# RECORD 3d555b719dcd66f5b773ee480ecb47ce9229f3fe # TITLE: Estimation of Residential Property Market Price: Comparison of Artificial Neural Networks and Hedonic Pricing Model # YEAR: 2020.0 VENUE: Emerging Science Journal DOI: 10.28991/esj-2020-01250 # AUTHORS: Michaela Štubňová; Marta Urbaníková; J. Hudáková; V. Papcunová # PAGES: 9 CANDIDATE TABLE PAGES (1-based): [4, 7] # 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: PDF ===== PAGE 1 (score 6, numeric-paren 0, table-words 0, var-words 6) ===== Available online at www.ijournalse.org Emerging Science Journal Vol. 4, No. 6, December, 2020 Page | 530 Estimation of Residential Property Market Price: Comparison of Artificial Neural Networks and Hedonic Pricing Model Michaela Štubňová a, Marta Urbaníková a*, Jarmila Hudáková a, Viera Papcunová a a Institute of Economics and Management, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, Trieda Andreja Hlinku 1, 949 01 Nitra, Slovak Republic 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. Keywords: Artificial Neural Network; Hedonic Regression Model; Price Estimation; Residential Property; Market Price. Article History: Received: 27 August 2020 Accepted: 28 November 2020 Published: 01 December 2020 1- Introduction The estimation of the right price of residential property is essential not only in the real estate market but also for collateral loans and property insurance. It is also significant in business practice for the estimation of the value of a company's real estate property [1]. Legal persons and institutions can estimate the market price of residential property using traditional or advanced appraisal methods. Pagourtzi et al. (2003) ranked the comparative method, the profits method, the contractor's/cost method, and the regression models among the traditional methods [2]. By the comparative method, the price is estimated by comparison with selling prices of recently sold similar properties in the same market location. However, this is only possible in areas with a developed real estate market. The profit method for estimating the market price of a property can be applied to a property that generates revenue and the market value of the property is estimated by the potential cash flow from the property ownership. The contractor's/cost method is based on the principle of estimating how much it would cost at the time of sale to construct a property similar to that valued, taking into account its obsolescence and depreciation. The method is based on the assumption that the buyer will not pay more for the property than he would pay for the construction of a new building relative to the existing one. Regression models are often used as evaluation methods [3]. The regression models represent the hedonic approach to property appraisal in academic research studies [4-6]. It is a quantitative method of the comparable approach. “The methodology of hedonic prices allows us to estimate the value contributed by each of the attributes (physical or otherwise) to a property, and to make predictions about the behavior of the rest of the properties when any of these elements vary” [7]. Doumpos et al. * CONTACT: murbanikova@ukf.sk DOI: http://dx.doi.org/10.28991/esj-2020-01250 © 2020 by the authors. Licensee ESJ, Italy. This is an open access article under the terms and conditions of the Creative Commons Attribution (CC-BY) license (https://creativecommons.org/licenses/by/4.0/). ===== PAGE 4 (score 29, numeric-paren 0, table-words 5, var-words 17) ===== Emerging Science Journal | Vol. 4, No. 6 Page | 533 Where 𝛼 and 𝛽 are parameters to optimize, 𝐸𝑤 is the sum of squares of network weights, 𝑛 is a number of data points,𝑒𝑖= 𝑦𝑖 −𝑦𝑖̂, where 𝑦𝑖 are target values, 𝑦𝑖̂ are output values [26, 27, 28]. 