.71 461-4217.29 46289159.76 463-840.24 46482800.58 4657199.42 46692900.00 46793478.66 468578.66 46993524.76 470624.76 47193748.96 472-848.96 47396000.00 474100241.91 4754241.91 476102498.06 4776498.06 478100927.01 479-4927.01 48082999.00 48183900.15 482901.15 48395122.18 48412123.18 48593122.31 486-10123.31 487488489===== PAGE 8 (score 10, numeric-paren 0, table-words 1, var-words 7) =====490491Emerging Science Journal | Vol. 4, No. 6492 493Page | 537 4945- Conclusion 495The paper analyzes the predictive ability of the automated valuation model using ANNs and the hedonic pricing 496model using the regression method. Regression pricing models are the traditional methods of residential property 497appraisal. With the increase in the use of soft computing techniques in various areas, researchers began to explore the 498possibilities of their use in the valuation of real estate properties. The paper analyzed ANN's ability to accurately estimate 499the market price of residential properties sold on the real estate market in the city of Nitra in the Slovak Republic. 60 500ANNs trained with the LM learning algorithm, the BR learning algorithm, and the SCG learning algorithm were 501constructed and validated. Based on the comparison of their prediction accuracy, it can be stated that neural networks 502trained with the BR learning algorithm achieved the best results in the estimation of the market price of residential 503properties. ANN trained with the BR learning algorithm comprising two hidden layers (10 neurons in the first hidden 504layer and 20 neurons in the second hidden layer) achieved the best results in the monitored performances indices 505𝑅2 =0.9749, 𝑀𝐴𝐸=3561.288, and 𝑀𝐴𝑃𝐸=3.39%. ANN trained with the BR learning algorithm comprising two 506hidden layers (15 neurons in both hidden layers) achieved the best results in the monitored performance index 𝑅𝑀𝑆𝐸=5076220.818. The regression pricing model constructed using the stepwise regression method with backward elimination 508achieved significantly worse values of the monitored performance indices R2=0.7898, RMSE=11454.91, 509MAE=8516.60, and MAPE=8.41%. The results of the analysis indicate the suitability of using ANN in the estimation 510of the market prices of residential properties. The use of the BR training algorithm, which achieved the highest predictive 511ability among the used training algorithms, is recommended. 5126- Funding 513This paper was supported by the University Grant Agency of Constantine the Philosopher University in Nitra UGA 514no. VII/16/2019. 5157- Conflict of Interest 516The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the 517ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double 518publication and/or submission, and redundancies have been completely observed by the authors. 5198- References 520[1] Korenkova, M. “Business in Slovakia.“ Sbornik prispevku z mezinarodni vedecke konference: Region v rozvoji spolecnosti 2016 521(October 2016): 459-469. 522[2] Pagourtzi, E., V. Assimakopoulos, T. Hatzichristos, and N. 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