1# RECORD 0e568775e77ac2d90b96f6f8ecad954135ed43b02# TITLE: Listing price estimation of apartments: A generalised linear model3# YEAR: 2019.0 VENUE: Journal of Economic and Financial Sciences DOI: 10.4102/jef.v12i1.2044# AUTHORS: Dane Bax; Mihalis Chasomeris5# PAGES: 11 CANDIDATE TABLE PAGES (1-based): [7]6# ABSTRACT: Orientation: Residential property is an important segment of the property market in South Africa. Residential property transactions are typically infrequent and relate to a highly differentiated set of items making measurement techniques complex and difficult. Research purpose: The aim of this research was to develop a statistical model to estimate listing prices of apartments in KwaZulu-Natal, South Africa, and build a software application to disseminate the results thereof. Motivation for the study: This study presents a novel alternative to the log linear (ordinary least squares) method of deriving a hedonic price function for residential property where the arithmetic mean is computed as the expected value and not the geometric mean. Research design, approach and method: Using a data set of 1314 residential apartments provided by Private Property (Pty) Ltd, this research derives a hedonic price function for residential property using a generalised linear model based on the gamma distribution and log-link function. Main findings: The results showed that floor area, number of bedrooms, number of bathrooms and a dummy variable for suburb (location) were statistically significant determinants of listing prices. Practical/managerial implications: A software application, called the listing price calculator , was developed to disseminate the results of the model for commercial use by real estate buyers, sellers and agents, bridging the gap between academia and business. Contribution/value-add: This study derives a hedonic price function for residential property using a generalised linear model based on the gamma distribution and log-link function, which is novel in South African research.789===== PAGE 1 (score 13, numeric-paren 0, table-words 0, var-words 13) =====1011https://www.jefjournal.org.za12Open Access13Journal of Economic and Financial Sciences 14ISSN: (Online) 2312-2803, (Print) 1995-707615Page 1 of 1116Original Research17Read online:18Scan this QR 19code with your 20smart phone or 21mobile device 22to read online.23Authors:24Dane Bax1 25Mihalis G. Chasomeris1 26Affiliations:271Graduate School of Business 28and Leadership, University of 29KwaZulu-Natal, Durban, 30South Africa31Corresponding author:32Mihalis Chasomeris, 33chasomerism1@ukzn.ac.za34Dates:35Received: 26 Mar. 201836Accepted: 18 Jan. 201937Published: 25 July 201938How to cite this article:39Bax, D. & Chasomeris, M.G., 402019, ‘Listing price 41estimation of apartments: 42A generalised linear model’, 43Journal of Economic and 44Financial Sciences 12(1), 45a204. https://doi.org/4610.4102/jef.v12i1.20447Copyright:48© 2019. The Authors. 49Licensee: AOSIS. This work 50is licensed under the 51Creative Commons 52Attribution License.53Introduction54Residential property is perceived as a fundamental barometer of individual and collective wealth, 55where its cumulative value is closely tracked by government statistical bureaus, banks and other 56economic establishments. Individual households, financial institutions and policymakers closely 57monitor residential property price trends to gauge real house price growth and financial stability, 58as well as to monitor the activity and condition of the credit market (De Haan & Erwin 2011).59Residential property is an important segment of the property market in South Africa; the large 60portfolio of residential property contributes significantly towards the wealth of the country where 61it’s capitalised on the household balance sheet in the set of national accounts (South African 62Reserve Bank 2015). Residential property transactions are typically infrequent and relate to a 63highly differentiated set of items, rendering effective measurement techniques complex and 64difficult (Hill 2011). The main objective of this research was to construct a hedonic pricing model 65to estimate listing prices for apartments within three