Application of robust estimation methods in real estate valuation

Tomasz Adamczyk

doi:10.31648/aspal.10726

Published: 2024-12-231

Vol. 23 No. 4 (2024)

Application of robust estimation methods in real estate valuation

Tomasz Adamczyk

Acta Scientiarum Polonorum Administratio Locorum

Section: Articles

https://doi.org/10.31648/aspal.10726

Abstract

Motives: Conducting real estate appraisals in well-developed markets presents a multitude of data analysis challenges. Some property price data may contain outliers that can significantly affect the valuation process and, as a result, the estimated value. In the case of real estate valuation regression models, estimation is most often based on the least squares method, where outliers are taken into account just like the rest of the data. Eliminating or minimizing the influence of outliers can lead to more reliable estimation results. Such problems can be solved by implementing robust regression methods.

Aim: The main goal is to determine whether robust estimation methods using M-estimators with multiple regression models can provide more accurate estimates of property values.

Results: Research has shown that multiple regression models using robust regression methods can be applied to estimate property values. The use of different types of M-estimators allows for the objective elimination of outliers through algorithms that operate on the entire data set. The calculations are carried out iteratively, and at each iteration step the residuals are verified and the observations are re-weighted. The following M-estimators were considered: Huber, Hampel, Tukey, Faire, Cauchy and Welsch. The reference point was the estimation results from the ordinary least squares method (OLS). All analysed M-estimators led to an increase in the coefficient of determination value and a decrease in standard estimation errors. Each algorithm detected the outliers. The valuation results for the selected properties were also more reliable. The results obtained depend on the characteristics of the data, and the choice of the best estimator may vary across different property markets. The selection of the best estimator may even vary within the same local property market, where the valuer makes subjective assessments of the location or other attributes.

Keywords:

robust regression, M-estimator, property valuation, multiple regression, robust estimators

Download files

PDF

Citation rules

Adamczyk, T. (2024). Application of robust estimation methods in real estate valuation. Acta Scientiarum Polonorum Administratio Locorum, 23(4), 349–360. https://doi.org/10.31648/aspal.10726

Cited by / Share

Licence

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

Abdulhafedh, A. (2022). Incorporating Multiple Linear Regression in Predicting the House Prices Using a Big Real Estate Dataset with 80 Independent Variables. Open Access Library Journal, 9(1). DOI: 10.4236/ oalib.1108346
Crossref
Google Scholar

Adamczyk, T. (2017). Application of the Huber and Hampel M-estimation in real estate value modeling. Geomatics and Environmental Engineering, 11(1), 15–23. DOI: dx.doi.org/10.7494/geom.2017.11.1.15
Google Scholar

Adamczyk, T. (September, 2017). Application of Huber and Hampel m-estimation in analysing of real estate price volatility over time [Conference proceedings]. Geographic Information Systems Conference and Ex¬hibition “GIS ODYSSEY 2017”, Trento – Vattaro, Italy.
Crossref
Google Scholar

Albuquerque, J. S, & Biegler, L. T. (1996). Data recon¬ciliation and gross-error detection for dynamic sys¬tems. AIChE Journal, 42(10), 2841–2856. https://doi. org/10.1002/aic.690421014
Crossref
Google Scholar

Anderws, D. F. (1974). A Robust Method for Multiple Lenear Regression. Technometrics, 16(4), 523–531. https://doi.org/10.2307/1267603
Crossref
Google Scholar

Arya, K. V., Gupta, P., Kalra, P. K., & Mitra, P. (2007). Image registration using robust M-estimators. Pattern Recognition Letters, 28(15), 1957–1968. https://doi. org/10.1016/j.patrec.2007.05.006
Crossref
Google Scholar

Banaś, M., & Ligas, M. (2014). Empirical test of performance of some M-estimators. Geodesy and Cartography, 63(2), 127–146. https://doi.org/10.2478/ geocart-2014-0010
Crossref
Google Scholar

Banaś, M., Czaja, J., & Dąbrowski, J. (2022). The Application of Regression Analysis for Estimating the Market Value of Commercial Real Estate. Geomatics and Environmental Engineering, 16(1), 17–35. DOI:10.7494/geom.2022.16.1.17
Crossref
Google Scholar

Chen, C. (2002). Robust Regression and Outlier Detection with the ROBUSTREG Procedure [Conference Paper]. Proceedings of the Twenty-Seventh Annual SAS Users Group International Conference, SAS Institute Inc., Cary, NC.
Google Scholar

Dehnel, G. (2015). Robust regression in Monthly Business Survey, Statistic in Transition new series, 16(1), 137–152. https://doi.org/10.59170/stattrans-2015-008
Crossref
Google Scholar

Dehnel, G., & Gołata, E. (2016). M-estimation in a Small Business Survey. Krakow Review of Economics and Management Zeszyty Naukowe Uniwersytetu Eko¬nomicznego W Krakowie, 1(949), 5–21. https://doi. org/10.15678/ZNUEK.2016.0949.0101
Crossref
Google Scholar

Grover, R., & Walacik, M. (2019). Property valuation and taxation for fiscal sustainability–lessons for Poland. Real Estate Management and Valuation, 27(1), 35–48. https://doi.org/10.2478/remav-2019-0004
Crossref
Google Scholar

Hampel, F. R. (1968). Contribusion to the theory of robust estimation. Univeristy of California.
Google Scholar

