# RECORD 3b145fc34a20579d69b10544f4da1eace43b32a3 # TITLE: Three-dimensional land-use configuration and property prices: A spatially filtered multi-level modelling perspective # YEAR: 2023.0 VENUE: Environment and Planning B Urban Analytics and City Science DOI: 10.1177/23998083231180213 # AUTHORS: Wei Zheng; Mingshu Wang # PAGES: 18 CANDIDATE TABLE PAGES (1-based): [9] # 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. ===== PAGE 1 (score 2, numeric-paren 0, table-words 0, var-words 2) ===== Article EPB: Urban Analytics and City Science 2024, Vol. 51(2) 438–455 © The Author(s) 2023 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/23998083231180213 journals.sagepub.com/home/epb Three-dimensional land-use configuration and property prices: A spatially filtered multi-level modelling perspective Wei Zheng Department of Planning & Environmental Management, Manchester Urban Institute, The University of Manchester, Manchester, UK Mingshu Wang School of Geographical & Earth Sciences, University of Glasgow, Glasgow, UK 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 config- uration. 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. Keywords Property value, three-dimensional land-use configuration, spatially filtered multi-level modelling, Beijing Introduction The hedonic method for evaluating housing prices is based on the understanding that the value of an individual property is the outcome of its intrinsic characteristics and the attributes of the context in which the property is situated (Bartholomew and Ewing, 2011). Unlike structural attributes, the Corresponding author: Mingshu Wang, School of Geographical & Earth Sciences, University of Glasgow, Glasgow G12 8QQ, UK. Email: Mingshu.Wang@glasgow.ac.uk Data Availability Statement included at the end of the article. ===== PAGE 9 (score 22, numeric-paren 0, table-words 5, var-words 7) ===== Pij ¼ γ00 þ γ01Zj þ γ10Yij   þ γ0 þ γ1e1 þ ::::: þ γnen ð Þ þ μ0 0j þ υ0 ij   (2) where Pij denotes housing price per square metre as the dependent variable; Yij is a set of variables at the property level, which may be structural, locational, or different land-use forms; Zj are the dependent variables at the higher spatial level of the broader neighbourhood/street; γ00 is the mean of the dependent variable after considering higher-level variables; and γ01 and γ10 pertain to the slopes of Zj and Yij, respectively. The fixed effect (Xβ in equation (1)) in the whole modelling framework is represented by γ00 þ γ01Zj þ γ10Yij. The spatial filtering component is represented by γ0 þ γ1e1 þ ::::: þ γnen that could account for the spatial effect defined by the Moran eigenvectors whilst μ 0 0j þ υ 0 ij refer to independent white noise. Both together denote the random effect Eγ þ ξ. Several statistical tests (e.g. correlation, variance inflation factor [VIF], and the Durbin–Watson test) were performed to avoid multicollinearity issues. Some variables related to land-use forms obtained high correlations and VIF values higher than 3 and, therefore, could not be included in a single model simultaneously due to potential multicollinearity. For a comparison, two single-level RE-ESF models and two SFML models were built using two sets of independent variables (Table 1). Furthermore, another two SFML models were developed to understand the cross-level interaction effects between floor levels and significant land-use composition variables at the street level. Development of SFML models for different zones. Having run the entire study area model, the whole dataset was separated into four groups to further illustrate the varying effects of the independent variables across spatial zones. Hence, the SFML models were built based on the samples from the Table 1. (continued) Variable RE-ESF 1 RE-ESF 2 SFML 1 SFML 2 SFML 3 SFML 4 Street bare rock or paved 564.73 900.99 2570.80 2515.03 2516.20 2509.32 Street bare soil or sand 853.65c 1479.36a 836.82 346.08 353.63 353.38 Metro station density 466.53 90.53 3043.01 3883.69 3888.82 3887.46 Function mix 234.27 140.80 1020.64 1173.29 1166.92 1153.67 Cross-level interaction Street open mid-risec floor level 1 — — — — 144.66 — Street open mid-risec floor level 2 — — — — 364.36 — Street compact low- risec floor level 1 — — — — — 397.36 Street compact low- risec floor level 2 — — — — — 694.61c Intercept 39225.13a 37765.81a 38762.29a 38662.22a 38692.43a 38523.42a Adjusted R2 0.767 0.766 0.779 0.779 0.779 0.779 2 log likelihood 1,777,344 1,777,750 1,773,444 1,773,685 1,773,656 1,773,654 AIC 1,777,426 1,777,832 1,773,528 1,773,769 1,773,744 1,773,742 BIC 1,777,810 1,778,215 1,773,912 1,774,163 1,774,156 1,774,154 Random SE 1020.21 942.05 1023.15 984.98 985.04 985.18 Moran’s I 0.511 0.504 0.485 0.463 0.463 0.463 Random SE group — — 6375.09 6387.33 6388.13 6387.71 asignificant at 0.001. bsignificant at 0.01. csignificant at 0.05. 