1# RECORD 09caaf09cd085f29d8f22c8f28dd86b492ec121d2# TITLE: ESTABLISHING DYNAMIC IMPACT FUNCTION FOR HOUSE PRICING BASED ON SURRENDING MULTI-ATTRIBUTES: EVIDENCE FROM TAIPEI CITY, TAIWAN3# YEAR: 2020.0 VENUE: nan DOI: 10.3846/ijspm.2020.110964# AUTHORS: Jieh-Haur Chen; Li-Ren Yang; V. T. Azzizi; Eric-Liluan Chu; Hsi-Hsien Wei5# PAGES: 11 CANDIDATE TABLE PAGES (1-based): [6, 7, 9]6# ABSTRACT: The objective of the research is aimed for a solution that is to establish the dynamic impact function of surrounding multi-attribute for house pricing. It is also able to measure the ripple effect and allows the hedonic parameter estimates to vary from point-to-point. A comprehensive literature review is carried out to obtain an adequate theoretical basis for the corresponding hypothesis and concepts. The proposed dynamic impact function for multiattributes is then constructed based on the characteristics of surrounding facilities. Adopting the convenience sampling criteria of 95% confidence level on the data sampling and 10% limit of error in a 5−95% proportion, we collect the empirical data of 39 yearly house sales in the investigated urban areas of Taipei city focusing on housing prices and then utilize them for evaluating and adjusting the function. The actual house price and that of proposed function affected by Mass Rapid Transit (MRT) stations are analysed, resulting in the correlation coefficient at 0.946 (single attribute) and 0.944 (multi-attribute), respectively. The findings support that proposed function can highly represent the house pricing pattern and be an accurate tool for appraisers.789===== PAGE 1 (score 15, numeric-paren 1, table-words 1, var-words 12) =====1011Copyright © 2020 The Author(s). Published by VGTU Press12This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unre-13stricted use, distribution, and reproduction in any medium, provided the original author and source are credited.14ESTABLISHING DYNAMIC IMPACT FUNCTION FOR HOUSE PRICING 15BASED ON SURRENDING MULTI-ATTRIBUTES: 16EVIDENCE FROM TAIPEI CITY, TAIWAN17Jieh-Haur CHEN1,*, Li-Ren YANG2, Vidya Trisandin AZZIZI1, Eric CHU1, Hsi-Hsien WEI3181 Department of Civil Engineering, National Central University, Jhongli, Taiwan192 Department of Business Administration, Tamkang University, Tamsui, Taiwan203 Department of Building and Real Estate, The Hong Kong Polytechnic University, Hong Kong, PR China21Received 10 September 2018; accepted 05 August 201922Abstract. The objective of the research is aimed for a solution that is to establish the dynamic impact function of surround-23ing multi-attribute for house pricing. It is also able to measure the ripple effect and allows the hedonic parameter estimates 24to vary from point-to-point. A comprehensive literature review is carried out to obtain an adequate theoretical basis for the 25corresponding hypothesis and concepts. The proposed dynamic impact function for multi- attributes is then constructed 26based on the characteristics of surrounding facilities. Adopting the convenience sampling criteria of 95% confidence level 27on the data sampling and 10% limit of error in a 5−95% proportion, we collect the empirical data of 39 yearly house sales 28in the investigated urban areas of Taipei city focusing on housing prices and then utilize them for evaluating and adjusting 29the function. The actual house price and that of proposed function affected by Mass Rapid Transit (MRT) stations are ana-30lysed, resulting in the correlation coefficient at 0.946 (single attribute) and 0.944 (multi-attribute), respectively. The find-31ings support that proposed function can highly represent the house pricing pattern and be an accurate tool for appraisers.32Keywords: house pricing theory, impact function, multi-attribute, financial engineering, property management.33Introduction34Over the last few years, the Taiwan government has ap-35plied a new policy regarding property tax within the real 36estate domain which has had a considerable impact on 37the Taiwan real estate market. The possible turnover index 38for the period from 2003 to 2005 had dropped from its 39original peak of 136.77 to 121.38. Furthermore, because 40of this property tax, some construction companies are re-41luctant to build new properties (Bahmani-Oskooee & Wu, 422018). Even the ones that have already started a project 43may be reluctant to complete it, because after completion, 44the contractor has to bear a huge tax burden even prior 45selling it. These circumstances have caused many investors 46to withdraw from the real estate market. The proportion 47of customers who buy their own homes or their own real 48estate has increased. The Ministry of the Interior’s real es-49tate platform has identified the following trend: the rate 50for residential demand for the first half year was 43%. 