2-3- Scaled Conjugate Gradient learning algorithm The SCG learning algorithm is based on the conjugate gradient method, which is suitable for large-scale problems. The step size scaling method is used to avoid line-search at each iteration, which makes the training process time- consuming. The calculations used in the algorithm are described in detail by Møller (1993) [29]. 3- Methodology and Data The data were obtained from the internet real estate portal TopReality (2019) in the period from Sept. 9, 2019, to Sept. 13, 2019 [30]. The search criteria for published properties were: property type = apartment, locations = city of Nitra, bid category = sale. Based on these search criteria, 711 properties were selected from which mislabeled properties that did not meet some of the criteria, duplicate properties, and properties that did not include all monitored parameters were excluded. 256 properties were obtained after the selection. Table 1 shows the monitored property parameters. The categorical parameters were converted to dummy variables. Table 2 shows their descriptive statistics for categorical parameters. Table 3 shows descriptive statistics for quantitative variables. Table 1. Property parameters. Parameter Type Values Variable name Price quantitative real number Price Location qualitative Old Town, Chrenová, Klokočina, Diely, Čermáň, Zobor Loc_1, Loc_2, Loc_3, Loc_4, Loc_5 Number of rooms quantitative integer Num_rooms Living area (m2) quantitative real number Area Floor qualitative ground floor, middle floor, upper floor Floor_1, Floor_2 Number of storeys qualitative 1 to 4 storeys building, 5 or more storeys building Num_storeys Elevator qualitative yes, no Elevator Balcony qualitative yes, no Balcony Cellar qualitative yes, no Cellar Apartment condition qualitative new building, complete reconstruction, partial reconstruction, original condition Cond_1, Cond_2, Cond_3 Storage room qualitative yes, no Storage Insulated building qualitative yes, no Insulation Parking space qualitative yes, no, can be purchased Parking_1, Parking_2 Table 2. Descriptive statistics for qualitative variables. Variable N % Variable N % Location Old Town 73 28.52% Balcony 180 70.31% Chrenová 58 22.66% Cellar 183 71.48% Klokočina 80 31.25% Apartment condition new building 21 8.20% Diely 25 9.77% complete reconstruction 106 41.41% Čermáň 15 5.86% partial reconstruction 92 35.94% Zobor 5 1.95% Floor ground floor 26 10.16% original condition 37 14.45% middle floor 182 71.09% Storage room 64 25.00% upper floor 48 18.75% Insulated building 209 81.64% Number of storeys 1 to 4 storeys building 73 28.52% Parking space yes 22 8.59% 5 or more storeys building 183 71.48% no 227 88.67% Elevator 190 74.22% can be purchased 7 2.73% ===== PAGE 5 (score 12, numeric-paren 0, table-words 3, var-words 6) ===== Emerging Science Journal | Vol. 4, No. 6 Page | 534 Table 3. Descriptive statistics for quantitative variables. Variable Min Max Average Median Transformation Price 47 000 219 000 101 471.5 97 800 log Number of rooms 0 4 2.519531 3 square root Living area [m2] 19 134 67.95703 67 log Figure 2 shows the flowchart of the research methodology. The pricing models were developed using the MATLAB R2019b program. The performance of the hedonic pricing model and ANNs train with the LM learning algorithm, the BR learning algorithm, and the SCG learning algorithm were compared. In the paper, the regression model represents hedonic pricing models: 𝑌𝑖= 𝛽0 + 𝛽1𝑋𝑖1 + 𝛽2𝑋𝑖2 + ⋯+ 𝛽𝑝𝑋𝑖𝑝+ 𝜀𝑖, (5) Where 𝑌𝑖 is the 𝑖 th observation of the dependent variable, 𝑋𝑖 is the 𝑖 th observation of the 1 × 𝑝 vector of the independent variables, 𝛽 is the (𝑝+ 1) × 1 vector of the parameters, where 𝛽0 is the intercept, and 𝜀𝑖 is the random error for the 𝑖th observation. The data were divided into a training and test set at a ratio of 85:15 for the regression model. 