446 EPB: Urban Analytics and City Science 51(2) ===== PAGE 10 (score 9, numeric-paren 1, table-words 1, var-words 5) ===== following zones: the old urban centre, the main urban zone, the inner suburban zone, and the outer suburban zone (see Fig S1 for the extent of each zone). Results and discussion Model fitting results Table 1 presents the estimation results of the RE-ESF and SFML models. RE-ESF model 1 and SFML model 1 excluded compact low-rise, open mid-rise, street compact low-rise, and street open mid-rise as independent variables. Conversely, RE-ESF model 2 and SFML model 2 excluded compact high-rise, open high-rise, street compact high-rise, and street open high-rise as explanatory variables to avoid potential multicollinearity. SFML model 3 and SFML model 4 included cross- level interaction effects based on SFML model 2 to capture the interaction effects between two significant land-use composition variables at the street level (Street open mid-rise and Street compact low-rise) and the floor level variables at the property level. SF models 1 and 2 suggest explicit spatial autocorrelation effects with Moran’s I values of 0.511 and 0.504, respectively. The reduced log-likelihood, AIC, and BIC values of the SFML models further illustrate that the SFML models displayed better modelling performance, especially the SFML model 4. The residual spatial components of SFML models 1 and 2 predicted by the ei- genvector spatial filtering process were mapped in Fig S2, which shows spatial dependency effects across the study area. https://journals.sagepub.com/doi/suppl/10.1177/23998083231180213 Impacts of the land-use configuration variables In SFML model 1, compact high-rise form, open high-rise form, open low-rise form, low plants, and bare soil or sand in the immediate neighbourhood displayed significant effects. Specifically, the variable low plants exhibited a positive effect with the highest coefficient (12942.21); open high-rise and bare soil/sand also exhibited positive effects (though with much smaller coefficients of 2792.81 and 1834.60, respectively); compact high-rise and open low-rise had negative coefficients with the former having a much larger effect (17672.54). In SFML model 2, low plants and bare soil/sand produced significantly positive coefficients at 11962.61 and 1905.95, respectively. This indicates the premium enjoyed by low plant land cover in the immediate neighbourhood. At the broader neighbourhood scale, street open mid-rise exerted a positive coefficient of 7455.27 in SFML model 2; and street compact low-rise was associated with a negative coefficient of 7657.79 in SFML model 2, which suggests that there is a premium attached to open mid-rise form in the wider neighbourhood environment. If the broader neighbourhood environment is associated with more compact low-rise land-use patterns, then properties within the area tend to have lower prices when other factors are controlled. These results suggest a premium from open high-rise and low plants forms in the immediate neighbourhood and from the open mid-rise form in the broader neighbourhood in the Beijing metropolitan area. These findings reinforce the previously noted economic benefits of urban green space as documented by many existent empirical studies (see, amongst others, Kim et al., 2018). With regard to the horizontal dimension, the open and compact low-rise forms were more related to lower property values than the open mid-rise and open high-rise forms in the immediate and broader neighbourhoods, and especially the compact low-rise form in the immediate and broader neigh- bourhoods. As open form is associated with green vegetation that can provide amenity value and environmental quality (Mei et al., 2018), it is not surprising that premium effects were found in variables relating to open forms in the immediate and broader neighbourhoods. From a vertical perspective, low-rise forms were not favoured in the immediate and broader neighbourhoods. A Zheng and Wang 447