51The change of housing demand accounted for 42%, with 52an increase of 4.7% in the second half of the year. This 53was the highest within the last five years, previously the 54rate had never gone above 4% (Bahmani-Oskooee & Wu, 552018). Consumers choosing self-built real estate take into 56account various factors such as the quality of housing, the 57surroundings, parking, traffic convenience, and so on. De-58spite the fact that accurate appraisals and consideration of 59impact factors have helped to improve consumer aware-60ness of real estate prices, it is still difficult for them to 61assess the impact of different factors on real estate prices. 62There has been little on the accurate assessment of the 63impact of real estate impact factors, therefore consumers 64do not have any basis of reference to follow.65The rational and effective allocation of information as 66well as resource integration has only been used by real 67estate producers for determination of prices. Consumers 68and government departments also need to pursue this 69goal. Rosen introduced the Hedonic price theory in 1974, 70which became the main method to solve the pricing prob-71lem with a wide range of applications. In addition to its 72application in real estate analysis, it is also used in agricul-73tural land use analysis, agricultural marketing, video game 74marketing, industrial product marketing, environmental 75International Journal of Strategic Property Management76ISSN: 1648-715X / eISSN: 1648-9179772020 Volume 24 Issue 2: 119–12978https://doi.org/10.3846/ijspm.2020.1109679*Corresponding author. E-mail: jhchen@ncu.edu.tw808182===== PAGE 6 (score 23, numeric-paren 0, table-words 4, var-words 11) =====838412485J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...86The value of α is always positive, because in house 87price convergence, the value of the house price is always 88greater than zero.894. Implementation and discussion90The research has provided a solution that is to establish the 91dynamic impact function of surrounding multi-attribute for 92house pricing. It is also able to measure the ripple effect and 93allows the hedonic parameter estimates to vary from point-94to-point. Thus, there are two implementations to evaluate 95the proposed function f(x). The first one is to evaluate the 96proposed function using a single main facility that affects 97house prices. The other one is for multi-attributes (main 98facilities). The following conditions must be met: (1) there 99must be no other major impact factor affecting housing 100prices in the MRT area; (2) the main impact on housing 101prices in the area is proximity to MRT facilities; (3) there 102are no other MRT stations within a investigated range, so it 103is clear which MRT station acts as the main facility that af-104fects house prices. After determining the area, the real estate 105locations are chosen using the Ministry of Interior real estate 106network transaction price inquiry service. The real estate is 107selected according to the following conditions, being similar 108in: (1) age; (2) size; (3) quality; and (4) terms of the reputa-109tion of the construction company that develops the real es-110tate. After the selection of real estate cases around the MRT 111station, information regarding location of the transaction, 112real estate area, transaction price, price per unit, room and 113housekeeping patterns, as well as floor height is obtained 114using the Ministry of Interior real estate transaction data 115base. Other real estate related information is obtained using 116Google earth, such as date, house age, the time it takes for 117the house to be sold, access to parking, number of floors, 118and real estate category. Analysis of position, distance from 119the MRT station, as well as status quo is carried out using 120GIS and survey data. For the feature price impact function 121affected by a single and multiple factors (numbers of MRT 122stations), we conduct 4 case studies: Beitou MRT station 123(single factor), Jingmei MRT (single factor), Houshanpi-124Kunyang MRT (2 factors), Dongmen-Zhongxiao-Xinsheng 125MRT (3 factors) stations in the investigated area based on 126convenient sampling. The prices of total 138 housing units 127sold in 2009 around