𝑝+ 1 parameters 𝛽𝑗, 𝑗= 0, ⋯, 𝑝 were estimated using the least square method of estimation. The stepwise regression method with backward elimination was used to decide which variables to include in the regression model. It starts with a full model containing all independent variables and eliminates one variable at each step. It chooses to eliminate the variable, which elimination will cause the least increase of the residual sum of square. It calculates 𝐹-test value (significance level to stay) for each variable and eliminates the variable with the smallest 𝐹 value. The backward elimination terminates when none of the 𝐹 values is less than the critical value for elimination, therefore, all remaining variables in the model meet the criterion to stay [31]. The data were divided into a training, validation, and test set at a ratio of 70:15:15 for ANNs trained with the LM and the SCG learning algorithms. The data were divided into a training and test set at a ratio of 85:15 for ANNs trained with the BR learning algorithm and for the regression model. Figure 2. Research methodology. The determination coefficient (𝑅2), root mean square error (𝑅𝑀𝑆𝐸), mean absolute error (𝑀𝐴𝐸) and the mean absolute percentage error (𝑀𝐴𝑃𝐸) were used to evaluate performance of the pricing model. 𝑅2 = 1 − ∑ (𝑦𝑖 −𝑦𝑖 ̂)2 𝑛 𝑖=1 ∑ (𝑦𝑖 −𝑦̅)2 𝑛 𝑖=1 , (6) 𝑅𝑀𝑆𝐸= √∑ (𝑦𝑖 −𝑦𝑖 ̂)2 𝑛 𝑖=1 𝑛 , (7) 𝑀𝐴𝐸= 1 𝑛∑ |𝑦𝑖 −𝑦𝑖̂| 𝑛 𝑖=1 , (8) 𝑀𝐴𝑃𝐸= 100 𝑛∑ | 𝑦𝑖 −𝑦𝑖 ̂ 𝑦𝑖 | 𝑛 𝑖=1 , (9) Where 𝑦̅ is the mean of target values. ===== PAGE 7 (score 29, numeric-paren 0, table-words 6, var-words 9) ===== Emerging Science Journal | Vol. 4, No. 6 Page | 536 Table 5. 𝑭 -test values for eliminated variables. Step Variable 𝑭-test 𝒑-value First Parking_2 0.00001 0.997062 Second Insulation 0.03127 0.859820 Third Cond_3 0.91591 0.339724 Fourth Storage 1.62997 0.203203 Fifth Loc_5 2.02780 0.156010 Sixth Loc_2 1.94719 0.164437 Seventh Floor_1 2.82345 0.094450 Eighth Balcony 2.23348 0.136610 In the last ninth step, no variable was eliminated from the model because the 𝐹- test values of all variables were greater than the critical value for elimination. The resulting model was constructed: 𝑃𝑟𝑖𝑐𝑒𝑖= 31722.79 −6591.80 𝐿𝑜𝑐_1𝑖−16651.07 𝐿𝑜𝑐_3𝑖−14488.27 𝐿𝑜𝑐_4𝑖+ 7993.72 𝑁𝑢𝑚_𝑟𝑜𝑜𝑚𝑠𝑖 + 462.55 𝐴𝑟𝑒𝑎𝑖+ 4908.63 𝐹𝑙𝑜𝑜𝑟_2𝑖+ 16595.35 𝑁𝑢𝑚_𝑠𝑡𝑜𝑟𝑒𝑦𝑠𝑖+ 10900.49 𝐸𝑙𝑒𝑣𝑎𝑡𝑜𝑟𝑖 + 3554.06 𝐶𝑒𝑙𝑙𝑎𝑟𝑖+ 17489.21 𝐶𝑜𝑛𝑑_1𝑖+ 13370.53 𝐶𝑜𝑛𝑑_2𝑖+ 8618.77 𝑃𝑎𝑟𝑘𝑖𝑛𝑔_1𝑖 (10) Table 6 shows the performance index values for constructed regression model. Table 6. Regression pricing models results. 𝑹𝟐 𝑹𝑴𝑺𝑬 𝑴𝑨𝑬 𝑴𝑨𝑷𝑬 0.7898 11454.91 8516.60 8.41% The best performing ANNs trained with the BR algorithm achieved 𝑀𝐴𝑃𝐸 values 3.39% and 3.58%, on the contrary, the regression pricing model achieved 𝑀𝐴𝑃𝐸 value 8.41%. Table 7 shows the estimated property prices for seven selected real estate properties from the test set. Based on the results, it can be stated that pricing models based on ANNs achieved a better predictive ability than the pricing model based on the regression method. Better prediction accuracy of ANNs compared to regression pricing models was reported by Moreno-Izquierdo et al. (2018), Tabales et al. (2013), Kutasi and Badics (2016), and Abidoye and Chan (2018) [7, 14-16]. These results are also supported by the literature review by Valier (2020), which examined research papers analyzing the accuracy of automated valuation models [32]. ANNs were indicated as more effective and reliable for mass evaluation of residential properties compared to regression models in 29 research papers. Compared to regression models, which were indicated as more effective compared to ANNS only in 6 research papers. Among the constructed neural networks, ANNs trained with the BR algorithm achieved the best results. Kayri (2016) analyzed the predictive