1# RECORD 3b145fc34a20579d69b10544f4da1eace43b32a32# TITLE: Three-dimensional land-use configuration and property prices: A spatially filtered multi-level modelling perspective3# YEAR: 2023.0 VENUE: Environment and Planning B Urban Analytics and City Science DOI: 10.1177/239980832311802134# AUTHORS: Wei Zheng; Mingshu Wang5# PAGES: 18 CANDIDATE TABLE PAGES (1-based): [9]6# ABSTRACT: The influence of neighbourhood characteristics on housing prices has gained increasing attention from scholars in recent decades. However, studies on the three-dimensional nature of urban space, and particularly the vertical dimension, have remained limited. This study investigates previously unexplored variables that can capture the vertical and horizontal dimensions of land-use configuration. In addition, this study proposes a spatially filtered multi-level approach to modelling variations in property values which can capture both spatial and multi-level effects. The research findings reveal a price premium for housing located in immediate neighbourhoods with more open mid-rise buildings and low plants. The results also demonstrate the varying effects of determinants of house pricing in spatially heterogeneous zones.789===== PAGE 1 (score 2, numeric-paren 0, table-words 0, var-words 2) =====1011Article12EPB: Urban Analytics and City Science132024, Vol. 51(2) 438–45514© The Author(s) 202315Article reuse guidelines:16sagepub.com/journals-permissions17DOI: 10.1177/2399808323118021318journals.sagepub.com/home/epb19Three-dimensional land-use20configuration and property21prices: A spatially filtered22multi-level modelling23perspective24Wei Zheng25Department of Planning & Environmental Management, Manchester Urban Institute, The University of Manchester,26Manchester, UK27Mingshu Wang28School of Geographical & Earth Sciences, University of Glasgow, Glasgow, UK29Abstract30The influence of neighbourhood characteristics on housing prices has gained increasing attention31from scholars in recent decades. However, studies on the three-dimensional nature of urban space,32and particularly the vertical dimension, have remained limited. This study investigates previously33unexplored variables that can capture the vertical and horizontal dimensions of land-use config-34uration. In addition, this study proposes a spatially filtered multi-level approach to modelling35variations in property values which can capture both spatial and multi-level effects. The research36findings reveal a price premium for housing located in immediate neighbourhoods with more open37mid-rise buildings and low plants. The results also demonstrate the varying effects of determinants of38house pricing in spatially heterogeneous zones.39Keywords40Property value, three-dimensional land-use configuration, spatially filtered multi-level modelling,41Beijing42Introduction43The hedonic method for evaluating housing prices is based on the understanding that the value of an44individual property is the outcome of its intrinsic characteristics and the attributes of the context in45which the property is situated (Bartholomew and Ewing, 2011). Unlike structural attributes, the46Corresponding author:47Mingshu Wang, School of Geographical & Earth Sciences, University of Glasgow, Glasgow G12 8QQ, UK.48Email: Mingshu.Wang@glasgow.ac.uk49Data Availability Statement included at the end of the article.505152===== PAGE 9 (score 22, numeric-paren 0, table-words 5, var-words 7) =====5354Pij ¼ γ00 þ γ01Zj þ γ10Yij555657þ γ0 þ γ1e1 þ ::::: þ γnen58ð59Þ þ60μ0610j þ υ062ij636465(2)66where Pij denotes housing price per square metre as the dependent variable; Yij is a set of variables at67the property level, which may be structural, locational, or different land-use forms; Zj are the68dependent variables at the higher spatial level of the broader neighbourhood/street; γ00 is the mean69of the dependent variable after considering higher-level variables; and γ01 and γ10 pertain to the70slopes of Zj and Yij, respectively. The fixed effect (Xβ in equation (1)) in the whole modelling71framework is represented by γ00 þ γ01Zj þ γ10Yij. The spatial filtering component is represented by72γ0 þ γ1e1 þ ::::: þ γnen that could account for the spatial effect defined by the Moran eigenvectors73whilst μ740750j þ υ76077ij refer to independent white noise. Both together denote the random effect Eγ þ ξ.78Several statistical tests (e.g. correlation, variance inflation factor [VIF], and the Durbin–Watson79test) were performed to avoid multicollinearity issues. Some variables related to land-use forms80obtained high correlations and VIF values higher than 3 and, therefore, could not be included in a81single model simultaneously due to potential multicollinearity. For a comparison, two single-level82RE-ESF models and two SFML models were built using two sets of independent variables (Table 1).83Furthermore, another two SFML models were developed to understand the cross-level interaction84effects between floor levels and significant land-use composition variables at the street level.85Development of SFML models for different zones. Having run the entire study area model, the whole86dataset was separated into four groups to further illustrate the varying effects of the independent87variables across spatial zones. Hence, the SFML models were built based on the samples from the88Table 1. (continued)89Variable90RE-ESF 191RE-ESF 292SFML 193SFML 294SFML 