investigated MRT stations are selected, 128which satisfies 95% confidence level on the data sampling 129and 5% limit of error in a 10–90% proportion (Chen & Hsu, 1302008; Chen, Yang, Su, & Lin, 2010). The observations cover 131house sold data in the investigated area in a limited time pe-132riod (May, 2009) in 2009. This can minimize the impact by 133force majeure such domestic macro-economy, global trade 134volatility, and major disasters. The reason to use past data is 135due to the data/case sensitivity themselves. It may influence 136house transactions/price if revealing latest information. For 137Case Study 1 and 2, they can be inferred as the significant 138factor because there are no other factors that affect the price 139of housing in the surrounding area. Beitou MRT station is 140located in the Taipei north region approximately 6 km away 141from downtown center and Jingmei MRT station is in the 142south side of the city, also approximately 6 km away from 143downtown center. For Case Study 3 and 4, Houshanpi-Ku-144nyang MRT stations (2 factors) are approximate 1 km away 145from the main shopping district of Taipei and Dongmen-146Zhongxiao-Xinsheng MRT stations (3 factors) are right at 147the most prosperous center of the city.148The chosen housing units sold from 3 to 7 years old are 149all located in the investigated regions. None of the chosen 150apartment buildings had first-floor storefronts, and the se-151lected units are located on the 2nd to 10th floors. Each unit 152is between 30 and 60 pings (100 to 200 meter2) in area. It 153can be seen that the theoretical house price curve is similar 154to the actual house price curve, and shows the same trend. 155The correlation between the two lines is analyzed using 156the distance between the actual housing unit and the MRT 157station. The CORREL (array1, array2) function in Micro-158soft Excel allows users to calculate correlation coefficient r 159by inserting the real price data and estimated price by the 160proposed function. The value of the correlation is between 1611 and −1. The closer to 1 the greater the correlation, the 162higher the degree of similarity between the two curves, im-163plying that the proposed function can be applied in prac-164tice. By inserting the dynamic impact function (Equation 16515), the actual house price and the theoretical house price 166are analysed using the CORREL function in Microsoft Ex-167cel. Tables 1−3 show that all of their correlation coefficients 168r > 0.9 (0.946, 0.981, and 0.944 respectively).169Table 1. The actual distance and case prices affected by a single 170impact factor (Beitou MRT station, Taipei)171Observation172Distance 173(m)174Actual 175house price 176(million NTD/m2)177Predicted house 178price (million 179NTD/m2)18011817018214.9218315.11184218511018616.1218716.26188318914519016.6419116.64192419319619416.6119516.64196519723419815.9719915.23200620130020215.4020313.94204720531420614.2420713.77208820931421014.1521113.77212921333621413.6521513.552161021736421813.5021913.322201122140022213.1822313.102241222544522612.6122712.882281322945423012.4923112.852321423351323412.3223512.652361523756823812.6223912.512401624165324212.5724312.352441724567924611.7724712.312481824969425010.8525112.29252Correlation coefficient r = 0.946253254255===== PAGE 7 (score 23, numeric-paren 0, table-words 4, var-words 3) =====256257International Journal of Strategic Property Management, 2020, 24(2): 119–129258125259Table 2. The actual distance and case prices affected by a single 260impact factor (Jingmei MRT station, Taipei)261Observation262Distance 263from 264Jingmei 265MRT 266station 267(m)268Actual 269house price 270(million NTD/m2)271Predicted house 272price (million 273NTD/m2)274127519127612.3027712.30278227920328012.2228112.22282328324728411.9328511.93286428727028811.312899.95290529127229211.4229311.31294629527429611.0629711.4229872993013009.833018.8530283033073049.453059.4530693073113088.923098.92310103113163128.893138.62314113153273168.763178.49318123193463208.753218.49322133233513248.743258.48326143273553288.653298.39330153313583328.593338.16334163353753368.263377.85338173393983408.243417.83342183434033448.063457.66346193474253488.063497.66350203515113528.023537.62354213555283567.923577.53358223595503607.903617.51362233635543647.793657.79366243675573687.773697.77370253715583727.763737.76374263755593767.743777.74378273795613807.693817.69382283835703847.643857.64386293875883887.623897.62390303915933927.543937.54394313956043967.473977.47398323996334007.464017.46402334037234047.394057.39406344077454087.384097.38410354118134127.354137.35414364158304167.304177.30418374198344207.264217.26422384238404247.244257.24426394278474287.234297.23430404318494327.224337.22434Correlation