KwaZulu-Natal coastal regions based on 66statistically significant structural and locational attributes. It appears that no similar study has 67been conducted on any property segment in KwaZulu-Natal province of South Africa. This study 68develops a hedonic price function using a generalised linear model based on the gamma 69distribution and log-link function, which has not been attempted before in South African research, 70and finding global research employing this methodology has proven difficult where no existing 71studies have been identified. This study presents an alternative to the log linear (ordinary least 72squares) method of deriving a hedonic price function for residential property where the arithmetic 73Orientation: Residential property is an important segment of the property market in South 74Africa. Residential property transactions are typically infrequent and relate to a highly 75differentiated set of items making measurement techniques complex and difficult.76Research purpose: The aim of this research was to develop a statistical model to estimate 77listing prices of apartments in KwaZulu-Natal, South Africa, and build a software application 78to disseminate the results thereof.79Motivation for the study: This study presents a novel alternative to the log linear (ordinary 80least squares) method of deriving a hedonic price function for residential property where the 81arithmetic mean is computed as the expected value and not the geometric mean.82Research design, approach and method: Using a data set of 1314 residential apartments 83provided by Private Property (Pty) Ltd, this research derives a hedonic price function for 84residential property using a generalised linear model based on the gamma distribution and 85log-link function. 86Main findings: The results showed that floor area, number of bedrooms, number of bathrooms 87and a dummy variable for suburb (location) were statistically significant determinants of 88listing prices. 89Practical/managerial implications: A software application, called the listing price calculator, 90was developed to disseminate the results of the model for commercial use by real estate buyers, 91sellers and agents, bridging the gap between academia and business.92Contribution/value-add: This study derives a hedonic price function for residential property 93using a generalised linear model based on the gamma distribution and log-link function, 94which is novel in South African research.95Keywords: residential property; listing price estimation; hedonic valuation; economics; 96geospatial modelling; generalised linear model.97Listing price estimation of apartments: 98A generalised linear model99Read online:100Scan this QR 101code with your 102smart phone or 103mobile device 104to read online.105106107===== PAGE 7 (score 60, numeric-paren 39, table-words 4, var-words 13) =====108109Page 7 of 11110Original Research111https://www.jefjournal.org.za112Open Access113is less than null deviance indicating that the saturated model 114is a better fit than the null model.115Interpretation of the coefficients of the generalised linear 116model:117• A 1% increase in square metres or size of an apartment 118increases the price by approximately 0.733%.119• A one-unit increase in the number of bathrooms of an 120apartment increases the price by approximately 20.3%.121• A one-unit increase in the number of bedrooms of an 122apartment increases the price by approximately 3.85%.123• Each suburb coefficient is the percentage difference 124between the reference suburb.125The signs for all the coefficients are as expected based on a 126priori expectations, unlike what was experienced in the study 127by Dodds (2011). The number of bedrooms is statistically 128significant, which was not the case in the study of Els and 129Von Fintel (2010). The generalised linear model results show 130that there are 35 suburb coefficients, yet there is a total of 36 131in the data. This is because one of the suburbs was withheld 132from the model output that all the other suburbs were 133compared to. The suburb that was withheld is Albert Park, in 134Durban Central, a comparatively low-priced suburb. The 135suburb coefficients presented