395SFML 496Street bare rock or97paved98564.7399900.991002570.801012515.031022516.201032509.32104Street bare soil or105sand106853.65c1071479.36a108836.82109346.08110353.63111353.38112Metro station density113466.5311490.531153043.011163883.691173888.821183887.46119Function mix120234.27121140.801221020.641231173.291241166.921251153.67126Cross-level interaction127Street open mid-risec128floor level 1129—130—131—132—133144.66134—135Street open mid-risec136floor level 2137—138—139—140—141364.36142—143Street compact low-144risec floor level 1145—146—147—148—149—150397.36151Street compact low-152risec floor level 2153—154—155—156—157—158694.61c159Intercept16039225.13a16137765.81a16238762.29a16338662.22a16438692.43a16538523.42a166Adjusted R21670.7671680.7661690.7791700.7791710.7791720.7791732 log likelihood1741,777,3441751,777,7501761,773,4441771,773,6851781,773,6561791,773,654180AIC1811,777,4261821,777,8321831,773,5281841,773,7691851,773,7441861,773,742187BIC1881,777,8101891,778,2151901,773,9121911,774,1631921,774,1561931,774,154194Random SE1951020.21196942.051971023.15198984.98199985.04200985.18201Moran’s I2020.5112030.5042040.4852050.4632060.4632070.463208Random SE group209—210—2116375.092126387.332136388.132146387.71215asignificant at 0.001.216bsignificant at 0.01.217csignificant at 0.05.218446219EPB: Urban Analytics and City Science 51(2)220221222===== PAGE 10 (score 9, numeric-paren 1, table-words 1, var-words 5) =====223224following zones: the old urban centre, the main urban zone, the inner suburban zone, and the outer225suburban zone (see Fig S1 for the extent of each zone).226Results and discussion227Model fitting results228Table 1 presents the estimation results of the RE-ESF and SFML models. RE-ESF model 1 and229SFML model 1 excluded compact low-rise, open mid-rise, street compact low-rise, and street open230mid-rise as independent variables. Conversely, RE-ESF model 2 and SFML model 2 excluded231compact high-rise, open high-rise, street compact high-rise, and street open high-rise as explanatory232variables to avoid potential multicollinearity. SFML model 3 and SFML model 4 included cross-233level interaction effects based on SFML model 2 to capture the interaction effects between two234significant land-use composition variables at the street level (Street open mid-rise and Street235compact low-rise) and the floor level variables at the property level.236SF models 1 and 2 suggest explicit spatial autocorrelation effects with Moran’s I values of 0.511237and 0.504, respectively. The reduced log-likelihood, AIC, and BIC values of the SFML models238further illustrate that the SFML models displayed better modelling performance, especially the239SFML model 4. The residual spatial components of SFML models 1 and 2 predicted by the ei-240genvector spatial filtering process were mapped in Fig S2, which shows spatial dependency effects241across the study area. https://journals.sagepub.com/doi/suppl/10.1177/23998083231180213242Impacts of the land-use configuration variables243In SFML model 1, compact high-rise form, open high-rise form, open low-rise form, low plants, and244bare soil or sand in the immediate neighbourhood displayed significant effects. Specifically, the245variable low plants exhibited a positive effect with the highest coefficient (12942.21); open high-rise246and bare soil/sand also exhibited positive effects (though with much smaller coefficients of 2792.81247and 1834.60, respectively); compact high-rise and open low-rise had negative coefficients with the248former having a much larger effect (17672.54). In SFML model 2, low plants and bare soil/sand249produced significantly positive coefficients at 11962.61 and 1905.95, respectively. This indicates250the premium enjoyed by low plant land cover in the immediate neighbourhood. At the broader251neighbourhood scale, street open mid-rise exerted a positive coefficient of 7455.27 in SFML model2522; and street compact low-rise was associated with a negative coefficient of 7657.79 in SFML253model 2, which suggests that there is a premium attached to open mid-rise form in the wider254neighbourhood environment. If the broader neighbourhood environment is associated with more255compact low-rise land-use patterns, then properties within the area tend to have lower prices when256other factors are controlled.257These results suggest a premium from open high-rise and low plants forms in the immediate258neighbourhood and from the open mid-rise form in the broader neighbourhood in the Beijing259metropolitan area. These findings reinforce the previously noted economic benefits of urban green260space as documented by many existent empirical studies (see, amongst others, Kim et al., 2018).261With regard to the horizontal dimension, the open and compact low-rise forms were more related to262lower property values than the open mid-rise and open high-rise forms in the immediate and broader263neighbourhoods, and especially the compact low-rise form in the immediate and broader neigh-264bourhoods. As open form is associated with green vegetation that can provide amenity value and265environmental quality (Mei et al., 2018), it is not surprising that premium effects were found in266variables relating to open forms in the immediate and broader neighbourhoods. From a vertical267perspective, low-rise forms were not favoured in the immediate and broader neighbourhoods. A268Zheng and Wang269447270