coefficient r = 0.981435Table 3. Actual distance and case prices affected by multiple 436impact factors (2 factors)437Observation438Distance 439from 440Houshanpi 441MRT 442station 443(m)444Distance 445from 446Kunyang 447MRT 448station 449(m)450Actual 451house 452price 453($million 454NTD/m2)455Predicted 456house 457price 458($million 459NTD/m2)46014611462139946312.2146412.25465246628467137346812.7346912.72470347166472133447313.0847413.52475447679477132147813.7947913.794805481248482115348314.5048414.494856486255487114548814.4648914.494907491263492113749313.9049414.304958496325497107549813.2349913.27500950143150296950312.7050412.595051050643150796950812.6450912.595101151152551287551311.3351412.315151251666551773551811.5751911.505201352183152256952314.4452413.675251452686152753952814.3952914.055301553190053250053314.8253414.825351653696553743553814.6753914.825401754197054243054313.6954414.8254518546100354739854814.3054914.8255019551118855221355314.1255414.5455520556124155715955814.1455914.37560215611395562556313.2856413.75565Correlation coefficient r = 0.944566Figures 2−4 illustrate the fitting between actual and 567predicting house sold price. For Case study 1, the pres-568ence of a park (Chengde Park) increases the quality of 569life in the surrounding area, making house prices higher 570than the theoretical curve, as indicated by results obtained 571after a field visit. It can be seen that the theoretical house 572price curve is similar to the actual house price curve, 573and shows the same trend. Accordingly, the findings in-574dicate that it is the facility characteristics which affect 575the level of housing prices. It can be seen that there is 576a convergence of housing prices in the same area. For 3 577or more attributes, assuming that there are N MRT sta-578tions affecting the same area, the dynamic function gives 579( )580( )581( )582( )583( )584( )585( )586( )587158825893590159125923593,594,595,596,597N598N599f600x601f602x603f604x605f606x f607x608f609x610f611x612f613x614…615…616. 617Thus, N-1 should be summed and deducted from α. The 618aggregate is as formulated follows:619( )620(621)6221623N624i625i626f627x628N629630−631−632α633634635∑636. 637(16)638639640===== PAGE 8 (score 2, numeric-paren 0, table-words 0, var-words 1) =====641642126643J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...644Actual price 645Theoretical 646house price 647Price/ping 648Price (in 64910.000 650NTD) 651Distance from MRT station 65260.0065350.0065440.0065530.0065620.0065710.006580.006590 660200 661400 662600 663800 (m)664Figure 2. Comparison between theoretical and actual house price curve influenced by single 665factor (Beitou MRT station, Taipei)666Figure 3. Comparison between theoretical and actual house price curve influenced by single 667factor (Jingmei MRT station, Taipei)6680 669500 6701000 6711500 (m)672Price/ping 673Price (in 67410.000 675NTD) 676Distance from MRT station 677Actual price 678Theoretical 679house price 68060.0068150.0068240.0068330.0068420.0068510.006860.00687Figure 4. Comparison between theoretical and actual house price curve influenced by 688multiple factors (2 factors)689690691===== PAGE 9 (score 18, numeric-paren 0, table-words 5, var-words 6) =====692693International Journal of Strategic Property Management, 2020, 24(2): 119–129694127695For example, if there are three MRT stations in the 696investigation area, 3^N types of function combination 697should be taken into consideration since each MRT sta-698tion has a combination of three dynamic functions. As a 699result, for Case Study 4 with 3 attributes (3 MRT stations), 700the resulting correlation coefficient is r = 0.912 still highly 701matching to the real housing price as shown in Table 4 702and Figure 5.703Figure 5 exhibits several peaks for the house price due 704to more attributes that can influence house price such as 705shopping malls, parks, stadiums, and schools. The dy-706namic impact function of surrounding multi-attributes for 707house pricing is then evaluated and ready for both further 708academic study and practical use.709Conclusions710This is an academic study focused on the construction of a 711dynamic impact function of surrounding multi-attributes 712for house pricing. This paper discusses not only real estate 713characteristics regarding distance effects but practical ap-714plications for improving appraisal