1. Introduction

The word "hedonic", which means pleasant, is derived from the Greek word "hedonikos". In economics, it refers to the utility or satisfaction brought by goods or services to consumers.

Residential products have the characteristics of durability and spatial fixation, and are heterogeneous commodities [1]. There are obvious differences among products in the characteristics that constitute the use value [1]. The hedonic price model (HPM) focuses on the impact of property characteristics on its price, including location, housing structure and neighborhood factors. Therefore, the HPM is well suitable for real estate appraisal.

2. Theoretical Framework

The HPM was first proposed by Court in 1939 [2]. Since being introduced by Rosen (1974) to the residential market, it has developed to one of the most widely used models in the real estate industry [3]. The theoretical foundation underpinning HPM predominantly comprises Lancaster’s preference theory and Rosen’s market supply and demand equilibrium model [4]. Lancaster (1966) argued that product demand is based on a product’s characteristics rather than on itself, and that goods are sold as collections of intrinsic characteristics [5]. Therefore, products cannot only be represented by a total price, but a series of prices should be used to reflect the quality of the product or the features it contains, which we call hedonic price ^[1]. Rosen (1974) established the market supply and demand equilibrium model based on hedonic theory, a theory that helps to value the characteristics of differentiated products [6]. According to Rosen's theory, we can use econometric methods to separate the implied price of product features and analyze the demand for product features ^[6]. Since the characteristic price corresponding to residential characteristics cannot be obtained directly, it is necessary to collect information on residential characteristics and market transaction data to build a functional model [3]. Following an understanding of this, the regression relationship between price and asset-related attributes can successfully be established. Economic theory, however, does not clearly reveal how the functional form of such price regression should be chosen [7]. Consequently, researchers have attempted to use various functional forms to explore optimal solutions.

Compared with Sthe three most widely useveral basic functional forms such as linear, semi-lod traditional methods in real estate appraisal (i.e., the cost, market and income methods), the HPM has the advantages of flexible modeling and it is intuitive in terms of the economic significance of variables. It also makes it easy to observe the impact of increasing and log-log formdecreasing variables in the modeling process. In the era of big data, a large number of housing price transaction cases have been applied toconsistently led to an urgent need for data processing and analysis capabilities. This makes the HPM, ^[8]with its strong multi-parameter processing capability more favorable among scholars [8-11].

3. Recent Developments

The traditional HPM is based on the ordinary least squares (OLS) linear regression ^[9][12]. With advancements in computer technology and the increasing application of such advancements in the real estate industry, scholars are no longer satisfied with linear hedonic pricing models (which are neither stable or accurate) ^{[9][10][11][12]}[12-15]. Additionally, the hedonic theory assumes all essential characteristics are considered in the hedonic equation, which is seldom fulfilled due to limited data availability. Therefore, in the new era, technical improvements include: (1) With the development of big daInterneta and related and computer technology, scholars are able to obtain residential characteristics that are difficult to obtain, extract and accurately quantify in traditional valuation processes (e.g., the combination of point of interest (POI) data and geographic information system (GIS) analysis technology can accurately quantify the neighborhood characteristics of the properties ^[13][16]; some researchers have used deep neural network model to quantify the visual impression of properties ^[14][9]), which will undoubtedly make the results more convincing. (2) Multiple linear regression has disadvantages such as its inability to solve the collinearity of parameters, its insufficient consideration of the spatiality of housing price data, its sensitivity to noise, and it can also easily fall into over-fitting and have poor-fitting accuracy ^[15][16][17,18]. The HPM in the new era has attracted and integrated the advanced theoretical achievements of many disciplines and is continually improving and innovating based on actual demand. At present, researchers are predominantly adopting new algorithms to replace the kernel-least squares regression of the traditional HPM, and the new algorithm kernel can bring significant improvements to model stability and prediction accuracy. For example, specific improvements include: Long et al. (2009) used the spatial lag and spatial error model to examine the housing prices in Beijing, China, and obtained higher accuracy than the OLS model ^[17][19]. Ma et al. (2020) regarded house price prediction as a classification problem of interval prediction and used the deep forest (DF) model to predict housing rent and prices in the United States ^[18][20]. IAddition recent years, extensive studies have shown that machine learnally, with rapid developments in related research, some researchers have begun to compare various advanced models toward determining the conditions for their optimal application [13].

Fingally, (ML) modelmass appraisal is based on hedonic pricereal estate appraisal theory have higher accuracy than tradition, relying on computer technology and using pre-established appraisal models ^[9][19][20].to Aevalthough ML models are black box models and have the disadvantage of low interpretability, they are still the future of automated valuation models (AVMs). Because they can move AVMs from low-risk valuations with suffuate multiple real estates at one time, which is an important direction of the real estate appraisal industry. It is also a choice for many scholars to use hedonic price method to construct the model of mass appraisal, and has achieved good results [12,15,21].

Reference:

1. Haicizhent comparables towards more complex valuations for all property types, W. Characteristic price of urban housing: Theoretical analysis and empirical study. Ph.D Thesis, ^[21].AddZhejiang University, Hangzhou, China, 2004.

2. Goodmanally, with rapid developments in rel, A.C. Andrew Court and the Invention of Hedonic Price Analysis. J. Urban Econ. 1998, 44, 291-298, doi:https://doi.org/10.1006/juec.1997.2071.

3. Watng, X. Thed research, some researchers have begun to compare various advanced of housing characteristic price in Shanghai based on hedonic models toward determining. Ph.D Thesis, Tongji University, Shanghai, China, 2006.

4. thWe conditions for their optimal applicationn, H.; Lu, J.; Fu, Y. Product differentiation and hedonic prices: An empirical analysis. In Proceedings ^[10].