ability of neural networks trained with BR and LM algorithms, he achieved higher predictive ability using the BR training algorithm [27]. The BR algorithm can approximate the price function well, despite a smaller data set containing 256 observations. The ability to merge training and validation data sets into a training set is an advantage of the BR algorithm for small data sets [26]. Based on previous research and the results of our work, it can be concluded that ANN with the BR learning algorithm and two hidden layers is suitable for the estimation of residential property market price. Table 7. Estimated property prices. Actual market price EUR ANN pricing model BR 10_20 ANN pricing model BR 15_15 Regression pricing model Estimated price EUR Residuals Estimated price EUR Residuals Estimated price EUR Residuals 101900.00 95716.64 -6183.36 95484.04 -6415.96 99432.76 2467.24 88400.00 103351.84 14951.84 104905.06 16505.06 102164.72 -13764.72 115000.00 116713.36 1713.36 115946.06 946.06 109295.56 5704.44 90000.00 85782.71 -4217.29 89159.76 -840.24 82800.58 7199.42 92900.00 93478.66 578.66 93524.76 624.76 93748.96 -848.96 96000.00 100241.91 4241.91 102498.06 6498.06 100927.01 -4927.01 82999.00 83900.15 901.15 95122.18 12123.18 93122.31 -10123.31 ===== PAGE 8 (score 10, numeric-paren 0, table-words 1, var-words 7) ===== Emerging Science Journal | Vol. 4, No. 6 Page | 537 5- Conclusion The paper analyzes the predictive ability of the automated valuation model using ANNs and the hedonic pricing model using the regression method. Regression pricing models are the traditional methods of residential property appraisal. With the increase in the use of soft computing techniques in various areas, researchers began to explore the possibilities of their use in the valuation of real estate properties. The paper analyzed ANN's ability to accurately estimate the market price of residential properties sold on the real estate market in the city of Nitra in the Slovak Republic. 60 ANNs trained with the LM learning algorithm, the BR learning algorithm, and the SCG learning algorithm were constructed and validated. Based on the comparison of their prediction accuracy, it can be stated that neural networks trained with the BR learning algorithm achieved the best results in the estimation of the market price of residential properties. ANN trained with the BR learning algorithm comprising two hidden layers (10 neurons in the first hidden layer and 20 neurons in the second hidden layer) achieved the best results in the monitored performances indices 𝑅2 =0.9749, 𝑀𝐴𝐸=3561.288, and 𝑀𝐴𝑃𝐸=3.39%. ANN trained with the BR learning algorithm comprising two hidden layers (15 neurons in both hidden layers) achieved the best results in the monitored performance index 𝑅𝑀𝑆𝐸= 6220.818. The regression pricing model constructed using the stepwise regression method with backward elimination achieved significantly worse values of the monitored performance indices R2=0.7898, RMSE=11454.91, MAE=8516.60, and MAPE=8.41%. The results of the analysis indicate the suitability of using ANN in the estimation of the market prices of residential properties. The use of the BR training algorithm, which achieved the highest predictive ability among the used training algorithms, is recommended. 6- Funding This paper was supported by the University Grant Agency of Constantine the Philosopher University in Nitra UGA no. VII/16/2019. 7- Conflict of Interest The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors. 8- References [1] Korenkova, M. “Business in Slovakia.“ Sbornik prispevku z mezinarodni vedecke konference: Region v rozvoji spolecnosti 2016 (October 2016): 459-469. [2] Pagourtzi, E., V. Assimakopoulos, T. Hatzichristos, and N. 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