accuracy. The analysis 715from the empirical implementation is carried out in order 716Table 4. Actual distance and case prices affected by multiple impact factors (3 factors)717Observation (59 in total)718Shortest distance to 719the closest MRT (m)720Longest distance to 721the farthest MRT 722(m)723Actual house price 724($million NTD/m2)725Predicted house 726price ($million 727NTD/m2)7281 (Shortest distance)7296273090773114.6273214.6273352 (Longest distance)734751735107373612.7273711.4473815 (Highest actual price)73921174084774115.7674214.9774320 (Highest predicted price)74432174586674615.7574715.7574857 (Lowest actual price)74936875074575110.4075210.407536 (Lowest predicted price)75414175590175610.6575710.33758Average75939176081876113.1076212.92763Standard Deviation7642027652457661.317671.37768Correlation coefficient r = 0.912769to test its impact on real estate pricing, to examine the real 770estate impact curve interpretation ability, and finally to 771apply the results to verify accuracy for the function. The 772implementation using empirical data is one of the contri-773butions demonstrating the feasibility of the proposed func-774tion. In addition, the function is verified by empirical cases 775and the results can enhance appraisal accuracy, real estate 776market development, and strategies in the future. From the 777findings of correlation coefficient r = 0.944 and 0.946 for a 778single and multi-attributes, respectively, we can convey that 779the proposed function is an effective method to express 780(1) the ripple effects by multi-attributes to the target house 781price, (2) a dynamic distance pattern to the house price. 782It, thus, gives appraisers an accurate model for estimating 783house prices. This study differs from the previous studies 784in that the relationship between the proximity to the facil-785ity and the real estate price is presented in the form of a 786mathematical function with high accuracy. A thorough un-787derstanding of real estate appraisal and related knowledge 788can help across the field. As a result, the implementation of 789the proposed model can be used to establish different vari-790ables such as distance factors and proximity to “YIMBY” 791facilities in the field of selected location.792Figure 5. Comparison between theoretical and actual house price curve influenced 793by multiple factors (3 factors)794795796===== PAGE 10 (score 11, numeric-paren 0, table-words 0, var-words 8) =====797798128799J.-H. Chen et al. Establishing dynamic impact function for house pricing based on surrending...800The findings explain real estate price well in a math-801ematical way based on distance; however, the model may 802be not applicable when other factors are out of current 803consideration or assumptions such as economic impact, 804political impact, force majeure, and long-run period. For 805example, economic status may be changed dramatically in 806a developing country. Political or unforeseen impact may 807create temporarily deviation in the investigated region. 808Any period longer than one year may also cause price 809escalation/de-escalation due to inflation/disinflation. The 810follow-up study is encouraged to deal with time integrated 811with macroeconomic issues that may lead practitioners to 812a different level of dynamic prediction model for real es-813tate pricing.814Acknowledgements815This work was partly supported by the Ministry of Sci-816ence and Technology (MOST), Taiwan, for promoting 817academic excellent of universities under grant numbers 818of MOST-106-2221-E-008-020-MY2.819Disclosure statement820All authors do not have any competing financial, profes-821sional, or personal interests from other parties.822References823Agyemang, F. O., Asamoah, P. K. B., & Obodai, J. (2018). Chang-824ing family systems in Ghana and its effects on access to urban 825rental housing: a study of the Offinso Municipality. Journal of 826Housing and the Built Environment, 33(4), 893-916. 827https://doi.org/10.1007/s10901-018-9604-7828Alexander, C., & Barrow, M. (1994). Seasonality and cointegra-829tion of regional house prices in the UK. Urban Studies, 31, 8301667-1689. https://doi.org/10.1080/00420989420081571831Antonakakis, N., Chatziantoniou, I., Floros, C., & Gabauer, D. 832(2018). The dynamic connectedness of UK regional property 833returns. Urban Studies, 55(14), 3110-3134. 834https://doi.org/10.1177/0042098017739569835Badarinza, C., & Ramadorai, T. (2018). Home away from home? 836Foreign demand and London house prices. Journal of Finan-837cial Economics, 130(3), 532-555. 838https://doi.org/10.1016/j.jfineco.2018.07.010839Bahmani-Oskooee, M., & Wu, T.-P. (2018). Housing prices and 840real effective exchange rates in 18 OECD countries: a boot-841strap multivariate panel Granger causality. Economic Analysis 842and Policy, 60, 119-126. 843https://doi.org/10.1016/j.eap.2018.09.005844Bhargava, B., Wu, X., Lu, Y., & Wang, W. (2004). Integrating 845heterogeneous wireless technologies: a cellular aided mobile 846ad hoc network (CAMA). Mobile Networks and Applications, 8479(4), 393-408. 848https://doi.org/10.1023/B:MONE.0000031606.04846.fa849Chen, P.-F., Chien, M.-S., & Lee, C.-C. (2011). Dynamic mod-850eling of regional house price diffusion in Taiwan. Journal of 851Housing Economics, 20(4), 315-332. 852https://doi.org/10.1016/j.jhe.2011.09.002853Chen, J.-H., Ong, C. F., Zhang, L., & Hsu, S.-C. (2017). Fore-854casting spatial dynamics of the housing market using support 855vector machine. International Journal of Strategic Property 856Management, 21(3), 273-283. 857https://doi.org/10.3846/1648715X.2016.1259190858Chen, J.-H., Yang, L.-R., Su, M.-C., & Lin, J.-Z. (2010). A rule 859extraction based approach in predicting derivative use for fi-860nancial risk hedging by construction companies. Expert Sys-861tems with Applications, 37(9), 6510-6514. 862https://doi.org/10.1109/ICIII.2011.101863Chen, J.-H., & Hsu, S. C. (2008). Quantifying impact factors of 864corporate financing: engineering consulting firms. Journal of 865Management in Engineering, 24(2), 96-104. 866https://doi.org/10.1061/(ASCE)0742-597X(2008)24:2(96)867Des Rosiers, F., Lagana, A., & Theriault, M. (2001). Size and 868proximity effects of primary schools on surrounding house 869values. Journal of Property Research, 18(2), 149-168. 870https://doi.org/10.1080/09599910110039905871Droes, M. I., & Francke, M. K. (2018). What causes the posi-872tive price-turnover correlation in European housing markets. 873Journal of Real Estate Finance and Economics, 57(4), 618-646. 874https://doi.org/10.1007/s11146-017-9602-7875Du, Q. Y., Wu, C., Ye, X. Y., Ren, F., & Lin, Y. J. (2018). Evaluating 876the effects of landscape on housing prices in urban China. Ti-877jdschrift Voor Economischie en Sociale Geografie, 109(4), 525-878541. https://doi.org/10.1111/tesg.12308879Gholipour, H. F., Al-Mulali, U., Lee, J. Y. M., & Hakim, A. M. 880(2016). Dynamic relationship between house prices in Ma-881laysia’s major economic regions and Singapore house prices. 882Regional Studies, 50, 657-670. 883https://doi.org/10.1080/00343404.2014.928408884Gholipour, H. F., & Lean, H. H. (2017). Ripple effect in regional 885housing and land markets in Iran: implications for portfo-886lio diversification. International Journal of Strategic Property 887Management, 21(4), 331-345. 888https://doi.org/10.3846/1648715X.2016.1272010889Gu, G. (2018). Hedonic price ripple effect and consumer choice: 890Evidence from new homes. Journal of Advanced Computa-891tional Intelligence and Intelligent Informatics, 22(6), 809-816. 892https://doi.org/10.20965/jaciii.2018.p0809893Hill, R. J., & Scholz, M. (2018). Can geospatial data improve 894house price indexes? A hedonic imputation approach with 895splines. Review of Income and Wealth, 64(4), 737-756. 896https://doi.org/10.1111/roiw.12303897Hui, H. C. (2010). House price diffusions across three urban ar-898eas in Malaysia. International Journal of Housing Markets and 899Analysis, 3, 369-379. 900https://doi.org/10.1108/17538271011080664901Jonkman, A., Janssen-Jansen, L., & Schilder, F. (2018). Rent in-902crease strategies and distributive justice: the socio-spatial ef-903fects of rent control policy in Amsterdam. Journal of Housing 904and the Built Environment, 33(4), 653-673. 905https://doi.org/10.1007/s10901-017-9573-2906Kopczewska, K., & Lewandowska, A. (2018). The price for sub-907way access: spatial econometric modelling of office rental 908rates in London. Urban Geography, 39(10), 1528-1554. 909https://doi.org/10.1080/02723638.2018.1481601910Lean, H. H., & Smyth, R. (2013). Regional house prices and 911the ripple effect in Malaysia. Urban Studies, 50(5), 895-922. 912https://doi.org/10.1177/0042098012459582913Lee, C. C., Liang, C. M., Chen, J. Z., & Tung, C. H. (2018). Effects 914of the housing price to income ratio on tenure choice in Tai-915wan: forecasting performance of the hierarchical generalized 916linear model and traditional binary logistic regression model. 917Journal of Housing and the Built Environment, 33(4), 675-694. 918https://doi.org/10.1007/s10901-017-9572-3919