4. The advantages of HPM in real estate appraisal

Comparedf with the three most widely used traditional methods in rethe 2005 International Conference on Services Systems and Services Management (ICSSSM), Chongquing, China, 13-15 June 2005; pp. 1259-1263.

5. Lal encastate appraisaler, K.J. A New Approach to Consumer Theory. J. Political Econ. 1966, 74, 132-157, (doi:https://doi.org/10.1086/259131.

6. Rosen, S., the cost, market and income methods) Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition. J. Political Econ. 1974, 82, the34-55, HPMdoi:https://doi.org/10.1086/260169.

7. hWas the advantages of flexible modeling and it is intuitive in terms of theng, D.; Huang, W. Effect of urban environment on residential property values by hedonic method: A case study of ShangHai. City Plan. Rev. 2007, 31, 34-41+46, econdomici:https://doi.org/10.3321/j.issn:1002-1329.2007.09.006.

8. sLignificance of variables. It also makes it easy to observe the impau, K.; Li, Z.; Zhang, X. Empirical research based on web data:An analysis on spatio-temporal effect of increasing and decreasing variables in the modeling procescity rail transit on residential house prices. InComput. Sci. 2015, the42, era199-203,213, of bigdoi:https://doi.org/10.11896/j.issn.1002-137X.2015.09.038.

9. dLata, a large number of housing price transaction cases have cw, S.; Paige, B.; Russell, C. Take a look around: Using street view and satellite images to estimate house prices. ACM Trans. Intell. Syst. Technol. 2019, 10, 1-19, doi:https://doi.org/10.1145/3342240.

10. Fu, X.; Jia, T.; Zhansg, X.; Listently led to an urgent need for data processing and, S.; Zhang, Y. Do street-level scene perceptions affect housing prices in Chinese megacities? An analysis capabilities. This makes theusing open access datasets and deep learning. HPMPLoS ONE 2019, 14, e0217505, wdoith:https://doi.org/10.1371/journal.pone.0217505.

11. Selits strong multi-parameter processing capability more favorablem, H. Determinants of house prices in Turkey: Hedonic regression versus artificial neural network. Expert Syst. Appl. 2009, am36, 2843-2852, doi:https://doi.org/10.1016/j.eswa.2008.01.044.

12. Hong, scholarsJ.; Choi, ^{[14][22][23][24]}H.; Additionally, mass appraisal isKim, W.-s. A house price valuation based on real estate athe random forest approach: the mass appraisal theory, relying on computer technology and using preof residential property in South Korea. Int. J. Strateg. Prop. Manag. 2020, 24, 140-establ152, doished:https://doi.org/10.3846/ijspm.2020.11544.

13. appTorraisal models to evaluate multiple real estates at one time, which is an important direction of the real estate aes-Pruñonosa, J.; García-Estévez, P.; Prado-Román, C. Artificial Neural Network, Quantile and Semi-Log Regression Modelling of Mass Appraisal industry Housing. ItMathematics 2021, 9, dois:https://doi.org/10.3390/math9070783.

14. alsZho a choice for many scholars to use hedonic price method to constructu, G.; JiChen, Y.; Chen, X.; Zhang, F. Artificial neural networks and the model of mass appraisal, and has of real estate. Int. J. Online Eng. 2018, 14, 180-187, achdoi:https://doi.org/10.3991/ijoe.v14i03.8420.

15. Pevted good resultsrson, S.; Flanagan, A. Neural ^[9][12][25].

5. Empirical Issues

Onetwork the other hand, thehedonic pricing models in mass real estate appraisal. baseJ. Real Estate Res. 2009, 31, 147-164, doi:https://doi.org/10.1080/10835547.2009.12091245.

16. onLi, HPM is most favored by scholars, but the complexity.; Wei, Y.D.; Wu, Y. Analyzing the private rental housing market in Shanghai with open data. Land Use Policy 2019, 85, 271-284, dofi:https://doi.org/10.1016/j.landusepol.2019.04.004.

17. uZambrano-Monse and some inherent defects limit its applicationrrate, M.A.; Ruano, M.A. Does environmental noise affect housing rental prices in developing countries? Evidence from Ecuador. Land Use Policy 2019, 87, 104059, doi:https://doi.org/10.1016/j.landusepol.2019.104059.

18. Yu, D.; Wu, C. In corpractice. Specific factors include: (1) As mentioned aboveorating remote sensing information in modeling house values: A regression tree approach. Photogramm. Eng. Remote Sens. 2006, 72, the129-138, theorydoi:https://doi.org/10.14358/PERS.72.2.129.

19. Lof hedonic pricing does not clearly reveal how the proper functional form shouldng, F.; Zheng, S.; Wang, Y.; Guo, M. Value estimates of local public services using a spatial econometric model. beJ. Tsinghua University. Sci. Technol. 2009, chosen;49, (2028-2) hedonic031, doi:https://doi.org/10.16511/j.cnki.qhdxxb.2009.12.028.

20. Ma, C.; prLice studies don't pay enough attention to market segmentationu, Z.; Cao, Z.; Song, W.; Zhang, J.; Zeng, W. Cost-sensitive deep forest for price prediction. Pattern Recogn. 2020, but107, 107499, doit:https://doi.org/10.1016/j.patcog.2020.107499.

21. Yousfis an important empirical issue; (3) the misspecification of variables will lead to inefficient or biased and inconsistent estimate, S.; Dubé, J.; Legros, D.; Thanos, S. Mass appraisal without statistical estimation: a simplified comparable sales approach based on a spatiotemporal matrix. Ann. Reg. Sci. 2020, 64, 349-365, d coefficients ^[8]i:https://doi.org/10.1007/s00168-019-00959-2.