Huber, P. (1964). Robust Estimator of a Location Parameter. Ann. Math. Statist, 35(1), 73–101. https:// doi.org/10.1214/aoms/1177703732
Crossref
Google Scholar

Lemeš, L., & Akagic, A. (2022). Prediction of Real Estate Market prices with Regression Algorithms. In Ademović, N., Mujčić, E., Mulić, M., Kevrić, J., Akšamija, Z. (Eds.), Advanced Technologies, Systems, and Applications VII. IAT 2022. Lecture Notes in Networks and Systems (Vol. 539) (pp. 401–411). Springer. http://dx.doi.org/10.1007/978-3-031-17697- 5_32
Crossref
Google Scholar

Jana, P., Rosadi, D., & Supandi, E. D. (2023). Comparison of robust estimation on multiple regression model. Journal of Mathematics and Its Applications, 17(2). https://doi.org/10.30598/ barekengvol17iss2pp0979-0988
Crossref
Google Scholar

Janssen, Ch., Söderberg, B. & Zhou, J. (2001). Robust estimation of hedonic models of price and income for investment property. Journal of Property Investment & Finance, 19(4), 342–360. http://dx.doi.org/10.1108/ EUM0000000005789
Crossref
Google Scholar

de Menezes, D. Q. F., Prata, D. M., Secchi, A. R. & Pinto J. C. (2021). A review on robust M-estimators for regression analysis. Computer & Chemical Engineering, 147, Article 107254. https://doi. org/10.1016/j.compchemeng.2021.107254
Crossref
Google Scholar

Mulry, M. H., Kaputa, S., & Thompson, K. J. (2018). Setting M-Estimation Parameters for Detection and Treatmen of Infuential Values. Journal of Office Statistics, 34(2), 483–501. https://doi.org/10.2478/jos- 2018-0022
Crossref
Google Scholar

Nowel, K. (2019). Squared Msplit(q) S-transformation of control network deformations. Journal of Geodesy, 93, 1025–1044. https://doi.org/10.1007/s00190-018-1221-4
Crossref
Google Scholar

Özyurt, D. B., & Pike, R. W. (2004). Theory and practice of simultaneous data reconciliation and gross error detect for chemical processes. Computer and Chemical Engineering, 28(3), 381–402. https://doi.org/10.1016/j. compchemeng.2003.07.001
Crossref
Google Scholar

Pires, R. C., Simoes Costa, A., & Mili, L. (1999). Iteratively Reweighted Least-Squares State Estimation Through Givens Rotations. IEEE Transactions on Power System, 14(4). https://doi.org/10.1109/59.801941
Crossref
Google Scholar

Raza, A., Talib, M., Noor-ul-Amin, M., Gunaime, N., Boukhris, I., & Nabi, M. (2024). Enhancing perfor¬mance in the presence of outliers with redescending M-estimators. Scientific Report, 14, Article 13529. https://doi.org/10.1038/s41598-024-64239-6
Crossref
Google Scholar

Ross, R. K., Zivich, P. N., Stringer, J. S. A., & Cole, S. R. (2024). M-estimation for common epidemiliological measures: introduction and applied examples. International Journal of Epidemiology, 53(2). https:// doi.org/10.1093/ije/dyae030
Crossref
Google Scholar

Ruckshtul, A. (2016). Robust Fitting of Parametric Models Based on M-Estimation. IDP Institute of Data Analysis and Process Design; ZHAW Zurich University of Applied Sciences in Winterthur. https://ethz.ch/ content/dam/ethz/special-interest/math/statistics/ sfs/Education/Advanced%20Studies%20in%20 Applied%20Statistics/course-material-1719/Robuste/ robstat18E.pdf
Google Scholar

Susanti, Y., Pratiwi, H., Sulistijowati, S. H., & Liana, T. (2014). M estimation, S estimation, and MM esti¬mation in robusty regression. International Journal of Pure and Applied Mathematics, 91(3), 349–360. https://doi.org/10.12732/ijpam.v91i3.7
Crossref
Google Scholar

Śpiewak, B. (2018). Application of Passive Methods of Robust Estimation: Baarda’s and Pope’s in Real Estate Market Analysis. Real Estate Management and Valuation, 26(1). http://dx.doi.org/10.2478/ remav-2018-0001
Crossref
Google Scholar

Śpiewak, B., & Barańska A. (2020). Chosen statistical methods for the detection of outliers in real estate market analysis. Acta Scientiarum Polonorum Administratio Locorum, 19(2), 109–118. https://doi. org/10.31648/aspal.4608
Crossref
Google Scholar

Walacik, M., Cellmer, R., & Źróbek, S. (2013). Mass appraisal–international background, Polish solutions and proposal of new methods application. Geodetski list, 67(4), 255–269.
Google Scholar

Wiśniewski, Z. (2009). Estimation of parameters in a split functional model of geodetic observations (Msplit estimation). Journal of Geodesy, 83(2), 105–120. https://doi.org/10.1007/s00190-008-0241-x
Crossref
Google Scholar

Wiśniewski, Z. (2010). Msplit(q) estimation: estimation of parameters in a multi split functional model of geodetic observations. Journal of Geodesy, 84, 355–372. https://doi.org/10.1007/s00190-010-0373-7
Crossref
Google Scholar