A Spatial Livability Index for dense urban centers

Abstract

This article introduces a Spatial Livability Index based on geographically weighted principal component analysis. We study the case of 203 subzones in Singapore which are dense geographic boundaries in terms of population and built-up area. These regions share spatial correlations of objective measures of livability such as open spaces or community facilities. The proposed objective indicator captures the “hidden” patterns of livability provided by neighboring locations. Moreover, the results allow to identify atypical areas, that is geographical units that score very good/bad under the spatial approach but very bad/good under the non-spatial framework of livability.

Keywords

Livability cities GWmodel Singapore

Introduction

According to the Atlas of the Human Planet 2016, elaborated by the European Commission, about 50% of the global population lives in areas which make up to only 2% of earth’s surface. There are more than 300,000 urban centers worldwide where more than 1/3 of global built-up and 2/3 of population are concentrated in Asia. Urban agglomerations provide huge challenges and opportunities in securing and managing the limited resources to ensure these expanding urban areas will remain sustainable and livable.

The concept of livable cities has been increasingly adopted by policy-makers for monitoring urban development. Livability is a mutable idea that stirs up debates about how a city might foster healthy environments and quality of life. As detailed in Charles Montgomery’s book Happy City, livability is often part of a broad context of distinct initiatives converging in their focus on ensuring people feel safe and happy while, at the same time, counteracting poverty and dysfunction. Livable places are created by planning for the short and long term future of the communities, yielding the creation or restoration of urban environmental amenities, demographic changes, and real estate price increases (Anguelovski et al., 2019). This process of land revaluation, greening, and displacement is now called “green gentrification” (Anguelovski, 2016). Similarly, research suggests that characteristics of the surrounding built environment in more livable places, such as green areas, can significantly influence health outcomes (Nieuwenhuijsen et al., 2017).

Although there exist sophisticated methodologies and conceptualizations of livability resulting in numerous rankings of cities worldwide (Okulicz-Kozaryn, 2013; Zanella et al., 2015), studies by neighborhoods within cities have recently appeared in the literature (Mouratidis, 2018; Saitluanga, 2014; Satu and Chiu, 2019). All these studies, as well as our own, are focused on variables related not only to greenery but also to transportation, healthcare, education, and so forth. The study of livability in small geographical units, such as neighborhoods, faces new challenges in relation to data availability/reliability and the definition of relevant indicators. Further on, when comparing two different cities, say, New York and Hong Kong, the researcher may account for the square meters of green space (parks) per person in each city. However, if this “environmental” dimension of livability is evaluated at neighborhood level, not all neighborhoods have green spaces. The distance to the nearest park could be a potential indicator of livability. Distance-based indicators have been used in the subjective measure approach of livability, in which researchers construct shared characteristics of residents’ experiences of livability using survey methods. Unfortunately, the subjective approach of livability has shown to be weakly correlated with objective measures such as unemployment rate, variety of opportunities for outdoor recreation, or cultural offerings. This is because people may still feel unhappy in livable areas, if, for instance, home ownership or an engaging social life remains out of their reach (Okulicz-Kozaryn, 2013; Quastel, 2017).

Composite indices at the city level have been also derived and applied in the literature. Lee et al. (2015) measure the performance of physical urban forms with respect to compact city policies. Satu and Chiu (2019) investigate subjective perception of public transport, community facilities, and open spaces. Paul and Sen (2018) evaluate livability in urban centers by means of housing density and employment rate. Zanella et al. (2015) develop a composite index of livability based on six dimensions (wealth and income inequality, unemployment, education and training, housing, accessibility and urban design, and health). Noticeably absent, however, is role of the spatial effects in the empirical analysis of livability in dense urban areas.

This study investigates the objective spatial component of livability in dense urban centers using data from 203 Subzones in Singapore. It proposes a Spatial Livability Index based on geographically weighted principal component analysis (GWPCA) constructed from 17 objective indicators. A total of eight dimensions of livability are considered, namely public transport, infrastructure, community facilities, open space and public space, healthcare, culture and environment, education, and employment. The results from the spatial composite index are compared with its non-spatial counterpart, based on principal component analysis (PCA), to illustrate how atypical areas can be identified, e.g. geographical units highly susceptible to exhibit high/low level of livability after the inclusion of spatial effects. The main contribution of this work is to address for the first time the spatial component of livability at the neighborhood level.

Livability and urban spaces in dense areas

Livability and its indicators

Livability can be studied by objective or subjective measures of quality of life. Methodologically speaking, the objective approach uses social indicators arguing that objective conditions such as infrastructure, accessibility, or transportation matter for subjective well-being. Conversely, the satisfaction approach investigates residents’ subjective perceptions about their lives, and it is usually based on self-reported life satisfaction. Although a combination of both methods is desirable, its implementation is not straightforward. For instance, some studies have found a weak correlation between objective livability and subjective satisfaction (Okulicz-Kozaryn, 2013).

The place-based approach of livability incorporates the geographical context. This framework is appropriate to investigate the understanding of the residential environment (Cutter, 1985; Yang, 2008), and it has been successfully applied to assess neighborhoods’ livability within dense urban centers (Cervero, 2013; Mouratidis, 2018; Saitluanga, 2014; Satu and Chiu, 2019). The output is a real-valued function in the form of a composite index allowing comparison (e.g. rank) among observations which are typically neighborhoods, zones, or districts.

Satu and Chiu (2019) study the case of five dense areas close to Dhaka, Bangladesh by investigating individual’s subjective perceptions of public transport, community facilities, open space, sense of community, sense of safety, and dwelling. Lee et al. (2015) develop a compact city index based on the railway systems of 41 Japanese cities. The authors involve community- and city-level considerations such as population density, proximity to local services and train stations. By constructing a composite index based on objective and subjective measures of livability, Saitluanga (2014) investigates how livability varies across 85 local councils in Aizawl, India. Similarly, Paul and Sen (2018) assess livability variations of constituent urban centers within Kolkata metropolitan area. Their strategy consists on clustering urban geographic factors such as housing density, employment rate, or percentage of open space. In the case of Europe, Mouratidis (2018) look at the metropolitan area of Oslo and compares compact versus sprawled neighborhoods using survey data from 45 neighborhoods. Zanella et al. (2015) propose a composite index computed by non-parametric techniques with the aim of evaluating measures of performance in 34 large European cities.

Even though the required objective indicators are context-dependent, most of the literature agrees on the dimensions to be evaluated. For example, the above-mentioned studies include dimensions of accessibility, transportation, healthcare, education, economic, social development or culture and leisure. Some examples of these objective indicators are as follows: length of public transport network per inhabitant (e.g. accessibility), number of transportation facilities per thousand population (p.t.p.) (transportation), number of hospitals p.t.p. (healthcare), number of schools p.t.p. (education), employment percent of residents aged 15–64 (economic), recreational centers p.t.p (social development), number of libraries p.t.p. (culture and leisure), and so forth. Additionally, the weights assigned to each indicator before computing the composite index are still under debate (Okulicz-Kozaryn, 2013). A plethora of tools from Factor Analysis, PCA, Data Envelopment Analysis, Analytic Hierarchy Process, or Expert’s evaluation have been implemented with the goal of assigning “optimal” weights to the composite index.

In dense urban areas, it is clear that not all neighborhoods boast all indicators. Open spaces, parks, or business areas concentrated at specific locations are case in point. Likewise, downtown areas have large influence on the usage of certain facilities such as shopping malls, metro stations, or hospitals (You and Tunçer, 2016). A way to overcome this problem is by including distance-based measures such as the distance to the nearest hospital or the distance to the nearest sport center (Lee et al., 2015; Mouratidis, 2018; Saitluanga, 2014; Satu and Chiu, 2019). Euclidean, Geodesic, Manhattan, or even Google Directions API distances are useful to tackle the location problem. Yet, to the best of our knowledge there are no studies addressing the spatial effects of the objective indicators within neighborhoods. The inclusion of the spatial component in assessing livability in dense urban areas is important because “hidden” spatial correlations can be captured and further incorporated in the form of weights of the composite index.

Singapore as case study

Singapore is an island city-state located at the southern tip of Peninsular Malaysia in South East Asia. According to the General Household Survey 2015 elaborated by the Department of Statistics Singapore, the country is home to 5.6 million people, with only an area of 712 square kilometers. The city has virtually no rural periphery to develop and it has a highly urbanized environment. The country is bigger than Manhattan but smaller than the five boroughs of New York. Singapore has been often described as a highly planned city where land development is strictly controlled, and land use is taken seriously (Teo, 2014; Yuen and Hien, 2005).

This city-state is an interesting case study for several reasons. First, it is one of the most densely populated countries in the world. Second, it is somehow disadvantaged in terms of natural resources and geographical location but still has grown into a global commerce achieving a highly developed market economy. Third, it ranks high on key measures of national social progress which includes education, healthcare, personal safety, and life expectancy (Keon et al., 2016). The main urban obstacles of the city-state originate from its small land size. For example, the compact urban environment exacerbates traffic congestion, difficulties in maintaining a livable environment with adequate open and public spaces, public transport, or housing provision.

The government authorities have responded to the challenge of land scarcity in different ways such as its comprehensive road pricing system, intensive public transport improvements (Monnot et al., 2017), adoption of three-dimensional garden for urban environment (rooftop gardens and other forms of skyrise greenery), and so forth. The city is constantly faced to reconcile livability, and it has become official government policy to make the city globally distinctive as a place to work and, most importantly, to live (Teo, 2014). Hence, different government institutions have included these objectives in their strategies. The concern of livability in Singapore’s urban space has led to an increasing number of studies (Benita et al., 2019; Teo, 2014; You and Tunçer, 2016; Yuen and Hien, 2005). Also, several international surveys on livability have positioned the city as one of the most livable places worldwide. The 2018 Global Liveability Survey by the Economist Intelligence Unit ranks the city 37th out of a total of 140 whereas the 2018 Mercer’s Quality of Living Survey ranks Singapore 25th out of 231. However, livability at the neighborhood level has not yet been investigated.

Research methodology

Selection of dimensions and indicators

The proposed index considers a total of 17 objective indicators covering eight dimensions addressed in the literature.

Public transport

A livable city should provide easy access to public transport. Thus, multi-modal public transportation systems allow limited car usage and lower levels of traffic. Two indicators measure this dimension, the number of metro stops p.t.p., and the percentage of neighborhoods that a resident can reach in a single journey without transfer. The first variable is widely used in the existing literature (Lee et al., 2015; Zanella et al., 2015), and it is a quantitative measure of the public transport system whereas the second one accounts for its quality.

Infrastructure

This dimension evaluates the quantity and quality of both the road network and the walkable streets. The Street Connectivity Index, proposed by the United Nations Human Settlements Programme in 2016, is an important index of built environments that results after mixing three variables: the length, the width, and the number of intersections. Larger values of the Street Connectivity Index are associated with better street connectivity. Alternatively, the Entropy Index combines multiple walkable destinations such as sidewalks, commercial and residential areas, parks, and open spaces. The Entropy Index takes values between 0 and 1, with 0 representing homogeneity (all land uses are of a single type), and 1 representing heterogeneity (Frank et al., 2005). Finally, both indicators are also novel as applied to the study of livability indices.

Community facilities

Livable cities offer a balance of typologies that facilitate community activities within neighborhood. The community facilities have high value on the planning process that help to maintain and enhance neighborhood’s community character (Paul and Sen, 2018). Two indicators are included, namely the number of community centers p.t.p. and the number of sport centers p.t.p.

Open space and public space

Open spaces and parks are central to the concept of livable cities according to new urbanists. They provide significant physical and mental health benefits to urban residents (Nieuwenhuijsen et al., 2017). Following the recent work of Rigolon and Németh (2018), four indicators are introduced to account for the quality of these areas planned for passive recreation: the amount of green spaces in m² per person, the number of access points to parks p.t.p., the number of exercise facilities p.t.p., and the number of playgrounds p.t.p.

Healthcare

In the view of Saitluanga (2014) and Zanella et al. (2015) among others, neighborhoods score better if they offer quality affordable private/public medical services. Three indicators measure this dimension: the number of hospitals p.t.p., the number of private clinics p.t.p., and the distance to the nearest hospital.

Culture and environment

This is a controversial dimension that bundles a multitude of indicators such as air quality, recreational amenities or food and drink outlets (Satu and Chiu, 2019; Zanella et al., 2015). We propose the use of a single variable to capture this dimension at the neighborhood level, that is the number of commercial areas p.t.p.

Education

Educational services within a neighborhood ensure inclusion for the youth. It shares an intrinsic link to quality of life and thus to livability (Lowe et al., 2015). Therefore, the number of educational institutions (primary, secondary, and high schools) p.t.p. is added into the analysis.

Employment

There is an obvious trade-off between the land allocated for residential purposes and the land used for business. However, livable cities offer a good combination of job opportunities (Krishnan, 2015; Lowe et al., 2015; Mouratidis, 2018). Two indicators can account for this economic characteristic. The percentage of land allocated to business areas may capture more job opportunities. Similarly, the number of business registered in a given time window (e.g. three years) can capture the economic dynamism of the areas.

Data

The Singapore’s Urban Redevelopment Authority divides the country into 5 Regions, 55 Planning Areas, and 323 Subzones. Subzones are divisions within a Planning Area which are usually centered around a focal point such as neighborhood center or activity node. There can be more than 10 Subzones within a Planning Area. We consider Subzones with at least 500 inhabitants, resulting in a total of 203 observations. Using this cut-off point will remove form the dataset (i) artificial offshore islands done through land reclamation efforts, (ii) reservoirs, (iii) largely rural areas, and (iv) military training areas. Figure 1 displays the spatial distribution of the Subzones and its population density. We observe that residents are distributed heterogeneously, and the geographical size of each Subzone varies as well. As small Subzones are not expected to have all 17 objective indicators, to account for spatial auto-correlation in the analysis of livability is fundamental. Finally, the full description of dimension, indicators, data sources, and dataset is available in the online Supplemental Material.

Figure 1.

Population density in Singapore, 2015; 203 Subzones with at least 500 inhabitants.

The Livability Index

PCA is a special case of Factor Analysis and it has been commonly employed in the assessment of livability indices (Benita, 2016; Krishnan, 2015; Saitluanga, 2014).

The input data is stored in an n × m-matrix composed by $n (n = 203)$ Subzones and $m (m = 17)$ objective indicators. Let j and i denote the indicator and Subzone, respectively. The first step is to standardize the indicators matrix to have a mean of zero and a standard deviation of one in each indicator. The standardization is needed because the original data are in different units. The new indicators matrix $A \in ℝ^{n \times m}$ has positive semi-definite covariance matrix $Σ \in ℝ^{m \times m}$ and therefore, it is possible to perform an eigen-decomposition of $Σ$ . In the second step, PCA transforms $Σ$ into

LV L^{⊤} = Σ

(1)

where

L \in ℝ^{m \times m}

is the matrix with eigenvectors and

V \in ℝ^{m \times m}

is the diagonal matrix of eigenvalues of

Σ

such that

V = diag (e_{1}, \dots, e_{m})

with

e_{1} \geq \dots \geq e_{m}

. The loading values of the principal components are stored in the L matrix and the components are ordered according to its eigenvalues.

Then, we compute the transformed component scores in matrix $B \in ℝ^{n \times m}$ such that

B = AL

(2)

where B is composed of linear combinations of matrix A . The third step decides how many components must be retained for computing the composite index. The Kaiser criterion is employed to retain those p (p < m) principal components with

e_{j'} \geq 1, (j' = 1, \dots, p)

. It is well-known that the percentage of explained variance by those components that meet Kaiser criterion is

100 \frac{\sum_{j' = 1}^{p} e_{j^{'}}}{\sum_{j = 1}^{m} e_{j}}

. Moreover, as detailed in Greenacre (2017), we expect to obtain values of 65% or higher on the total variance explained by the first p components. The final step consists in computing the composite index by a weighted combination of the components. Therefore, the Livability Index of Subzone i is given by

{Livability Index}_{i} = \sum_{j' = 1}^{p} (\frac{e_{j^{'}}}{\sum_{j = 1}^{m} e_{j}} \cdot b_{i j'})

(3)

where

b_{i j'}

are the components of the first p columns in B .

The Spatial Livability Index

The GWPCA uses a moving window weighting method where the indicators of each Subzone within the moving window are multiplied by their respective geographical weights and then PCA of the forms (1) and (2) is applied locally. The size of the window is controlled by the kernel’s bandwidth. Small bandwidths lead to higher spatial variation in the results whereas large bandwidths yield closer results to those obtained by equations (1) and (2) (Harris et al., 2011). The bandwidth is first selected by an automatic routine via cross-validation, as described in Gollini et al. (2015), and the sensitivity of this selection procedure is also investigated. Each indicator j has a pair of coordinates of the centroid of Subzone i listed as (u_i, v_i).

The GWPCA introduces the concept that indicators have certain dependence on their locality. The local variance–covariance matrix can be obtained by

Σ_{(u, v)} = A^{⊤} W_{(u, v)} A

(4)

where W is the diagonal matrix of geographical weights. Furthermore, the local principal components at Subzone i can be expressed as

L_{(u_{i}, v_{i})} V_{(u_{i}, v_{i})} L_{(u_{i}, v_{i})}^{⊤} = Σ_{(u_{i}, v_{i})}

(5)

where

L_{(u_{i}, v_{i})}, V_{(u_{i}, v_{i})} and Σ_{(u_{i}, v_{i})}

are the matrices of local eigenvector, the diagonal matrix of local eigenvalues, and the local variance–covariance matrix, respectively.

Similarly, the scores matrix at Subzone i can be found using $B_{(u_{i}, v_{i})} = A L_{(u_{i}, v_{i})}$ . To identify the proportion of the total variance in A explained by each local component, we need to divide each local eigenvalue by $trace (V_{(u_{i}, v_{i})})$ . Conversely to traditional PCA, there is no consensus on the number of local principal components to extract because before searching for an optimal bandwidth, it is necessary to decide a priory upon the number of components to retain (Tsutsumida et al., 2017). Therefore, to be consistent with the expected variance extracted by traditional PCA, it is reasonable to retain all components that explain at least 65% of the variance at each Subzone. Finally, an analogous Livability Index with spatial correction can be derived by adapting equation (3) with the corresponding local eigenvalues, $e_{j (u_{i}, v_{i})}$ , and local scores, $b_{i j (u_{i}, v_{i})}$ .

Consistency analysis

PCA is a useful tool for multivariate analysis of correlated variables. Therefore, a significant correlation between the livability indicators is needed. The Kaiser–Meyer–Olkin (KMO) and Bartlett’s test of sphericity are important prior to conducting PCA. The KMO is used to exhibit proportion of variance in variable. KMO values of 0.5 or smaller are considered to be improper to perform PCA whereas values close to 1 suggest that PCA can act efficiently. Bartlett’s test of sphericity verifies the null hypothesis that the correlation matrix associated to A is an identity matrix. On the other hand, before proceeding with GWPCA it is necessary to test if the geographically weighted eigenvalues $e_{j (u_{i}, v_{i})}$ vary significantly across space (Gollini et al., 2015). This requirement can be addressed by implementing Monte Carlo simulation as suggested in Harris et al. (2011). The idea is to determine the standard deviation of each $e_{j (u_{i}, v_{i})}$ in a rank distribution of the standard deviations obtained by applying GWPCA to each randomized dataset. We select a box-car kernel function distance because it is more likely to provide outputs that appear discontinuous over space (Harris et al., 2015). This is equivalent to setting weights to zero in observations that are farther than some fixed distance from the calibration point. This assumption can be satisfied by our setting because the spatial influence of Subzones that are extremely far from each could be assumed to be zero.

Results

Exploratory analysis

The first validation strategy consisted of the KMO test (with value of 0.55) and the Bartlett’s test of sphericity (p-value lower than 0.01). Therefore, PCA analysis is regarded to be suitable. We also have reversed the distance to the nearest hospital so that larger values (e.g. shorter distances) would be associated with higher livability.

Figure 2(a) displays the loading values of the first six (p = 6) principal components with eigenvalues larger than 1. The first principal component is associated with open spaces (playgrounds, fitness areas, and access points). The second principal component is related to a mixture of public transport, infrastructure, healthcare, and employment. In other words, the first two principal components can capture enough information from most of the dimensions related to livability. The proportion of the total variance explained is shown in Figure 2(b). The first two principal components explain 37.7% of the original data whereas the first six principal components (with eigenvalues greater than 1) combined explain 72.5%. The results from the 200 Monte Carlo simulations and the automated optimal bandwidth are summarized in Figure 2(c). The p-value equaling 0.04 obtained for the simulations suggests that the spatial invariant hypothesis about the local eigenvalues must be rejected. Thus, the objective indicators are, up to a certain degree, spatially non-stationary.

Figure 2.

Components of the Livability Index and spatial heterogeneity test. (a) PCA loadings, (b) percentage of explained variance, and (c) eigenvalue non-stationarity. p.t.p.: per thousand population.

Table 1 reports summary statistics of the percentage of variance explained by the GWPCs. Recall that the weighted PCAs are centered at each location and the loading values are computed for every Subzone. The result is a set of information related to each Subzone. The first GWPC (GWPC1) explains 17.65–45.48% of the variance of all Subzones. To be consistent with the PCA approach of the Livability Index, the GWPCA requires selecting those components that explain at least 70% of the variance for all Subzones. Hence, the first six GWPCs from Table 1 will enter the Spatial Livability Index.

Table 1.

Percentage of the variance accounted by the GWPCA.

	Min	Mean	Max
GWPC1	17.65	21.61	45.48
GWPC2	34.25	43.56	77.12
GWPC3	48.21	56.51	86.73
GWPC4	58.03	66.14	90.92
GWPC5	65.64	73.50	93.86
GWPC6	72.00	79.68	96.57

GWPCA: geographically weighted principal component analysis.

The study of the spatial variation is important because it allows one to identify differences between Subzones. Figure 3 illustrates these differences. Each spike represents one of the loading values (analogous to Figure 2(a)), and its magnitude is shown by the spike’s length. The positive loading values are shown in blue, while the negative ones in red. The difference in magnitude is clear in both cases of GWPC1 and GWPC2, whereas the differences in sign are more evident in GWPC2. The spatial trends are expected, for example Figure 3(a) says that GWPC1 is positively associated with southern areas but negatively correlated with northern areas.

Figure 3.

GWPC1 and GWPC2. (a) First localized principal component and (b) second localized principal component.

The Spatial Livability Index

After computing both indices, with and without spatial correction, a comparison of results is required to quantify the spatial influence of livability conditions among Subzones. Figure 4 plots the rank of Subzones derived by both approaches. The x-axis indicates the ranking of each observation after computing equation (3) whereas the y-axis demonstrates the ranking deduced from the Spatial Livability Index. The positive correlation is obvious as both approaches provide similar results. The normal 95% confidence ellipse clusters similar observations and Subzones outside the ellipse are atypical points. The Subzones outside the cluster are well positioned for liability under one approach whereas they perform badly under the second approach. By a visual inspection we argue that both frameworks are not independent but they are not too much correlated, either. In fact, the Spearman’s Rank-Order Correlation (SROC) test indicates a correlation of 0.37 and it is statistically significant (p-value < 0.01). Interestingly, these badly ranked Subzones have low values in many of the objective indicators such as metro stops, sport centers, or healthcare institutions. Five out of the seven atypical Subzones are located at the northeast corner of Singapore winch are undergoing rapid development under the ambition of the Housing & Development Board to transform them into a fully mature housing areas.

Figure 4.

Relation between Livability Index and Spatial Livability Index.

For the ease of exposition, the Spatial Livability Index is expressed on a [0–1] scale since the ranking of Subzones is not affected by a linear transformation. Figure 5(a) shows the final results and Figure 5(b) displays the average monthly residential rental price (in Singapore Dollar, SGD) using data from public websites.¹ Comparing both figures is particularly interesting. First, from Figures 1 and 5(b), we observe that the most expensive Subzones are somehow the less densely populated (SROC of −0.63 with p-value < 0.01). Downtown areas located at the center of the country are the most expensive zones to live in. High property prices indicate how much residents are willing to pay to live in top areas, and they have been shown to be positively correlated with higher livability (Okulicz-Kozaryn, 2013) and gentrification (Anguelovski et al., 2019). The Spatial Livability Index across Subzones reveals promising findings. It shows that most of the expensive zones are not necessarily the most livable (SROC of 0.03 with p-value = 0.73). Overall, the spatial composite indicator is quite homogeneous across Subzones as only few areas are reported to be either highly or lowly livable.

Figure 5.

Spatial Livability Index and residential rental price. (a) Spatial Livability Index and (b) average monthly rental price per room. SGD: Singapore Dollar.

Finally, using public data from the Housing & Development Board we also briefly examine gentrification’s association with Subzones rates of spatial livability. The data source contains housing resale flat transactions at constant prices in 25 planning areas between 2007 and 2019. We compared the average Spatial Livability Index by planning area with the property average annual percent change but Spearman’s correlation test was not statistically significant (SROC of −0.12 with p-value = 0.38). Thus, we confirm the null hypothesis that there is no association between livability and gentrification but further work is still required to refine the finding (such that the analysis of a larger dataset with property values by Subzones).

Sensitivity analysis

To investigate the sensitivity of our results, we look at two main sources of variability. First, the Spatial Livability Index depends on the bandwidth size. Second, livability scores may change if some evaluated dimensions are excluded. For example, how different are the results if the index does not consider public transport or healthcare?

By following the steps in Gollini et al. (2015) we found an “optimal” distance of 12.383 kilometers. Note that the average distance between any two Subzones is 10.5 kilometers (minimum of 317 meters and maximum of 32.4 kilometers). That said, weights of Subzones within 12.383 kilometers to each Subzone can contribute to its livability. This bandwidth distance suggests that Subzones are expanding through integration with other Subzones benefiting from potential agglomeration effects and enabling the sharing of resources.

The effect of different distances can be seen in Figure 6 in the form of density functions. An extremely small bandwidth, such as 5 kilometers or less, can lead to random results because of its small local sample size and less degrees of freedom (Tsutsumida et al., 2017). The figure shows that Livability Index (PCA) scores are particularly low in most of the Subzones. The results do not imply a lack of livability conditions, on the contrary, they suggest that most of the Subzones are homogeneous in livability and only few of them present large values of the composite index. These highly scored livable Subzones can be seen as atypical areas due to statistical procedure, i.e. the spatial component has not been taken into account. The Spatial Livability Index (GWPCA) with the optimal bandwidth of 12.383 kilometers shifts the distribution to the right so one can see that the spatial adjustment “improves” livability scores. Distances of 5, 10, 15, and 20 kilometers are compared, and we note that small distances such as 5 and 10 kilometers tend to score higher most of the observations. Next, Table 2 enlists the combination of distances and excluded dimensions. The elements of the table represent the number of atypical Subzones when the Spatial Livability Index is compared with its counterpart. For example, the element between the row “All indicators” and the column “12.4 km” says that seven Subzones scored very good/bad under PCA but very bad/good under GWPCA. These observations correspond to the seven dots in the outer region of the normal ellipse in Figure 4. The table provides interesting insights into the decision about which dimensions need to be evaluated to develop a robust Livability Index. If education, culture and environment, healthcare, or open and public spaces are excluded within a distance between 12.4 and 15 kilometers, the number of atypical Subzones is relatively low. This can be interpreted so that Singapore offers a well distributed education/healthcare system with multiple schools/healthcare institutions across the country. In the case of culture and environment dimension, shopping malls around the city play a vital role in the social life since they are where large part of the social interaction takes place (Ooi and Sim, 2007). In contrast, public transportation and infrastructure seem to be more heterogeneous, and therefore, livability scores are more sensitive to its inclusion/exclusion. The sensitivity results suggest that these two dimensions need to be addressed properly.

Figure 6.

Kernel density estimation. GWPCA: geographically weighted principal components analysis; PCA: principal component analysis.

Table 2.

Livability Index and Spatial Livability Index, atypical Subzones.

Dimension/Distance	5 km	10 km	12.4 km	15 km	20 km
All indicators	7	10	7	7	8
No public transport	36	31	27	27	23
No infrastructure	41	30	23	22	26
No community facilities	44	23	26	22	23
No open space and public space	43	25	20	17	19
No healthcare	37	28	17	20	20
No culture and environment	37	29	16	17	27
No education	29	29	18	15	25
No employment	39	23	24	20	16

Discussion and concluding remarks

Discussion of empirical results

The results from this work show the spatial non-stationarity of livability in Singapore. These “hidden” correlations are nothing else but spatial associations of livability between each Subzone and its neighbors. Although the intuition behind these correspondences is obvious, there is a gap in the literature linking spatial associations of livability. From the results, we observe evident similarities between the non-Spatial Livability Index and its spatial counterpart (see Figure 4). Yet, it is worth emphasizing the relevance of the spatial version of livability indicators over the non-spatial indicators, because it considers the geographic component in the distribution of open spaces, parks, hospitals, schools, or metro stations. The relevance of the spatial framework can be appreciated in the form of atypical areas as shown in Figure 4 and Table 2. Very small geographical polygons may lack private clinics, large parks, or business areas and thus, the Livability Index will rank them as poor livable areas. The Spatial Livability Index can suggest some corrections toward this problem by assigning “optimal” weights to the composite function. Overall, the results demonstrate that Subzones in Singapore are homogeneous in livability, especially when they are compared to property prices as shown in Figure 5. This implies that even the cheaper areas can contribute as much to residents’ physical, social, and mental well-being as the more expensive zones. The finding reconfirms the effectiveness of current strategies of Singapore’s public housing system (accommodating almost 80% of households) designed to promote social cohesion, integration of income diversity, and support mixed land uses (Teo, 2014; Yuen and Hien, 2005).

Policy implications

Our methodology acts as a reference source for livability assessment at localized and finer scales within the city. It provides detailed integration of objective indicators covering main livability dimensions and attributes. This comprehensive framework can improve stakeholder and community engagement in plan-making. It allows the identification and diagnosis of livability in spatial areas that do not have surrounding public spaces or a mix of amenities, but perhaps adjacent areas are able to exert positive influence for livability over them. Such interested stakeholders could benefit from our methodology to guide budget allocations, land use plans, or change neighborhood’s layout. The role of food centers, community malls, good access to schools, childcare, clinics, recreational facilities, and green spaces take on increasing significance when delivering enhanced livability in higher-density neighborhoods. Thus, our methodology might be effective for monitoring the performance of these areas as livable communities, built to be self-sufficient in terms of jobs, facilities, and preempting residents from having to travel long distances for necessities and amenities. The Spatial Livability Index can be also used for the localized livability assessment process which consists of (i) establishing a baseline (initial local conditions of livability), (ii) identifying neighborhood-level strategies (design of plans and programs that will be impacting on the livability), (iii) iterative evaluation (using the Spatial Livability Index), (iv) identification of new opportunities (adjusting localized policies or recommending amendments), and (v) monitoring outcomes (tracking the benefits).

While the empirical results of this study are specific to the geographical and social context of Singapore, the results may be applied to higher-density neighborhoods elsewhere. In the case of global megalopolises like London, New York, Tokyo, Sydney, among others, the data required to feed the Spatial Livability Index can be easily obtained from the public websites of the departments of transportation, health, education, or urban planning. Alternatively, open public data sources, such as OpenStreetMap, provide a powerful way to understand and measure urban environments worldwide.

Limitations

Creating a composite index that allows for ranking of observations would depend on the relative weighting indicators. