Comparative Analysis of Centrality Measures in Explaining Activity Locations Through Land Value Variability: A Case Study of Porto Alegre, Brazil

Comparative Analysis of Centrality Measures in Explaining Activity Locations Through Land Value Variability: A Case Study of Porto Alegre, Brazil | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparative Analysis of Centrality Measures in Explaining Activity Locations Through Land Value Variability: A Case Study of Porto Alegre, Brazil Ramon Lucato de Aguilar, Alexander Hellervik This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6264491/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract This study compares the performance of five spatial centrality measures in explaining urban land value variation in Porto Alegre, Brazil. Land value reflects the level of competition for a specific piece of land and its potential to attract various activities. We analyze three accessibility measures - Closeness Centrality (CC), Eigenvector Centrality, and Preferential Centrality (PC) - and two intermediation measures - Betweenness Centrality (BC) and Freeman-Krafta Centrality (FK). PC and FK are enhanced versions of traditional metrics, incorporating agglomeration factors and distance decay, respectively. Using multi-model, multi-scale spatial regression analysis, we find that the enhanced measures outperform classical ones in explaining land value variation, with accessibility measures, especially PC, being more responsive. At the disaggregated level, intermediation measures exhibit negative correlations with land value, suggesting adverse effects of high-traffic locations. However, at the neighborhood scale, both measure types show positive correlations, indicating that while proximity to major roads enhances accessibility, immediate adjacency may reduce property values due to traffic-related externalities. Spatial centrality Preferential centrality Freeman-Krafta centrality Land value Porto Alegre Figures Figure 1 Figure 2 Figure 3 Figure 4 1. Introduction Various spatial centrality measures have emerged from graph theory to analyze urban spatial differentiation, broadly categorized into accessibility and intermediation measures. Accessibility measures evaluate the ease of access between locations and potential for human interactions, with Closeness Centrality (CC), based on distance, being the most fundamental (Crucitti et al. 2006 ). Eigenvector Centrality extends this concept by measuring accessibility to highly accessible locations (Agryzkov et al. 2019 ; Curado et al. 2020 ). Intermediation measures, conversely, evaluate a node's control over network movement, with Betweenness Centrality (BC) counting shortest paths through nodes (Freeman 1977 , Ozuduru et al. 2021 ; Porta et al. 2009 ; Sevtsuk 2014 ; Ullah et al. 2021 ). Traditional centrality measures, however, often overlook crucial urban dynamics. To address this, enhanced metrics have been developed: Preferential Centrality (PC), which incorporates activity estimations based on location and network topology (Hellervik et al. 2019 ), and Freeman-Krafta Centrality (FK), which improves BC by considering distance decay and attraction factors (Krafta 1994 ). These measures capture different aspects of urban circulation: PC focuses on proximity-driven interactions, while FK measures movement intensity at path convergence points. Both aim to address the limitations of their more common counterparts, and studies suggest that these enhanced metrics are more effective in explaining socioeconomic phenomena (Gao et al. 2013 ; Hellervik et al. 2019 ; Wu et al. 2022 ). Land value reflects the desirability of urban spaces due to locational advantages, and centrality measures are expected to correlate with this economic indicator (Aguilar and Maraschin 2024 ; Chakrabarti et al. 2022 ; He 2020 ; Heyman and Sommervoll 2019 ). Metrics that are more sensitive to local conditions are anticipated to better capture such value differentials. Therefore, this article compares the performance of five centrality metrics – CC, Eigenvector, PC, BC, and FK – in explaining land value variability in Porto Alegre, Brazil. We hypothesize that PC and FK, through their incorporation of additional urban factors, more effectively explain this variation. The paper is structured as follows: Section 2 introduces the centrality measures, Section 3 reviews comparative studies, Section 4 outlines materials and methods, Section 5 presents and discusses results, and Section 6 offers conclusions. 2. Centrality measures 2.1. Closeness Centrality (CC) Closeness centrality is defined as the inverse of the distance between a node and all other nodes in an urban system (Sevtsuk and Mekonnen 2012 ), reflecting proximity and ease of access (Crucitti, Latora, and Porta 2006 ). Hansen ( 1959 ) describes it as the potential for interaction, where greater accessibility correlates with economic potential and growth. Ingram ( 1971 ) further links accessibility variations to changes in population density and land prices, a relationship confirmed by studies in diverse urban contexts (Aguilar and Maraschin 2024 ; Chakrabarti et al. 2022 ; He 2020 ). 2.2. Betweenness Centrality (BC) Developed by Freeman ( 1977 ), Betweenness Centrality measures the probability that a node serves as the shortest path between others, indicating its control over communication flows. Since the 1980s, BC has been used in urban studies to analyse traffic flow (Gao et al. 2013 ), identify centres (Ozuduru et al. 2021 ; Ullah et al. 2021 ), locate economic activities (Porta et al. 2009 ; Sevtsuk 2014 ), and estimate land value (Heyman and Sommervoll 2019 ; Wang and Chen 2020 ; Filippova and Sheng 2020 ). However, BC has been criticized for ignoring the intensity and distribution of urban activities and the effect of distance decay (Gao et al. 2013 ; Hellervik et al. 2019 ). Additionally, Wu et al. ( 2022 ) censure the consideration of all shortest paths as identical, despite variations in interactions. Recent studies have adapted BC to account for these limitations (Gao et al. 2013 ; Wu et al. 2022 ). 2.3. Preferential Centrality (PC) Preferential Centrality goes beyond network configuration, positing that the development and decline of urban activities depend on access to other activities mediated by the transportation networks. PC is a "minimal model" aiming to explain the location of urban activities using only few parameters. In this regard, urban activity refers to interactions at a location, including both monetary and non-monetary land uses (Hellervik 2021a ). Economic value is attributed to locations based on the willingness to pay for interactions. This unifying concept of activity, encompassing services, commerce, and housing, makes land value a suitable proxy, reflecting areas with high competitiveness for land uses (Alonso 1964 ). Hellervik et al. ( 2019 ) base PC on eigenvector centrality, originally developed by Bonacich ( 1972 ) for analysing popularity in social networks and later adapted for urban studies (Agryzkov et al. 2019 ; Curado et al. 2020 ). Eigenvector centrality measures accessibility to highly accessible locations. PC enhances this by incorporating urban activity as an agglomerative force, using an iterative calculation to find activities where each node's incoming and outgoing interaction reach equilibrium. This approach better captures economic phenomena than movement-based measures, as most movement is directed toward attractive locations. 2.4. Freeman-Krafta Centrality (FK) In the 1990s, Krafta ( 1994 ) introduced Freeman-Krafta Centrality as an improvement to BC to address its key limitations. FK accounts for metric distance, recognizing that longer paths hinder movement by reducing flows and interactions as distance increases. It also allows nodes to be weighted by various attributes, recognizing that the importance of paths depends not only on network configuration but also on attractors and the distances travelled. FK has been applied in urban analyses (Krafta and Silva 2020 ; Maraschin et al. 2021 ) but is rarely linked to urban land value. Intermediation measures like BC and FK can predict movement intensity along road segments and, therefore, be associated with negative externalities, such as congestion and pollution. For this reason, while CC generally shows a positive relationship with land value, findings for BC and FK are mixed. Aguilar and Maraschin ( 2024 ) found weakly positive relationships for FK in a Brazilian city, whereas Heyman and Sommervoll ( 2019 ) and Wang and Chen ( 2020 ) reported negative correlations between BC and residential prices in Oslo and Columbus. Otherwise, high flow locations may benefit non-residential functions, enhancing land values, although the type of movement is crucial, with pedestrian flow often being more advantageous than vehicular flow (Antunes et al. 2023 ; Liao et al. 2021 ; Porta et al. 2009 ). 3. Comparisons of centrality measures Several studies have compared centrality measures for their effectiveness in capturing social and economic phenomena. Batool and Niazi ( 2014 ) evaluated various metrics, finding that BC lacked a clear pattern compared to CC and Eigenvector Centrality. Crucitti, Latora, and Porta ( 2006 ) showed that CC highlights the geometric centre of a system, while BC captures important network paths, making it suitable for analysing urban traffic flows (Agryzkov et al. 2019 ; Lin and Ban 2017). However, Gao et al. ( 2013 ) noted that BC’s limitations reduce its effectiveness in capturing movement compared to measures that consider additional factors. Faria et al. ( 2024 ), in this regard, emphasize the importance of distance and activity locations. Wu et al. ( 2022 ) also highlight that BC's neglect of human interactions is a significant weakness, as it tends to emphasize system bridges, even in sparsely populated areas. For pedestrian movements, Yue and Zhu ( 2019 ) found that BC more closely correlates with presence than CC, whereas the opposite is true for driving. Regarding the ability to predict activity's location, Rui and Ban ( 2014 ) found that in Stockholm, green areas are concentrated in regions with high CC, while public services and residential areas are more frequently associated with higher BC values. However, CC is better at describing public service locations, as it reflects how people navigate the city. This is supported by Wang et al. ( 2018 ), who assert that CC is superior to BC in measuring locational advantages. They also note that centrality measures correlate more strongly with urban activity locations at aggregated levels than at disaggregated levels. In a comparative analysis of BC and FK, Faria et al. ( 2024 ) indicate that FK is more sensitive to a node's relative position in the network, a crucial attribute for urban analysis. This sensitivity is significant because the probability of movement varies among nodes that might otherwise appear identical, which is critical for the location of certain economic activities, such as retail. Hellervik et al. ( 2019 ) found that PC is more effective than Eigenvector Centrality in predicting urban activity locations, which are often contested for profitable uses, leading to higher land values. Similarly, Vichiensan et al. ( 2023 ) analysed the impact of various centrality measures, including CC, BC, and Eigenvector Centrality, on land values in Bangkok's railway network, concluding that CC offers superior explanatory power. This indicates that agglomeration or proximity effects in a monocentric context are more significant than intermediation hierarchy effects. Based on the literature, different centrality measures reflect various socioeconomic factors. While BC can indicate preferential pathways for flows, measures that address its shortcomings – like Freeman-Krafta Centrality (FK) – are more effective by incorporating human activities and distance decay. Conversely, human interactions and activity concentration are more closely related to proximity than to road network hierarchy, being more effectively captured by CC and Eigenvector Centrality. When proximity is adjusted for potential activities and travel time, as with PC, the spatial concentration of activities – maximizing human interactions – can be better predicted. Thus, PC is suggested to be more effective than other measures in anticipating urban land values. 4. Materials and Methods 4.1. Study area This research focuses on Porto Alegre, Brazil, with a population of 1,332,845 in 2022, distributed across 214.91 km², yielding a density of 6,201.88 inhabitants/km² - among the highest in Brazilian metropolises. The city’s GDP per capita was approximately US $ 9,836.53 in 2021, placing it in the top 15% nationally. The average monthly salary for formal workers in 2022 was US $ 1,041.60, ranking in the top 0.42% in the country (IBGE 2023). Throughout the 20th century, Porto Alegre transitioned from industrial-port activities along the Guaíba lakefront to a service-oriented economy. This shift followed the migration of elites from the Historic Centre to the eastern zone, near the Iguatemi Shopping Mall, benefiting from scenic landscapes, a mild microclimate, and flood protection (Cabral 1982 ; Sanfelici 2009 ). Figure 1 shows the study area. 4.2. Network preparation and centrality measures calculation The measurements were performed on a drive-network represented geometrically and divided into 29,978 segments, except for the buffer of approximately 2 km included in the calculations to minimize edge effects. The CC, BC, and FK were calculated using the Graph Analysis of Urban Systems (GAUS) plugin, developed for QGIS by Dalcin and Krafta ( 2021 ). Equations 1, 2, and 3 formalize them: CC(i) = \(\:\sum\:_{j=0}^{i,jϵG}\frac{1}{{d}_{ij}}\) (1) In which, CC(i) is the Closeness Centrality of segment i pertaining to the graph G and d ij is the shortest path between i and j , in metres. BC(k) = \(\:\sum\:_{k\ne\:i\ne\:j}^{i,jϵG}\frac{{g}_{ij}\left(k\right)}{{g}_{ij}}\) (2) In which, BC(k) is the Betweenness Centrality of segment k , g ij (k) is the number of shortest paths connecting i e j that cross k and g ij is the total number of shortest paths that link i and j . FK(k) = \(\:\sum\:_{k\ne\:i\ne\:j}^{i,jϵG}\frac{{g}_{ij}\left(k\right)\:{W}_{i}{W}_{j}}{{g}_{ij}\:{d}_{ij}}\) (3) In which, FK(k) is the Freeman-Krafta Centrality of segment k , and W i and W j are the weights of entities i and j , respectively. In this study weights are not used and set to 1. The PC was calculated through the tool SpatCent (Hellervik 2021b ). Its formulation is described by Eq. 4 . $$\:{a}_{j}=\left({\gamma\:a}_{j}+{R}_{j}\right){\sum\:}_{i}\frac{{a}_{i}f\left({c}_{ij}\right)}{{\sum\:}_{k}\left({\gamma\:a}_{k}+{R}_{k}\right)f\left({c}_{ik}\right)}$$ 4 In which, the left-hand side corresponds to “outgoing” interaction from each zone, and the right-hand side corresponds to “incoming” interaction. The incoming interaction is attracted from other zones by a combination of activity ( \(\:{a}_{j})\) and local weights ( \(\:{R}_{j})\) and is modulated by an interaction function. Competition between zones to attract incoming interactions is also handled by the divisor within the summation. The term a j corresponds to activity value for zone j , and when a static state is reached, this will correspond to PC; γ is an agglomeration parameter; R j is a local static weight; f(c ij ) corresponds to the interaction function, with the generalized cost c ij as input. In this work, active street segments 1 are used as zones. The local static weights could be any non-changing value that should capture the local capacity for activity. In this study, R j was set to be the “buildable” area of segment j , considering a 30 meters buffer 2 . The interaction function f(c ij ) has the form: f(c ij ) = \(\:{{c}_{ij}}^{-\beta\:}\) (5) In which β is set to be 2. The generalized cost for an interaction between zones i and j is described by c ij . For a driving network, c ij is calculated by the travel time using the shortest path in the network (taking speed limits into account). A constant “start-and-end-penalty” of 5 minutes is added to the travel time, aiming to capture the extra time of getting into and out of the car and walking to the final destinations. In this work two different PC measures were tested. PC1 (where γ = 1), and PC2 ( γ = 0). Since PC2 is without the agglomeration factor, it works as an Eigenvector Centrality (Hellervik et al. 2019 ). 4.3. Land data Land value data for 2022 was sourced from the Porto Alegre Municipality's Finance Department, covering 36,578 real estate transactions across residential, retail, service, and industrial sectors. These records were georeferenced using Google Earth (version 7.3.6.9796). Each address corresponds to a single plot, although multiple units may share an address. Using R software (version 4.4.0), sales records were aggregated by address to calculate the land unit value, defined as the total value of real estate on a plot divided by its area. Four scenarios were considered: (1) a plot with one unit, which was sold. In this case the unit's value was divided by the plot area; (2) a plot with multiple units but one sale, replicating the sold unit's value across all units, summing them, and dividing by the plot area; (3) a plot with several sold units, where the mean value of sold units was assigned to all units, summed, and divided by the plot area; and (4) plots without sales records were excluded from the analysis. This method allowed for an indirect estimate of land value, as updated "pure" land value data is unavailable for Brazilian cities. This procedure yielded 9,033 real estate observations, to which five centrality measures for the corresponding road segments were added. Observations with BC or PC values of zero were excluded (866 exclusions), along with those deemed outliers based on the interquartile range criterion (400 exclusions), which leads to 7,767 remaining addresses. 4.4. Statistical behaviour of centrality measures and land values To compare the statistical behaviour of the six variables, we calculated their relative range , distribution , and hierarchy . The relative range is defined as the range (maximum – minimum) divided by the mean. The distribution is the standard deviation divided by the mean, multiplied by 100. The hierarchy reflects the concentration of the highest values in a few segments, measured by the Pareto Index, which sums the values of the top 20% of segments and divides this total by the sum of the values in the bottom 80%. 4.5. Levels of aggregation The data were analysed at two levels of aggregation: disaggregated , considering each of the 7,767 addresses as individual observations; and aggregated, where Porto Alegre was divided into 821 hexagons, each measuring 21.67 hectares (500 meters between centres). This distance approximates a neighbourhood unit or walkable area (Gehl 2015 ). For each hexagon, averages of land unit values and accessibility measures, along with the summed values of the intermediation measures, were calculated from the point observations (Fig. 2 ). For both levels of aggregation, spatially adjusted regression models were constructed. Based on the results of the Lagrange Multiplier tests (LM), the chosen model specification was the Spatial Durbin Model (SDM). The SDM simultaneously addresses spatial dependence in both the residuals and the endogenous variable, making it superior to other models as it captures the effects of unmodeled neighbourhood attributes (Herath et al. 2015). Additionally, it handles misspecified functional forms and spatial heterogeneity in estimated parameters (Osland 2010). The models were run in two stages. In the first stage, each centrality measure was considered as an independent variable alongside the plot area, which significantly impacted the results. Colwell and Munneke ( 1997 ) showed that as one moves away from the centre, increases in plot areas do not correspond to proportional increases in values. This results in a decline in the unit value curve, reflecting reduced competitiveness in areas with lower accessibility. However, in Porto Alegre, the reduction in areas toward the periphery is only partial; a peripheral arc of lower social status neighbourhoods features smaller plots than those in the centre, despite not having as high unit values as more central areas (see Figure A1, Online Resource). In the second stage, the effect of area was disregarded, and only the centrality measures were included separately as independent variables. In all models, the dependent variable is the unit land value (value per m²). Table 1 details their specifications. Table 1 Types and variables in each regression model Dependent variable Independent variables Models Disagg. Agg. Unit value CC + area 1A 6A CC 1B 6B BC + area 2A 7A BC 2B 7B FK + area 3A 8A FK 3B 8B PC1 + area 4A 9A PC1 4B 9B PC2 + area 5A 10A PC2 5B 10B 5. Results and Discussions 5.1. Comparison between measures This section provides a comparative analysis of the performance of the five centrality measures. While Fig. 3 exhibits the spatial distribution of the measures as well as the land unit values, Table 2 presents the Pearson correlations between the measures. Additionally, figure A2 (Online Resource) displays the scatter plots of PC1 and PC2 against CC, BC and FK. Table 2 Pearson Correlation between centrality measures (in natural log form). All correlations are significant at p < 0.001 CC PC1 PC2 BC FK CC 1 / / / / PC1 .9236 1 / / / PC2 .9464 .9722 1 / / BC .1284 .1735 .1770 1 / FK .1762 .2272 .2306 .9129 1 Land unit values follow a downward curve from the Historic Centre to the periphery (figure A3, Online Resource), with a notable concentration of high values along the Historic Centre – Iguatemi Shopping Mall axis (exceeding US $ 2,889). Surrounding this area is a zone of slightly lower values (between US $ 1,804 and US $ 2,889), forming a clear Hoyt-like spatial pattern (Hoyt 1939 ). As one moves away from this axis, values decrease steadily until reaching the outskirts, where unit values do not exceed US $ 433 and can even drop below US $ 60 in sparsely urbanized areas to the south. The CC reveals a strong edge effect by highlighting the geometric centre of the system (buffer not shown in the figure). Both BC and FK display similar spatial patterns, emphasizing roads with the highest traffic flow (intermediation) hierarchy. The FK, in particular, tends to show higher values in areas with greater accessibility, since it accounts for the effect of distance decay. Notably, the agglomeration factor (γ), which defines activity concentration in PC1, further accentuates the centre-periphery centrality gradient. When γ = 0, PC2 (Eigenvector Centrality) shows a wider dispersion of high-centrality zones and a less pronounced gradient. The exceptionally high correlations between PCs and CC are notable (around 0.93), indicating the similarity of the phenomena they capture – accessibility between segments. Since PC2 ignores the agglomerative factor, its linear correlation with CC is slightly higher (0.9464). Regarding intermediation measures, the correlations obtained between PCs and FK values are higher than the correlations between PCs and BC values (around 0.23), reflecting the greater sensitivity of PCs and FK in capturing phenomena influenced by distance. Table 3 displays the measures’ distributions (relative standard deviation), hierarchy, and regularity, comparing them with land unit values. Table 3 Centrality measures and land values statistic behaviour Centrality measures Mean Median Relative Range Distribution Hierarchy PC1 2.01 1.92 3.06 54.58 0.90 PC2 1.25 1.34 1.01 19.74 0.83 CC 6.58 6.92 0.92 15.67 0.83 BC 1.235E + 06 1.9753E + 05 34.94 240.97 0.99 FK 1.0574E + 04 2,815.60 25.63 198.05 0.98 Land values Mean Median Relative Range Distribution Hierarchy Land values 6,622.941 5,086.21 3.84 92.02 0.94 The two groups of measures are easily discernible: accessibility metrics exhibit lower relative ranges and distributions, and, therefore, are less hierarchical, resulting in less differentiation within the urban space. Among these, PC1 stands out as the most differentiating. Its hierarchy is roughly equidistant between CC/PC2 and the intermediation measures, reflecting its ability to capture the uniqueness of urban spatiality through the uneven potential distribution of activities. In contrast, the intermediation measures are more dispersed and hierarchical, with few segments (arterial roads) showing high centrality, while the majority have relatively low significance. Among the centrality measures evaluated, the relative range, distribution, and hierarchy of land values most closely align with PC1. Assuming land value reflects socio-spatial phenomena, this alignment supports validating PC1 and its integration of the agglomerative factor as an effective metric for capturing or predicting these phenomena. In the next section, we will further explore this relationship and reinforce the mentioned support through multi-model and multi-scale spatial regression analysis. 5.2. Explanation of land value by centrality measures This section focuses on the explanatory power of the centrality measures regarding land value. Correlations are shown in Table 4 and scatter plots in Fig. 4 , followed by Table 5 , presenting the results of the spatial regression models. Table 4 Correlations between unit land values and centrality measures (in natural log form) (continue) Disaggregated Aggregated Pearson Measure Correlation Pearson Measure Correlation PC1 0.3907*** PC1 0.5427*** PC2 0.3705*** PC2 0.5039*** CC 0.2617*** CC 0.4634*** BC -0.0095 BC 0.1831*** FK -0.0267* FK 0.2221*** (conclusion) pearman Measure Correlation Spearman Measure Correlation PC1 0.3287*** PC1 0.5652*** PC2 0.2623*** PC2 0.4909*** CC 0.0893*** CC 0.3975*** BC -0.0352*** BC 0.1680*** FK -0.0097 FK 0.2135*** *** p < 0.001; ** p < 0.01; * p < 0.05; . P < 0.1. Table 5 Spatially adjusted regression models (continue) Disaggregated Model 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B Coefficients (p-value) Area -0.3716 (< 0.001) *** - -0.3619 (< 0.001) *** - -0.3599 (< 0.001) *** - -0.3595 (< 0.001) *** - -0.3677 (< 0.001) *** - CC 1.0077 (< 0.001) *** 0.5905 (< 0.01) ** - - - - - - - - BC - - -0.0038 (0.4608) -0.0268 (< 0.001) *** - - - - - - FK - - - - -0.0203 (< 0.01) ** -0.0618 (< 0.001) *** - - - - (conclusion) PC1 - - - - - - 0.3925 (< 0.001) *** 0.8222 (< 0.001) *** - - PC2 - - - - - - - - -0.0107 (0.9234) 2.1938 (< 0.001) *** LM Tests - p-value RSerr < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 Rslag < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 adjRSerr < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 adjRSlag < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 0.3346 < 0.001 0.0893 pseudo-Adjusted R² 0.0740 0.2292 0.4205 0.1625 0.4212 0.0296 0.4036 0.1409 0.4213 0.3554 Aggregated Model 6A 6B 7A 7B 8A 8B 9A 9B 10A 10B Coefficients (p-value) Area -0.2407 (< 0.001) *** - -0.2408 (< 0.001) *** - -0.2407 (< 0.001) *** - -0.2241 (< 0.001) *** - -0.2293 (< 0.001) *** - CC 0.0844 (< 0.01) ** 0.0706 (< 0.05) * - - - - - - - - BC - - 0.0703 (< 0.01) ** 0.0555 (0.0576). - - - - - - FK - - - - 0.0844 (< 0.01) ** 0.0706 (< 0.05) * - - - - PC1 - - - - - - 1.1482 (< 0.001) *** 1.1846 (< 0.001) *** - - PC2 - - - - - - - - 0.6264 (0.0660). 0.7403 (0.0810). LM Tests - p-value Rserr < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 Rslag < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 adjRSerr < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 adjRlag 0.8672 0.4546 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.001 < 0.01 < 0.05 pseudo-Adjusted R² 0.4695 0.4210 0.4738 0.4219 0.4695 0.3409 0.3226 0.2769 0.4760 0.4169 Authors’ elaboration. Among the accessibility measures, at both levels of aggregation, PC1 shows the highest correlations with land value, followed by PC2 (Eigenvector) and CC, all in a positive direction. Nevertheless, very high CC values seem to be related to a decrease in land costs, a phenomenon not observed with PC1 and PC2. When controlling for plot area, the regression models at the disaggregated level reveal that although CC has a higher coefficient (1.0077), the fit of model 1A is quite low (7.40%). In contrast, in model 4A, the coefficient for PC1 is lower (0.3925), but the model achieves a considerably higher fit (40.36%), attesting that the measure can better capture non modelled spatial influences. On the other hand, the coefficient for PC2 is not significant when controlling for area (model 5A). It is noteworthy that the area coefficients, at both levels of aggregation, are negative, confirming the hypothesis that unit value decreases as plot surface increases. When area is not controlled, PC2 shows the most significant results, with a coefficient of 2.1938 and a fit of 35.54% (model 5B), while the values for PC1 are 0.8222 and 14.09%, respectively (model 4B); and for CC, 0.5905 and 22.92%, in the same order (model 1B). This discrepancy demonstrates that PC1 is more sensitive to variations in land value that are not explained by the plot dimensions, but rather by locational factors. At the aggregated level, when controlling for area, PC1 is also the most efficient in explaining land value, with a coefficient of 1.1482 and a fit of 32.26% (model 9A). Although the pseudo-Adjusted R² of model 6A is higher (46.95%), the coefficient for CC is significantly lower at 0.0844. At this level of aggregation, PC2 does not show significance at p < 5% in either the model where area is used as a control variable (10A) or the one without area control (10B). Without controlling for area, PC1 again performs better, with a coefficient of 1.1846 and a fit of 27.69% (model 9B). Regarding CC (model 6B), although the pseudo-Adjusted R² is higher (42.10%), the coefficient for the independent variable is considerably reduced (0.0706). Regarding intermediation measures, FK outperforms BC in explaining variations in land value, although both are less effective than accessibility measures. At the disaggregated level, the correlation is negative and significant for FK, while it is not significant for BC. This may suggest that at the road segment level, negative externalities associated with higher traffic capacity tend to negatively impact land value, which could discourage investment along busier roads. On the other hand, at the aggregated level the correlations for FK remain stronger than those for BC (which also become significant), and both correlations are positive. This implies that conversely to the immediate contiguity, the general proximity to arterial roads – and the ease of access these locations offer – is typically valued, even though the property itself is located on less busy "interior" roads. The disaggregated-level regression models reveal interesting dynamics regarding the significance of BC and FK when controlling for area. In model 2A, where area is considered, the coefficient for BC is not significant. However, in model 3A, the coefficient for FK is -0.0203, and the pseudo-Adjusted R² is 42.12%. When area is excluded, BC becomes significant with a coefficient of -0.0268, though the model fit (pseudo-Adjusted R²) drops to 16.25%. Interestingly, when area is not considered, the coefficient for FK in model 3B increases in magnitude (-0.0618), but the pseudo-Adjusted R² falls dramatically to 2.96%, contrasting with the stronger fit seen for BC. This suggests that the explanatory power of BC at the disaggregated level is heavily influenced by plot area: BC loses significance when area is included, but gains explanatory power in its absence. The reduction in pseudo-Adjusted R² when area is removed from the model with FK is much more pronounced than for BC, indicating that the effect of area remains partially present in the BC model. Despite the lower pseudo-Adjusted R², the coefficients for FK remain consistently significant. The described phenomenon results from the inclusion of distance in the calculation of FK. Indeed, the linear correlations between area and both FK and BC are positive and similar (0.1451 and 0.1255, respectively), indicating that larger plots are found on roads of higher hierarchy. However, the unit values of the land are significantly and inversely related to FK, suggesting that larger plots on roads that are more accessible, and presumably more congested, tend to be less valued than larger plots on roads that are less congested (more distant). This effect is not captured by BC, which considers roads with the same number of shortest paths to be equivalent, regardless of distance, making BC coefficients more sensitive to area variation. At the aggregated level, FK exhibits higher coefficients in both the model that includes area as a control variable (8A) and the model that does not include it (8B): 0.0844 and 0.0706, respectively, with the fit of the models being 46.95% and 34.09%, in that order. The models that consider BC as an explanatory variable show higher pseudo-Adjusted R² values (47.38% with area and 42.19% without area), although the coefficients are lower – 0.0703 in the first case and 0.0555 (not significant at p < 5%) in the second. At this level, the greater diversity in plot sizes within the cell dramatically reduces their linear correlations with both BC and FK, rendering them insignificant. This allows BC to capture part of the variation in land value even when area is controlled, unlike what occurs at the disaggregated level. 6. Final Remarks This study compared two groups of spatial centrality measures in Porto Alegre, Brazil, evaluating how effectively they capture locational advantages reflected in urban land values. The methodological enhancements of PC1 and FK - incorporating agglomeration factors and distance decay, respectively - proved more effective in identifying characteristics that foster urban activity concentration and increase land values. PC1, in particular, demonstrated a stronger correlation with land value variations compared to CC and PC2 (Eigenvector Centrality), especially when controlling for plot size and using aggregated data, which mitigates heteroscedasticity and the impact of unmodeled factors. These results are consistent with findings from Hellervik et al. ( 2019 ) in Scandinavia. Additionally, our study supports Wang et al. ( 2018 ), emphasizing that centrality measures show stronger correlations with activity locations at an aggregated level. Regarding the intermediation measures, while FK is effective in identifying local characteristics, both FK and BC showed a negative correlation with land values at the disaggregated level, likely due to the adverse effects of high-hierarchy roads. These findings align with those of Heyman and Sommervoll ( 2019 ) and Wang and Chen ( 2020 ). Conversely, at the aggregated level, the relationship between intermediation measures and land value was positive – though less significant than that of accessibility measures – indicating that while proximity to major roads can enhance access, immediate adjacency to traffic-related nuisances may lower property values. Overall, the analyses revealed stronger correlations between centrality and land value for accessibility measures, supporting the idea that proximity to the broader urban system is more influential in determining location choices for urban paying activities 3 . Notwithstanding, it is crucial to note that in a Global South metropolis, various unmodeled factors linked to a highly segregated urban structure (such as informality, crime, congestion, and pollution) can influence land values. Future studies should incorporate these factors, along with non-motorized accessibility measures, to enhance model accuracy. Declarations Ethical considerations : there are no human or animal participants in this article and informed consent is not required. Consent to participate: not applicable. Consent for publication: not applicable. Declaration of conflicting interest : the authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Financial interests the authors declare they have no financial interests. Funding statement This study was funded by the Swedish Transport Administration [grant number TRV 2020/25561] and by “Coordenação de Aperfeiçoamento de Pessoal de Nível Superior” – CAPES [Coordination for the Improvement of Higher Education Personnel – CAPES] [grant number 88887.936632/2024-00]. Author Contribution Both authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by R.L.A. and A.H. The first draft of the manuscript was written by R.L.A and both authors commented on previous versions of the manuscript. Both authors read and approved the final manuscript. Acknowledgement The paper has benefitted from discussions and support in the context of the Spatial Morphology Group at Chalmers University of Technology. We also acknowledge the Finance Department of the municipality of Porto Alegre for providing the data related to the real estate transactions. Data Availability Data is provided within the supplementary information files References Agryzkov T, Tortosa L, Vicent JF et al. (2019) A centrality measure for urban networks based on the eigenvector centrality concept. Environment and Planning B – Urban Analytics and City Science 46(4):668-689. https://doi.org/10.1007/s00421-008-0955-8. Aguilar RL, Maraschin C (2024) Relationships between urban network centrality and apartment prices in Porto Alegre, Brazil. Finisterra 60(126):1-16. 10.18055/Finis34731. Alonso W (1964) Location and Land Use : toward a general theory of land rent. Harvard University Press, Cambridge. Antunes FS, Wang F, Fernandes MC (2023) Multiple centrality assessment of location preferences of retail and services in Petrópolis, Brazil. Papers in Applied Geography 9:136-148. https://doi.org/10.1080/23754931.2022.2128859. Batool K, Niazi MA (2014) Towards a Methodology for Validation of Centrality Measures in Complex Networks. 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Hellervik A (2021b). SpatCent. https://www.spatcent.se/models. Accessed 02 July 2024. Hellervik A, Nilsson L, Andersson C (2019) Preferential centrality – A new measure unifying urban activity, attraction and accessibility. Environment and Planning B – Urban Analytics and City Science 46(7):1331-1346. https://doi.org/10.1177/2399808318812888. Herat S, Choumert J, Maier G (2015) The value of the greenbelt in Vienna: a spatial hedonic analysis. The Annals of Regional Science 54:349-374. https://doi.org/10.1007/s00168-015-0657-1. Heyman AV, Sommervoll DE (2019) House prices and relative location. Cities 95:1-14. https://doi.org/10.1016/j.cities.2019.06.004. Hoyt H (1939) The structure and growth of residential neighborhoods in American cities. United States Government Printing Office, Washington, D.C. Instituto Brasileiro de Geografia e Estatística – IBGE (2010) Censo 2010:resultados. [ Census 2010: results ]. https://censo2010.ibge.gov.br/resultados.html. Accessed 25 January 2024. Instituto Brasileiro de Geografia e Estatística – IBGE (2023) Porto Alegre. https://cidades.ibge.gov.br/brasil/rs/porto-alegre/panorama. Accessed 09 August 2024. Ingram DR (1971) The concept of accessibility: A search for an operational form. Regional Studies 5(2):101-107. https://doi.org/10.1080/09595237100185131. Krafta R (1994) Modelling intraurban configurational development. Environment and Planning B: Planning and Design 21(1):67-82. https://doi.org/10.1068/b210067. Krafta R, Silva EB (2020) Self-organized Criticality and Urban Form Systems Dynamics with Reference to a Brazilian City. Area Development & Policy 5(3):324-333. https://doi.org/10.1080/23792949.2019.1631124. Liao C, Dai T, Zhao P et al. (2021) Weighted Centrality and Retail Store Locations in Beijing, China: A Temporal Perspective from Dynamic Public Transport Flow Networks. Applied Sciences 11(19):1-15. https://doi.org/10.3390/app11199069. Maraschin C, Machado ALM, Damiani RM (2021) Modelling Spatial Centrality of Logistics Activities: Study in the Porto Alegre Metropolitan Region, Brazil. In: 21st international conference on computational science and its applications, Cagliari, Italy, 13-16 September 2021, pp. 688-703. Springer Science and Business Media Deutschland GmbH, Berlin. Ozuduru BH, Webster CJ, Chiaradia AJF et al. (2021). Associating street network centrality with spontaneous and planned subcentres. Urban Studies 58(10):2059–2078. https://doi.org/10.1177/0042098020931302. Porta S, Strano E, Iacoviello V et al. (2009) Street centrality and densities of retail and services in Bologna, Italy. Environment and Planning B: Planning and Design 36(3):450-465. https://doi.org/10.1068/b34098. Rui Y and Ban Y (2014) Exploring the relationship between street centrality and land use in Stockholm. International Journal of Geographical Information Science 28(7):1425-1438. https://doi.org/10.1080/13658816.2014.893347. Sanfelici DM (2009) A produção do espaço como mercadoria: novos eixos de valorização imobiliária em Porto Alegre/RS. [The production of space as commodity: new vectors of real estate valorisation in Porto Alegre/RS]. Dissertation, University of São Paulo, Brazil. Sevtsuk A (2014) Location and agglomeration: The distribution of retail and food businesses in dense urban environments. Journal of Planning Education and Research 34(4):374-392. https://doi.org/10.1177/0739456X14550401. Sevtsuk A and Mekonnen M (2012) Urban Network Analysis: A New Toolbox for ArcGIS. Revue Internationale de Géomatique 22(2):287-305. https://doi.org/10.3166/rig.22.287-305. Ullah A, Wang B, Sheng J et al. (2021). Identifying vital nodes from local and global perspectives in complex networks. Expert Systems with Applications 186:1-10. https://doi.org/10.1016/j.eswa.2021.115778. Vichiensan V, Wasuntarasook V, Prakayaphun T et al. (2023) Influence of Urban Railway Network Centrality on Residential Property Values in Bangkok. Sustainability 15:1-25. https://doi.org/10.3390/su152216013. Wang C and Chen N (2020) A geographically weighted regression approach to investigating local built‑environment effects on home prices in the housing downturn, recovery, and subsequent increases. Journal of Housing and the Built Environment 35:1283-1302. https://doi.org/10.1007/s10901-020-09742-8. Wang S, Xu G, and Guo Q (2018) Street Centralities and Land Use Intensities Based on Points of Interest (POI) in Shenzhen, China. International Journal of Geo-Information 7(425):1-15. https://doi.org/10.3390/ijgi7110425. Wu X, Cao W, Wang J et al. (2022) A spatial interaction incorporated betweenness centrality measure. PLoS ONE 17(5):1-20. https://doi.org/10.1371/journal.pone.0268203. Yue H and Zhu X (2019) Exploring the Relationship between Urban Vitality and Street Centrality Based on Social Network Review Data in Wuhan, China. Sustainability 11:1-19. https://doi.org/10.3390/su11164356. Footnotes Some roads, such as motorways, are not considered active, since they in general do not provide access to urban activities. These roads, however, are still used to find shortest paths. The buffers are non-overlapping, which means that each surrounding piece of land is only attributed to a single active road. However, since this study is based on property prices, we have no information about non-paying activities. Additional Declarations No competing interests reported. Supplementary Files Supplemetarymaterial.zip Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Jul, 2025 Reviews received at journal 15 Jul, 2025 Reviewers agreed at journal 15 Jul, 2025 Reviews received at journal 07 May, 2025 Reviewers agreed at journal 06 May, 2025 Reviewers agreed at journal 04 May, 2025 Reviewers invited by journal 01 May, 2025 Editor assigned by journal 20 Mar, 2025 Submission checks completed at journal 20 Mar, 2025 First submitted to journal 19 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6264491","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":451668447,"identity":"445cc550-17fe-4c07-a72c-1e996c45b920","order_by":0,"name":"Ramon Lucato de Aguilar","email":"","orcid":"","institution":"Federal University of Rio Grande do Sul","correspondingAuthor":false,"prefix":"","firstName":"Ramon","middleName":"Lucato","lastName":"de Aguilar","suffix":""},{"id":451668448,"identity":"fea30be4-b2a0-484c-9728-35784d402913","order_by":1,"name":"Alexander Hellervik","email":"data:image/png;base64,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","orcid":"","institution":"Chalmers University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Alexander","middleName":"","lastName":"Hellervik","suffix":""}],"badges":[],"createdAt":"2025-03-19 21:08:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6264491/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6264491/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82176539,"identity":"8a7950e0-f6f4-4010-964a-866604349c0e","added_by":"auto","created_at":"2025-05-07 11:14:06","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1719860,"visible":true,"origin":"","legend":"\u003cp\u003eLocalization of Porto Alegre and monthly household income by census tract. Values are in U.S. dollars (US$), based on the 2010 census and adjusted for January 2023\u003c/p\u003e\n\u003cp\u003eAuthors’ elaboration using QGIS, version 3.32.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/a5ba482ed9c20a22eb3b8a31.png"},{"id":82176545,"identity":"3222037e-3b33-4ebb-9468-f6721c68fafd","added_by":"auto","created_at":"2025-05-07 11:14:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":515463,"visible":true,"origin":"","legend":"\u003cp\u003eDisaggregated (left) and aggregated (right) unit land values (Vuni) and centrality measures\u003c/p\u003e\n\u003cp\u003eAuthors` elaboration using QGIS, version 3.32.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/d66f06d2ad383215087b5eb2.png"},{"id":82176544,"identity":"c47d2863-9e27-47ae-8e69-4decc9f1127e","added_by":"auto","created_at":"2025-05-07 11:14:06","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":2492314,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of\u003cstrong\u003e \u003c/strong\u003eunit\u003cstrong\u003e \u003c/strong\u003eland values (a), Closeness Centrality (b), Betweenness Centrality (c), Freeman-Krafta Centrality (d), Preferential Centrality - PC1 (e), and Preferential / Eigenvector Centrality - PC2 (f). Results spatially aggregated\u003c/p\u003e\n\u003cp\u003eAuthors` elaboration using QGIS, version 3.32.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/80bc983119a3a02b21df8c9f.png"},{"id":82176538,"identity":"486d8546-a879-4207-84a5-daf88007fa07","added_by":"auto","created_at":"2025-05-07 11:14:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":226637,"visible":true,"origin":"","legend":"\u003cp\u003eScatter plots of PC1 against CC (a), BC (b) and FK (c), and of PC2 against CC (d), BC (e) and FK (f)\u003c/p\u003e\n\u003cp\u003eAuthors`elaboration using R, version 4.4.0.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/ae13e7b895949cafbd648500.png"},{"id":82179534,"identity":"f2015143-77e5-4266-ac68-573341d15805","added_by":"auto","created_at":"2025-05-07 11:38:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5801421,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/a6f489c5-6d17-417b-a7a5-3dada193d1de.pdf"},{"id":82176549,"identity":"63ee6e19-a8ba-4122-b190-7f521ea8ea51","added_by":"auto","created_at":"2025-05-07 11:14:06","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":13717983,"visible":true,"origin":"","legend":"","description":"","filename":"Supplemetarymaterial.zip","url":"https://assets-eu.researchsquare.com/files/rs-6264491/v1/ce3c5392f87474f8dba5dfc1.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eComparative Analysis of Centrality Measures in Explaining Activity Locations Through Land Value Variability: A Case Study of Porto Alegre, Brazil\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eVarious spatial centrality measures have emerged from graph theory to analyze urban spatial differentiation, broadly categorized into accessibility and intermediation measures. \u003cem\u003eAccessibility\u003c/em\u003e measures evaluate the ease of access between locations and potential for human interactions, with Closeness Centrality (CC), based on distance, being the most fundamental (Crucitti et al. \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Eigenvector Centrality extends this concept by measuring accessibility to highly accessible locations (Agryzkov et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Curado et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). \u003cem\u003eIntermediation\u003c/em\u003e measures, conversely, evaluate a node's control over network movement, with Betweenness Centrality (BC) counting shortest paths through nodes (Freeman \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1977\u003c/span\u003e, Ozuduru et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Porta et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Sevtsuk \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Ullah et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTraditional centrality measures, however, often overlook crucial urban dynamics. To address this, enhanced metrics have been developed: Preferential Centrality (PC), which incorporates activity estimations based on location and network topology (Hellervik et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), and Freeman-Krafta Centrality (FK), which improves BC by considering distance decay and attraction factors (Krafta \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). These measures capture different aspects of urban circulation: PC focuses on proximity-driven interactions, while FK measures movement intensity at path convergence points. Both aim to address the limitations of their more common counterparts, and studies suggest that these enhanced metrics are more effective in explaining socioeconomic phenomena (Gao et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Hellervik et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wu et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eLand value reflects the desirability of urban spaces due to locational advantages, and centrality measures are expected to correlate with this economic indicator (Aguilar and Maraschin \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chakrabarti et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; He \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Heyman and Sommervoll \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Metrics that are more sensitive to local conditions are anticipated to better capture such value differentials. Therefore, this article compares the performance of five centrality metrics \u0026ndash; CC, Eigenvector, PC, BC, and FK \u0026ndash; in explaining land value variability in Porto Alegre, Brazil. We hypothesize that PC and FK, through their incorporation of additional urban factors, more effectively explain this variation.\u003c/p\u003e \u003cp\u003eThe paper is structured as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e introduces the centrality measures, Section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e3\u003c/span\u003e reviews comparative studies, Section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e4\u003c/span\u003e outlines materials and methods, Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents and discusses results, and Section \u003cspan refid=\"Sec17\" class=\"InternalRef\"\u003e6\u003c/span\u003e offers conclusions.\u003c/p\u003e"},{"header":"2. Centrality measures","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Closeness Centrality (CC)\u003c/h2\u003e \u003cp\u003eCloseness centrality is defined as the inverse of the distance between a node and all other nodes in an urban system (Sevtsuk and Mekonnen \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), reflecting proximity and ease of access (Crucitti, Latora, and Porta \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). Hansen (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1959\u003c/span\u003e) describes it as the potential for interaction, where greater accessibility correlates with economic potential and growth. Ingram (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1971\u003c/span\u003e) further links accessibility variations to changes in population density and land prices, a relationship confirmed by studies in diverse urban contexts (Aguilar and Maraschin \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Chakrabarti et al. \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; He \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Betweenness Centrality (BC)\u003c/h2\u003e \u003cp\u003eDeveloped by Freeman (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1977\u003c/span\u003e), Betweenness Centrality measures the probability that a node serves as the shortest path between others, indicating its control over communication flows. Since the 1980s, BC has been used in urban studies to analyse traffic flow (Gao et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), identify centres (Ozuduru et al. \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Ullah et al. \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), locate economic activities (Porta et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Sevtsuk \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), and estimate land value (Heyman and Sommervoll \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Wang and Chen \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Filippova and Sheng \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). However, BC has been criticized for ignoring the intensity and distribution of urban activities and the effect of distance decay (Gao et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Hellervik et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Additionally, Wu et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) censure the consideration of all shortest paths as identical, despite variations in interactions. Recent studies have adapted BC to account for these limitations (Gao et al. \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Wu et al. \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Preferential Centrality (PC)\u003c/h2\u003e \u003cp\u003ePreferential Centrality goes beyond network configuration, positing that the development and decline of urban activities depend on access to other activities mediated by the transportation networks. PC is a \"minimal model\" aiming to explain the location of urban activities using only few parameters. In this regard, urban activity refers to interactions at a location, including both monetary and non-monetary land uses (Hellervik \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2021a\u003c/span\u003e). Economic value is attributed to locations based on the willingness to pay for interactions. This unifying concept of activity, encompassing services, commerce, and housing, makes land value a suitable proxy, reflecting areas with high competitiveness for land uses (Alonso \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e1964\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eHellervik et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) base PC on eigenvector centrality, originally developed by Bonacich (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e1972\u003c/span\u003e) for analysing popularity in social networks and later adapted for urban studies (Agryzkov et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Curado et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Eigenvector centrality measures accessibility to highly accessible locations. PC enhances this by incorporating urban activity as an agglomerative force, using an iterative calculation to find activities where each node's incoming and outgoing interaction reach equilibrium. This approach better captures economic phenomena than movement-based measures, as most movement is directed toward attractive locations.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Freeman-Krafta Centrality (FK)\u003c/h2\u003e \u003cp\u003eIn the 1990s, Krafta (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1994\u003c/span\u003e) introduced Freeman-Krafta Centrality as an improvement to BC to address its key limitations. FK accounts for metric distance, recognizing that longer paths hinder movement by reducing flows and interactions as distance increases. It also allows nodes to be weighted by various attributes, recognizing that the importance of paths depends not only on network configuration but also on attractors and the distances travelled.\u003c/p\u003e \u003cp\u003eFK has been applied in urban analyses (Krafta and Silva \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Maraschin et al. \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) but is rarely linked to urban land value. Intermediation measures like BC and FK can predict movement intensity along road segments and, therefore, be associated with negative externalities, such as congestion and pollution. For this reason, while CC generally shows a positive relationship with land value, findings for BC and FK are mixed. Aguilar and Maraschin (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) found weakly positive relationships for FK in a Brazilian city, whereas Heyman and Sommervoll (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and Wang and Chen (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) reported negative correlations between BC and residential prices in Oslo and Columbus. Otherwise, high flow locations may benefit non-residential functions, enhancing land values, although the type of movement is crucial, with pedestrian flow often being more advantageous than vehicular flow (Antunes et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Liao et al. \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Porta et al. \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2009\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Comparisons of centrality measures","content":"\u003cp\u003eSeveral studies have compared centrality measures for their effectiveness in capturing social and economic phenomena. Batool and Niazi (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) evaluated various metrics, finding that BC lacked a clear pattern compared to CC and Eigenvector Centrality. Crucitti, Latora, and Porta (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) showed that CC highlights the geometric centre of a system, while BC captures important network paths, making it suitable for analysing urban traffic flows (Agryzkov et al. \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Lin and Ban 2017). However, Gao et al. (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) noted that BC\u0026rsquo;s limitations reduce its effectiveness in capturing movement compared to measures that consider additional factors. Faria et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), in this regard, emphasize the importance of distance and activity locations. Wu et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) also highlight that BC's neglect of human interactions is a significant weakness, as it tends to emphasize system bridges, even in sparsely populated areas. For pedestrian movements, Yue and Zhu (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) found that BC more closely correlates with presence than CC, whereas the opposite is true for driving.\u003c/p\u003e \u003cp\u003eRegarding the ability to predict activity's location, Rui and Ban (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) found that in Stockholm, green areas are concentrated in regions with high CC, while public services and residential areas are more frequently associated with higher BC values. However, CC is better at describing public service locations, as it reflects how people navigate the city. This is supported by Wang et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), who assert that CC is superior to BC in measuring locational advantages. They also note that centrality measures correlate more strongly with urban activity locations at aggregated levels than at disaggregated levels. In a comparative analysis of BC and FK, Faria et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) indicate that FK is more sensitive to a node's relative position in the network, a crucial attribute for urban analysis. This sensitivity is significant because the probability of movement varies among nodes that might otherwise appear identical, which is critical for the location of certain economic activities, such as retail.\u003c/p\u003e \u003cp\u003eHellervik et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) found that PC is more effective than Eigenvector Centrality in predicting urban activity locations, which are often contested for profitable uses, leading to higher land values. Similarly, Vichiensan et al. (\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) analysed the impact of various centrality measures, including CC, BC, and Eigenvector Centrality, on land values in Bangkok's railway network, concluding that CC offers superior explanatory power. This indicates that agglomeration or proximity effects in a monocentric context are more significant than intermediation hierarchy effects.\u003c/p\u003e \u003cp\u003eBased on the literature, different centrality measures reflect various socioeconomic factors. While BC can indicate preferential pathways for flows, measures that address its shortcomings \u0026ndash; like Freeman-Krafta Centrality (FK) \u0026ndash; are more effective by incorporating human activities and distance decay. Conversely, human interactions and activity concentration are more closely related to proximity than to road network hierarchy, being more effectively captured by CC and Eigenvector Centrality. When proximity is adjusted for potential activities and travel time, as with PC, the spatial concentration of activities \u0026ndash; maximizing human interactions \u0026ndash; can be better predicted. Thus, PC is suggested to be more effective than other measures in anticipating urban land values.\u003c/p\u003e"},{"header":"4. Materials and Methods","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Study area\u003c/h2\u003e \u003cp\u003eThis research focuses on Porto Alegre, Brazil, with a population of 1,332,845 in 2022, distributed across 214.91 km\u0026sup2;, yielding a density of 6,201.88 inhabitants/km\u0026sup2; - among the highest in Brazilian metropolises. The city\u0026rsquo;s GDP per capita was approximately US\u003cspan\u003e$\u003c/span\u003e 9,836.53 in 2021, placing it in the top 15% nationally. The average monthly salary for formal workers in 2022 was US\u003cspan\u003e$\u003c/span\u003e 1,041.60, ranking in the top 0.42% in the country (IBGE 2023). Throughout the 20th century, Porto Alegre transitioned from industrial-port activities along the Gua\u0026iacute;ba lakefront to a service-oriented economy. This shift followed the migration of elites from the Historic Centre to the eastern zone, near the Iguatemi Shopping Mall, benefiting from scenic landscapes, a mild microclimate, and flood protection (Cabral \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1982\u003c/span\u003e; Sanfelici \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the study area.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Network preparation and centrality measures calculation\u003c/h2\u003e \u003cp\u003eThe measurements were performed on a drive-network represented geometrically and divided into 29,978 segments, except for the buffer of approximately 2 km included in the calculations to minimize edge effects. The CC, BC, and FK were calculated using the \u003cem\u003eGraph Analysis of Urban Systems\u003c/em\u003e (GAUS) plugin, developed for QGIS by Dalcin and Krafta (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Equations\u0026nbsp;1, 2, and 3 formalize them:\u003c/p\u003e \u003cp\u003e \u003cem\u003eCC(i) =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{j=0}^{i,jϵG}\\frac{1}{{d}_{ij}}\\)\u003c/span\u003e\u003c/span\u003e (1)\u003c/p\u003e \u003cp\u003eIn which, \u003cem\u003eCC(i)\u003c/em\u003e is the Closeness Centrality of segment \u003cem\u003ei\u003c/em\u003e pertaining to the graph \u003cem\u003eG\u003c/em\u003e and \u003cem\u003ed\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is the shortest path between \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e, in metres.\u003c/p\u003e \u003cp\u003e \u003cem\u003eBC(k) =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{k\\ne\\:i\\ne\\:j}^{i,jϵG}\\frac{{g}_{ij}\\left(k\\right)}{{g}_{ij}}\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e \u003cp\u003eIn which, \u003cem\u003eBC(k)\u003c/em\u003e is the Betweenness Centrality of segment \u003cem\u003ek\u003c/em\u003e, \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e(k)\u003c/em\u003e is the number of shortest paths connecting \u003cem\u003ei\u003c/em\u003e e \u003cem\u003ej\u003c/em\u003e that cross \u003cem\u003ek\u003c/em\u003e and \u003cem\u003eg\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is the total number of shortest paths that link \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e.\u003c/p\u003e \u003cp\u003e \u003cem\u003eFK(k) =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\sum\\:_{k\\ne\\:i\\ne\\:j}^{i,jϵG}\\frac{{g}_{ij}\\left(k\\right)\\:{W}_{i}{W}_{j}}{{g}_{ij}\\:{d}_{ij}}\\)\u003c/span\u003e\u003c/span\u003e (3)\u003c/p\u003e \u003cp\u003eIn which, \u003cem\u003eFK(k)\u003c/em\u003e is the Freeman-Krafta Centrality of segment \u003cem\u003ek\u003c/em\u003e, and \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e are the weights of entities \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e, respectively. In this study weights are not used and set to 1.\u003c/p\u003e \u003cp\u003eThe PC was calculated through the tool \u003cem\u003eSpatCent\u003c/em\u003e (Hellervik \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021b\u003c/span\u003e). Its formulation is described by Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{a}_{j}=\\left({\\gamma\\:a}_{j}+{R}_{j}\\right){\\sum\\:}_{i}\\frac{{a}_{i}f\\left({c}_{ij}\\right)}{{\\sum\\:}_{k}\\left({\\gamma\\:a}_{k}+{R}_{k}\\right)f\\left({c}_{ik}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn which, the left-hand side corresponds to \u0026ldquo;outgoing\u0026rdquo; interaction from each zone, and the right-hand side corresponds to \u0026ldquo;incoming\u0026rdquo; interaction. The incoming interaction is attracted from other zones by a combination of activity (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{a}_{j})\\)\u003c/span\u003e\u003c/span\u003e and local weights (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{j})\\)\u003c/span\u003e\u003c/span\u003e and is modulated by an interaction function. Competition between zones to attract incoming interactions is also handled by the divisor within the summation. The term \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e corresponds to activity value for zone \u003cem\u003ej\u003c/em\u003e, and when a static state is reached, this will correspond to PC; \u003cem\u003eγ\u003c/em\u003e is an agglomeration parameter; \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e is a local static weight; \u003cem\u003ef(c\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e corresponds to the interaction function, with the generalized cost \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e as input. In this work, active street segments\u003csup\u003e1\u003c/sup\u003e are used as zones.