in the results of the model will 136always be in comparison with the Albert Park suburb.137The first plot in Figure 2 is the jacknife standardised deviance 138residuals against the fitted values, indicating homogeneous 139TABLE 4: Generalised linear model output.140Coefficients141Estimate142SE143Pr(> |t|)144(Intercept)1459.462201460.15252147***148log(Size)1490.732961500.03107151***152NumBaths1530.202981540.01878155***156NumBeds1570.038511580.01830159*160Suburb_Ballito1611.161611620.10722163***164Suburb_Beachfront1650.582671660.10742167***168Suburb_Berea1690.746981700.10904171***172Suburb_Brettenwood Coastal Estate1731.170381740.23149175***176Suburb_Carrington Heights1770.485211780.17941179**180Suburb_Congella181-0.433051820.17914183*184Suburb_Dunkirk Estate1850.809401860.14942187***188Suburb_Durban CBD1890.234171900.11202191*192Suburb_Esplanade1930.274141940.11193195*196Suburb_Essenwood1970.836921980.13930199***200Suburb_Glenwood2010.549022020.10918203***204Suburb_La Lucia2051.335532060.11921207***208Suburb_Morningside2090.718462100.10923211***212Suburb_Mt Edgecombe2131.078652140.14735215***216Suburb_Musgrave2170.715632180.11761219***220Suburb_New Town Centre Gateway2211.284712220.11707223***224Suburb_Overport2250.419422260.13919227**228Suburb_Palm Lakes Estate2290.766192300.15888231***232Suburb_Point Waterfront2331.147132340.10878235***236Suburb_Prestondale2370.956262380.23121239***240Suburb_Salt Rock2410.986522420.14048243***244Suburb_Seaward Estates2450.553252460.18071247**248Suburb_Shakas Rock2491.191572500.11020251***252Suburb_Sheffield Beach2530.896792540.11114255***256Suburb_Sherwood2570.533232580.23222259*260Suburb_Simbithi Ballito2610.866592620.11347263***264Suburb_Sunningdale2650.753342660.23265267**268Suburb_Sydenham2690.430972700.16861271*272Suburb_Tinley Manor and surrounds2730.857322740.23219275***276Suburb_Umbilo2770.322502780.12199279**280Suburb_Umhlanga Ridge2811.389172820.11254283***284Suburb_Umhlanga Rocks2851.712702860.10895287***288Suburb_Westridge2890.589782900.14650291***292Suburb_Windermere2930.778232940.16723295***296Suburb_Zimbali2971.092512980.12327299***300NumBeds, number of bedrooms; NumBaths, number of bathrooms; CBD, central business 301district, SE, standard deviation.302***, p < 0.001;**, p < 0.01;*, p < 0.05.303Null deviance: 1091.47 on 1313 degrees of freedom.304Residual deviance: 104.44 on 1275 degrees of freedom.305TABLE 3: Variance inflation factor results.306Variables307VIF308Size3093.23310NumBeds3112.89312NumBaths3133.59314Suburb3151.09316NumBeds, number of bedrooms; NumBaths, number of bathrooms; VIF, variance inflation 317factor.318–3319123201332114322153231632417325Linear predictor326Residuals327–1328132933300.03310.003320.023330.23340.43350.63360.83371.0338h/(1-h)339Cook sta s c3400341200342400343600344Case3450.00346Cook sta s c3470.023488003491,0003501,200351–3352Ordered deviance residuals353Quan les of standard354normal355–3356–135713583359–2360–1361036213632364 3365FIGURE 2: Generalised linear model residual plots.366367368===== PAGE 8 (score 24, numeric-paren 0, table-words 6, var-words 12) =====369370Page 8 of 11371Original Research372https://www.jefjournal.org.za373Open Access374TABLE 5: Bootstrapped generalised linear model.375Variables376Original377BootBias378BootSE379BootMed380(Intercept)3819.462201382-0.0082911753830.1390053849.449233385log(Size)3860.7329603870.0011693523880.0336353890.734793390NumBaths3910.2029843920.0004096103930.0210853940.203209395NumBeds3960.038513397-0.0006708993980.0197423990.038008400Suburb_Ballito4011.1616144020.0033476194030.0688754041.164911405Suburb_Beachfront4060.5826684070.0026224344080.0760794090.584300410Suburb_Berea4110.7469794120.0038658324130.0696614140.749166415Suburb_Brettenwood Coastal Estate4161.1703754170.0022212224180.0718064191.172913420Suburb_Carrington Heights4210.4852134220.0037058774230.0678184240.490015425Suburb_Congella426-0.433046427-0.0133497844280.190698429-0.437814430Suburb_Dunkirk Estate4310.809397432-0.0009373524330.0997514340.813618435Suburb_Durban CBD4360.2341674370.0027232814380.0729444390.237637440Suburb_Esplanade4410.2741454420.0026876794430.0675124440.276546445Suburb_Essenwood4460.8369234470.0018123164480.0805134490.835307450Suburb_Glenwood4510.5490244520.0037861604530.0689674540.553202455Suburb_La Lucia4561.3355344570.0035884774580.0883164591.341386460Suburb_Morningside4610.7184604620.0035796254630.0685444640.721921465Suburb_Mt Edgecombe4661.0786504670.0016250044680.1475744691.085874470Suburb_Musgrave4710.7156264720.0005040244730.0812114740.717503475Suburb_New Town Centre Gateway4761.2847054770.0033534664780.0722594791.287007480Suburb_Overport4810.4194164820.0013474564830.1017204840.423324485Suburb_Palm Lakes Estate4860.7661874870.0016667094880.0871864890.769822490Suburb_Point Waterfront4911.1471314920.0032432694930.0691624941.152322495Suburb_Prestondale4960.9562614970.0037115084980.0681274990.957237500Suburb_Salt Rock5010.986517502-0.0043241995030.1522975040.987189505Suburb_Seaward Estates5060.553246507-0.0006428865080.0996875090.554347510Suburb_Shakas Rock5111.1915715120.0026347245130.0709735141.192938515Suburb_Sheffield Beach5160.8967945170.0038263005180.0695485190.901282520Suburb_Sherwood5210.5332335220.0012325885230.1052125240.533948525Suburb_Simbithi Ballito5260.8665935270.0023699345280.0725585290.869840530Suburb_Sunningdale5310.7533375320.0040923895330.0732775340.758305535Suburb_Sydenham5360.430975537-0.0039359705380.1626565390.430606540Suburb_Tinley Manor and surrounds5410.8573165420.0037838325430.0663665440.861646545Suburb_Umbilo5460.3224955470.0019029805480.0836755490.324751550Suburb_Umhlanga Ridge5511.3891725520.0025860085530.0716935541.392348555Suburb_Umhlanga Rocks5561.7126985570.0024582905580.0746155591.715394560Suburb_Westridge5610.5897765620.0028388805630.0868245640.594515565Suburb_Windermere5660.778229567-0.0011569385680.0972105690.782636570Suburb_Zimbali5711.0925085720.0000321885730.0993515741.091839575NumBeds, number of bedrooms; NumBaths, number of bathrooms; BootBias, represents the difference between the average bootstrapped value of the statistic and its original sample value; 576BootSE, are the bootstrap estimates of the standard errors which are computed as the standard deviation of the bootstrap replicates; BootMED, bootstrap estimate; CBD, central business district.577variance and no curvilinear pattern of the standardised 578deviance residuals. The second plot is of the standardised 579deviance residuals, indicating normality thereof. The bottom 580two plots relate to observations with high influence. Upon 581inspection of these data points, no clear outliers are evident, 582indicating that these points may have high degrees of 583leverage or influence on the model.584Bourassa et al. (2010) found that property price predictions 585were more accurate when submarket dummy locational 586variables were used and the presence of spatial autocorrelation 587was mitigated. In order to formally test for the presence of 588spatial autocorrelation the Mantel test was computed. 589Distances between the apartments were computed in 590kilometres and saved as a distance matrix. The distance matrix 591was then passed to the Mantel test function along with a 592matrix of the residuals from the generalised linear model. The 593Mantel test then tested the null hypothesis of no relationship 594between the residuals and the distance matrix, providing a test 595of spatial autocorrelation. The correlation between the distance 596matrix and the residual matrix was −0.02411 and the p-value 597was 0.999, providing sufficient evidence not to reject the null 598hypothesis of no spatial autocorrelation. The use of the Mantel 599test to detect the presence of spatial autocorrelation in this 600study was consistent with the assertion of Borcard and 601Legendre (2012) and Diniz-Filho et al. (2013).602Reliability of results: Bootstrapping603Bootstrapping was used as a means of model validation 604where 5000 random samples were drawn with replacement. 605A model was then developed for each sample and the average 606of the 5000 models computed was performed. The results 607indicate that bootstrapped coefficients are similar to the 608generalised linear model coefficient which is evident by 609comparing the column headed ‘original’ with the column 610headed ‘bootMed’ in Table 5. Simulating many random 611sampling distributions provides a measure of reliability for 612