\u003c/p\u003e \u003cp\u003eThe local static weights could be any non-changing value that should capture the local capacity for activity. In this study, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e was set to be the \u0026ldquo;buildable\u0026rdquo; area of segment \u003cem\u003ej\u003c/em\u003e, considering a 30 meters buffer\u003csup\u003e2\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe interaction function \u003cem\u003ef(c\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e has the form:\u003c/p\u003e \u003cp\u003e \u003cem\u003ef(c\u003c/em\u003e \u003csub\u003e \u003cem\u003eij\u003c/em\u003e \u003c/sub\u003e \u003cem\u003e) =\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{{c}_{ij}}^{-\\beta\\:}\\)\u003c/span\u003e\u003c/span\u003e (5)\u003c/p\u003e \u003cp\u003eIn which β is set to be 2. The generalized cost for an interaction between zones \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e is described by \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e. For a driving network, \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is calculated by the travel time using the shortest path in the network (taking speed limits into account). A constant \u0026ldquo;start-and-end-penalty\u0026rdquo; of 5 minutes is added to the travel time, aiming to capture the extra time of getting into and out of the car and walking to the final destinations.\u003c/p\u003e \u003cp\u003eIn this work two different PC measures were tested. PC1 (where \u003cem\u003eγ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1), and PC2 (\u003cem\u003eγ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0). Since PC2 is without the agglomeration factor, it works as an Eigenvector Centrality (Hellervik et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Land data\u003c/h2\u003e \u003cp\u003eLand value data for 2022 was sourced from the Porto Alegre Municipality's Finance Department, covering 36,578 real estate transactions across residential, retail, service, and industrial sectors. These records were georeferenced using Google Earth (version 7.3.6.9796). Each address corresponds to a single plot, although multiple units may share an address. Using R software (version 4.4.0), sales records were aggregated by address to calculate the land unit value, defined as the total value of real estate on a plot divided by its area. Four scenarios were considered: (1) a plot with one unit, which was sold. In this case the unit's value was divided by the plot area; (2) a plot with multiple units but one sale, replicating the sold unit's value across all units, summing them, and dividing by the plot area; (3) a plot with several sold units, where the mean value of sold units was assigned to all units, summed, and divided by the plot area; and (4) plots without sales records were excluded from the analysis. This method allowed for an indirect estimate of land value, as updated \"pure\" land value data is unavailable for Brazilian cities.\u003c/p\u003e \u003cp\u003eThis procedure yielded 9,033 real estate observations, to which five centrality measures for the corresponding road segments were added. Observations with BC or PC values of zero were excluded (866 exclusions), along with those deemed outliers based on the interquartile range criterion (400 exclusions), which leads to 7,767 remaining addresses.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Statistical behaviour of centrality measures and land values\u003c/h2\u003e \u003cp\u003eTo compare the statistical behaviour of the six variables, we calculated their \u003cem\u003erelative range\u003c/em\u003e, \u003cem\u003edistribution\u003c/em\u003e, and \u003cem\u003ehierarchy\u003c/em\u003e. The \u003cem\u003erelative range\u003c/em\u003e is defined as the range (maximum \u0026ndash; minimum) divided by the mean. The \u003cem\u003edistribution\u003c/em\u003e is the standard deviation divided by the mean, multiplied by 100. The \u003cem\u003ehierarchy\u003c/em\u003e reflects the concentration of the highest values in a few segments, measured by the Pareto Index, which sums the values of the top 20% of segments and divides this total by the sum of the values in the bottom 80%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.5. Levels of aggregation\u003c/h2\u003e \u003cp\u003eThe data were analysed at two levels of aggregation: \u003cem\u003edisaggregated\u003c/em\u003e, considering each of the 7,767 addresses as individual observations; and aggregated, where Porto Alegre was divided into 821 hexagons, each measuring 21.67 hectares (500 meters between centres). This distance approximates a neighbourhood unit or walkable area (Gehl \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). For each hexagon, averages of land unit values and accessibility measures, along with the summed values of the intermediation measures, were calculated from the point observations (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eFor both levels of aggregation, spatially adjusted regression models were constructed. Based on the results of the Lagrange Multiplier tests (LM), the chosen model specification was the Spatial Durbin Model (SDM). The SDM simultaneously addresses spatial dependence in both the residuals and the endogenous variable, making it superior to other models as it captures the effects of unmodeled neighbourhood attributes (Herath et al. 2015). Additionally, it handles misspecified functional forms and spatial heterogeneity in estimated parameters (Osland 2010).\u003c/p\u003e \u003cp\u003eThe models were run in two stages. In the first stage, each centrality measure was considered as an independent variable alongside the plot area, which significantly impacted the results. Colwell and Munneke (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) showed that as one moves away from the centre, increases in plot areas do not correspond to proportional increases in values. This results in a decline in the unit value curve, reflecting reduced competitiveness in areas with lower accessibility. However, in Porto Alegre, the reduction in areas toward the periphery is only partial; a peripheral arc of lower social status neighbourhoods features smaller plots than those in the centre, despite not having as high unit values as more central areas (see Figure A1, Online Resource).\u003c/p\u003e \u003cp\u003eIn the second stage, the effect of area was disregarded, and only the centrality measures were included separately as independent variables. In all models, the dependent variable is the unit land value (value per m\u0026sup2;). Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e details their specifications.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eTypes and variables in each regression model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDependent variable\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eIndependent variables\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eModels\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDisagg.\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAgg.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"9\" rowspan=\"10\"\u003e \u003cp\u003eUnit value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u0026thinsp;+\u0026thinsp;area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBC\u0026thinsp;+\u0026thinsp;area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e7B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFK\u0026thinsp;+\u0026thinsp;area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e8B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC1\u0026thinsp;+\u0026thinsp;area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e9B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u0026thinsp;+\u0026thinsp;area\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10A\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Results and Discussions","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e5.1. Comparison between measures\u003c/h2\u003e \u003cp\u003eThis section provides a comparative analysis of the performance of the five centrality measures. While Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e exhibits the spatial distribution of the measures as well as the land unit values, Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the Pearson correlations between the measures. Additionally, figure A2 (Online Resource) displays the scatter plots of PC1 and PC2 against CC, BC and FK.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePearson Correlation between centrality measures (in natural log form). All correlations are significant at p\u0026thinsp;\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.9236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.9464\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.9722\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.1284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.1735\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.1770\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e.1762\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e.2272\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e.2306\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e.9129\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eLand unit values follow a downward curve from the Historic Centre to the periphery (figure A3, Online Resource), with a notable concentration of high values along the Historic Centre \u0026ndash; Iguatemi Shopping Mall axis (exceeding US\u003cspan\u003e$\u003c/span\u003e2,889). Surrounding this area is a zone of slightly lower values (between US\u003cspan\u003e$\u003c/span\u003e1,804 and US\u003cspan\u003e$\u003c/span\u003e2,889), forming a clear Hoyt-like spatial pattern (Hoyt \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1939\u003c/span\u003e). As one moves away from this axis, values decrease steadily until reaching the outskirts, where unit values do not exceed US\u003cspan\u003e$\u003c/span\u003e433 and can even drop below US\u003cspan\u003e$\u003c/span\u003e60 in sparsely urbanized areas to the south.\u003c/p\u003e \u003cp\u003eThe CC reveals a strong edge effect by highlighting the geometric centre of the system (buffer not shown in the figure). Both BC and FK display similar spatial patterns, emphasizing roads with the highest traffic flow (intermediation) hierarchy. The FK, in particular, tends to show higher values in areas with greater accessibility, since it accounts for the effect of distance decay. Notably, the agglomeration factor (γ), which defines activity concentration in PC1, further accentuates the centre-periphery centrality gradient. When γ\u0026thinsp;=\u0026thinsp;0, PC2 (Eigenvector Centrality) shows a wider dispersion of high-centrality zones and a less pronounced gradient.\u003c/p\u003e \u003cp\u003eThe exceptionally high correlations between PCs and CC are notable (around 0.93), indicating the similarity of the phenomena they capture \u0026ndash; accessibility between segments. Since PC2 ignores the agglomerative factor, its linear correlation with CC is slightly higher (0.9464). Regarding intermediation measures, the correlations obtained between PCs and FK values are higher than the correlations between PCs and BC values (around 0.23), reflecting the greater sensitivity of PCs and FK in capturing phenomena influenced by distance.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e displays the measures\u0026rsquo; distributions (relative standard deviation), hierarchy, and regularity, comparing them with land unit values.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCentrality measures and land values statistic behaviour\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCentrality measures\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMedian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRelative\u003c/p\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDistribution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHierarchy\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e54.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e19.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e15.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.235E\u0026thinsp;+\u0026thinsp;06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.9753E\u0026thinsp;+\u0026thinsp;05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e34.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e240.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.0574E\u0026thinsp;+\u0026thinsp;04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2,815.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e198.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eLand values\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMedian\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eRelative\u003c/p\u003e \u003cp\u003eRange\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eDistribution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHierarchy\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLand\u003c/p\u003e \u003cp\u003evalues\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6,622.941\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5,086.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e92.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe two groups of measures are easily discernible: accessibility metrics exhibit lower relative ranges and distributions, and, therefore, are less hierarchical, resulting in less differentiation within the urban space. Among these, PC1 stands out as the most differentiating. Its hierarchy is roughly equidistant between CC/PC2 and the intermediation measures, reflecting its ability to capture the uniqueness of urban spatiality through the uneven potential distribution of activities. In contrast, the intermediation measures are more dispersed and hierarchical, with few segments (arterial roads) showing high centrality, while the majority have relatively low significance.\u003c/p\u003e \u003cp\u003eAmong the centrality measures evaluated, the relative range, distribution, and hierarchy of land values most closely align with PC1. Assuming land value reflects socio-spatial phenomena, this alignment supports validating PC1 and its integration of the agglomerative factor as an effective metric for capturing or predicting these phenomena. In the next section, we will further explore this relationship and reinforce the mentioned support through multi-model and multi-scale spatial regression analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.2. Explanation of land value by centrality measures\u003c/h2\u003e \u003cp\u003eThis section focuses on the explanatory power of the centrality measures regarding land value. Correlations are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and scatter plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, followed by Table \u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, presenting the results of the spatial regression models.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCorrelations between unit land values and centrality measures (in natural log form) (continue)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eDisaggregated\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c6\" namest=\"c4\"\u003e \u003cp\u003e\u003cem\u003eAggregated\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003ePearson\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeasure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003ePearson\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMeasure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003ePC1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.3907***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003ePC1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.5427***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.3705***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.5039***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2617***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4634***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1831***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eFK\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.0267*\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eFK\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.2221***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e(conclusion)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003epearman\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMeasure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003eSpearman\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMeasure\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eCorrelation\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003ePC1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.3287***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003ePC1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.5652***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2623***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4909***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0893***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.3975***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eBC\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.0352***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1680***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.0097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003eFK\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.2135***\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"6\" nameend=\"c6\" namest=\"c1\"\u003e \u003cp\u003e*** p\u0026thinsp;\u0026lt;\u0026thinsp;0.001;\u003c/p\u003e \u003cp\u003e** p\u0026thinsp;\u0026lt;\u0026thinsp;0.01;\u003c/p\u003e \u003cp\u003e* p\u0026thinsp;\u0026lt;\u0026thinsp;0.05;\u003c/p\u003e \u003cp\u003e. P\u0026thinsp;\u0026lt;\u0026thinsp;0.1.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSpatially adjusted regression models (continue)\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"12\" nameend=\"c12\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eDisaggregated\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e5A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e5B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"6\" rowspan=\"7\"\u003e \u003cp\u003eCoefficients (p-value)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eArea\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.3716\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.3619\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.3599\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.3595\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-0.3677\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.0077\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.5905\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.01)\u003c/p\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.0038\u003c/p\u003e \u003cp\u003e(0.4608)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.0268\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.0203\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.01)\u003c/p\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.0618\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"11\" nameend=\"c12\" namest=\"c2\"\u003e \u003cp\u003e(conclusion)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.3925\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.8222\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-0.0107\u003c/p\u003e \u003cp\u003e(0.9234)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e2.1938\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLM Tests - \u003c/p\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRSerr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRslag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eadjRSerr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eadjRSlag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.3346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.0893\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003epseudo-Adjusted R\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0740\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.2292\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4205\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.1625\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.4212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.4036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.4213\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.3554\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"12\" nameend=\"c12\" namest=\"c1\"\u003e \u003cp\u003e\u003cem\u003eAggregated\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e7A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e8A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e9A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e9B\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e10A\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e10B\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"5\" rowspan=\"6\"\u003e \u003cp\u003eCoefficients (p-value)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eArea\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-0.2407\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-0.2408\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.2407\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.2241\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-0.2293\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0844\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.01)\u003c/p\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0706\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.05)\u003c/p\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0703\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.01)\u003c/p\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.0555\u003c/p\u003e \u003cp\u003e(0.0576).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFK\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0844\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.01)\u003c/p\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0706\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.05)\u003c/p\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.1482\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.1846\u003c/p\u003e \u003cp\u003e(\u0026lt;\u0026thinsp;0.001)\u003c/p\u003e \u003cp\u003e***\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.6264\u003c/p\u003e \u003cp\u003e(0.0660).\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.7403\u003c/p\u003e \u003cp\u003e(0.0810).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLM Tests - \u003c/p\u003e \u003cp\u003ep-value\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRserr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRslag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eadjRSerr\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eadjRlag\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.8672\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4546\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003epseudo-Adjusted R\u0026sup2;\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.4695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4738\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.4695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.3409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.3226\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.2769\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.4760\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.4169\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAuthors\u0026rsquo; elaboration.\u003c/p\u003e \u003cp\u003eAmong the accessibility measures, at both levels of aggregation, PC1 shows the highest correlations with land value, followed by PC2 (Eigenvector) and CC, all in a positive direction. Nevertheless, very high CC values seem to be related to a decrease in land costs, a phenomenon not observed with PC1 and PC2. When controlling for plot area, the regression models at the disaggregated level reveal that although CC has a higher coefficient (1.0077), the fit of model 1A is quite low (7.40%). In contrast, in model 4A, the coefficient for PC1 is lower (0.3925), but the model achieves a considerably higher fit (40.36%), attesting that the measure can better capture non modelled spatial influences. On the other hand, the coefficient for PC2 is not significant when controlling for area (model 5A). It is noteworthy that the area coefficients, at both levels of aggregation, are negative, confirming the hypothesis that unit value decreases as plot surface increases. When area is not controlled, PC2 shows the most significant results, with a coefficient of 2.1938 and a fit of 35.54% (model 5B), while the values for PC1 are 0.8222 and 14.09%, respectively (model 4B); and for CC, 0.5905 and 22.92%, in the same order (model 1B). This discrepancy demonstrates that PC1 is more sensitive to variations in land value that are not explained by the plot dimensions, but rather by locational factors.\u003c/p\u003e \u003cp\u003eAt the aggregated level, when controlling for area, PC1 is also the most efficient in explaining land value, with a coefficient of 1.1482 and a fit of 32.26% (model 9A). Although the pseudo-Adjusted R\u0026sup2; of model 6A is higher (46.95%), the coefficient for CC is significantly lower at 0.0844. At this level of aggregation, PC2 does not show significance at p\u0026thinsp;\u0026lt;\u0026thinsp;5% in either the model where area is used as a control variable (10A) or the one without area control (10B). Without controlling for area, PC1 again performs better, with a coefficient of 1.1846 and a fit of 27.69% (model 9B). Regarding CC (model 6B), although the pseudo-Adjusted R\u0026sup2; is higher (42.10%), the coefficient for the independent variable is considerably reduced (0.0706).\u003c/p\u003e \u003cp\u003eRegarding intermediation measures, FK outperforms BC in explaining variations in land value, although both are less effective than accessibility measures. At the disaggregated level, the correlation is negative and significant for FK, while it is not significant for BC. This may suggest that at the road segment level, negative externalities associated with higher traffic capacity tend to negatively impact land value, which could discourage investment along busier roads. On the other hand, at the aggregated level the correlations for FK remain stronger than those for BC (which also become significant), and both correlations are positive. This implies that conversely to the immediate contiguity, the general proximity to arterial roads \u0026ndash; and the ease of access these locations offer \u0026ndash; is typically valued, even though the property itself is located on less busy \"interior\" roads.\u003c/p\u003e \u003cp\u003eThe disaggregated-level regression models reveal interesting dynamics regarding the significance of BC and FK when controlling for area. In model 2A, where area is considered, the coefficient for BC is not significant. However, in model 3A, the coefficient for FK is -0.0203, and the pseudo-Adjusted R\u0026sup2; is 42.12%. When area is excluded, BC becomes significant with a coefficient of -0.0268, though the model fit (pseudo-Adjusted R\u0026sup2;) drops to 16.25%.\u003c/p\u003e \u003cp\u003eInterestingly, when area is not considered, the coefficient for FK in model 3B increases in magnitude (-0.0618), but the pseudo-Adjusted R\u0026sup2; falls dramatically to 2.96%, contrasting with the stronger fit seen for BC. This suggests that the explanatory power of BC at the disaggregated level is heavily influenced by plot area: BC loses significance when area is included, but gains explanatory power in its absence. The reduction in pseudo-Adjusted R\u0026sup2; when area is removed from the model with FK is much more pronounced than for BC, indicating that the effect of area remains partially present in the BC model. Despite the lower pseudo-Adjusted R\u0026sup2;, the coefficients for FK remain consistently significant.\u003c/p\u003e \u003cp\u003eThe described phenomenon results from the inclusion of distance in the calculation of FK. Indeed, the linear correlations between area and both FK and BC are positive and similar (0.1451 and 0.1255, respectively), indicating that larger plots are found on roads of higher hierarchy. However, the unit values of the land are significantly and inversely related to FK, suggesting that larger plots on roads that are more accessible, and presumably more congested, tend to be less valued than larger plots on roads that are less congested (more distant). This effect is not captured by BC, which considers roads with the same number of shortest paths to be equivalent, regardless of distance, making BC coefficients more sensitive to area variation.\u003c/p\u003e \u003cp\u003eAt the aggregated level, FK exhibits higher coefficients in both the model that includes area as a control variable (8A) and the model that does not include it (8B): 0.0844 and 0.0706, respectively, with the fit of the models being 46.95% and 34.09%, in that order. The models that consider BC as an explanatory variable show higher pseudo-Adjusted R\u0026sup2; values (47.38% with area and 42.19% without area), although the coefficients are lower \u0026ndash; 0.0703 in the first case and 0.0555 (not significant at p\u0026thinsp;\u0026lt;\u0026thinsp;5%) in the second. At this level, the greater diversity in plot sizes within the cell dramatically reduces their linear correlations with both BC and FK, rendering them insignificant. This allows BC to capture part of the variation in land value even when area is controlled, unlike what occurs at the disaggregated level.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Final Remarks","content":"\u003cp\u003eThis study compared two groups of spatial centrality measures in Porto Alegre, Brazil, evaluating how effectively they capture locational advantages reflected in urban land values. The methodological enhancements of PC1 and FK - incorporating agglomeration factors and distance decay, respectively - proved more effective in identifying characteristics that foster urban activity concentration and increase land values.\u003c/p\u003e \u003cp\u003ePC1, in particular, demonstrated a stronger correlation with land value variations compared to CC and PC2 (Eigenvector Centrality), especially when controlling for plot size and using aggregated data, which mitigates heteroscedasticity and the impact of unmodeled factors. These results are consistent with findings from Hellervik et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) in Scandinavia. Additionally, our study supports Wang et al. (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), emphasizing that centrality measures show stronger correlations with activity locations at an aggregated level.\u003c/p\u003e \u003cp\u003eRegarding the intermediation measures, while FK is effective in identifying local characteristics, both FK and BC showed a negative correlation with land values at the disaggregated level, likely due to the adverse effects of high-hierarchy roads. These findings align with those of Heyman and Sommervoll (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) and Wang and Chen (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Conversely, at the aggregated level, the relationship between intermediation measures and land value was positive \u0026ndash; though less significant than that of accessibility measures \u0026ndash; indicating that while proximity to major roads can enhance access, immediate adjacency to traffic-related nuisances may lower property values. Overall, the analyses revealed stronger correlations between centrality and land value for accessibility measures, supporting the idea that proximity to the broader urban system is more influential in determining location choices for urban paying activities\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNotwithstanding, it is crucial to note that in a Global South metropolis, various unmodeled factors linked to a highly segregated urban structure (such as informality, crime, congestion, and pollution) can influence land values. Future studies should incorporate these factors, along with non-motorized accessibility measures, to enhance model accuracy.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003cb\u003eEthical considerations\u003c/b\u003e: there are no human or animal participants in this article and informed consent is not required.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent to participate:\u003c/strong\u003e \u003cp\u003enot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cstrong\u003eConsent for publication:\u003c/strong\u003e \u003cp\u003enot applicable.\u003c/p\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eDeclaration of conflicting interest\u003c/b\u003e: the authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.\u003c/p\u003e\u003cp\u003e \u003ch2\u003e \u003cb\u003eFinancial interests\u003c/b\u003e \u003c/h2\u003e \u003cp\u003ethe authors declare they have no financial interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding statement\u003c/h2\u003e \u003cp\u003eThis study was funded by the Swedish Transport Administration [grant number TRV 2020/25561] and by \u0026ldquo;Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior\u0026rdquo; \u0026ndash; CAPES [Coordination for the Improvement of Higher Education Personnel \u0026ndash; CAPES] [grant number 88887.936632/2024-00].\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eBoth authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by R.L.A. and A.H. The first draft of the manuscript was written by R.L.A and both authors commented on previous versions of the manuscript. Both authors read and approved the final manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eThe paper has benefitted from discussions and support in the context of the Spatial Morphology Group at Chalmers University of Technology. We also acknowledge the Finance Department of the municipality of Porto Alegre for providing the data related to the real estate transactions.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData is provided within the supplementary information files\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAgryzkov T, Tortosa L, Vicent JF et al. (2019) A centrality measure for urban networks based on the eigenvector centrality concept. Environment and Planning B \u0026ndash; Urban Analytics and City Science 46(4):668-689. https://doi.org/10.1007/s00421-008-0955-8.\u003c/li\u003e\n\u003cli\u003eAguilar RL, Maraschin C (2024) Relationships between urban network centrality and apartment prices in Porto Alegre, Brazil. Finisterra 60(126):1-16. 10.18055/Finis34731.\u003c/li\u003e\n\u003cli\u003eAlonso W (1964) Location and Land Use\u003cem\u003e: \u003c/em\u003etoward a general theory of land rent. Harvard University Press, Cambridge.\u003c/li\u003e\n\u003cli\u003eAntunes FS, Wang F, Fernandes MC (2023) Multiple centrality assessment of location preferences of retail and services in Petr\u0026oacute;polis, Brazil. Papers in Applied Geography 9:136-148. https://doi.org/10.1080/23754931.2022.2128859.\u003c/li\u003e\n\u003cli\u003eBatool K, Niazi MA (2014) Towards a Methodology for Validation of Centrality Measures in Complex Networks. 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PLoS ONE 17(5):1-20. https://doi.org/10.1371/journal.pone.0268203.\u003c/li\u003e\n\u003cli\u003eYue H and Zhu X (2019) Exploring the Relationship between Urban Vitality and Street Centrality Based on Social Network Review Data in Wuhan, China. Sustainability 11:1-19. https://doi.org/10.3390/su11164356.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Some roads, such as motorways, are not considered active, since they in general do not provide access to urban activities. These roads, however, are still used to find shortest paths.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e The buffers are non-overlapping, which means that each surrounding piece of land is only attributed to a single active road.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e However, since this study is based on property prices, we have no information about non-paying activities.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"networks-and-spatial-economics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nets","sideBox":"Learn more about [Networks and Spatial Economics](http://link.springer.com/journal/11067)","snPcode":"11067","submissionUrl":"https://submission.nature.com/new-submission/11067/3","title":"Networks and Spatial Economics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Spatial centrality, Preferential centrality, Freeman-Krafta centrality, Land value, Porto Alegre","lastPublishedDoi":"10.21203/rs.3.rs-6264491/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6264491/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study compares the performance of five spatial centrality measures in explaining urban land value variation in Porto Alegre, Brazil. Land value reflects the level of competition for a specific piece of land and its potential to attract various activities. We analyze three accessibility measures - Closeness Centrality (CC), Eigenvector Centrality, and Preferential Centrality (PC) - and two intermediation measures - Betweenness Centrality (BC) and Freeman-Krafta Centrality (FK). PC and FK are enhanced versions of traditional metrics, incorporating agglomeration factors and distance decay, respectively. Using multi-model, multi-scale spatial regression analysis, we find that the enhanced measures outperform classical ones in explaining land value variation, with accessibility measures, especially PC, being more responsive. At the disaggregated level, intermediation measures exhibit negative correlations with land value, suggesting adverse effects of high-traffic locations. However, at the neighborhood scale, both measure types show positive correlations, indicating that while proximity to major roads enhances accessibility, immediate adjacency may reduce property values due to traffic-related externalities.\u003c/p\u003e","manuscriptTitle":"Comparative Analysis of Centrality Measures in Explaining Activity Locations Through Land Value Variability: A Case Study of Porto Alegre, Brazil","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-07 11:14:01","doi":"10.21203/rs.3.rs-6264491/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-07-16T07:57:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-07-15T18:04:17+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"110040682783955829259223185671461771028","date":"2025-07-15T17:25:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-05-07T20:17:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"164667051646581860613392977553509710539","date":"2025-05-06T13:50:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"110040682783955829259223185671461771028","date":"2025-05-04T13:54:55+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-01T12:48:41+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-20T23:09:56+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-20T23:09:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"Networks and Spatial Economics","date":"2025-03-19T20:54:35+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"networks-and-spatial-economics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nets","sideBox":"Learn more about [Networks and Spatial Economics](http://link.springer.com/journal/11067)","snPcode":"11067","submissionUrl":"https://submission.nature.com/new-submission/11067/3","title":"Networks and Spatial Economics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"a01a47e5-baea-4f2e-9f21-5e6be7ffec8f","owner":[],"postedDate":"May 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-01-19T08:28:29+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-07 11:14:01","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6264491","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6264491","identity":"rs-6264491","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}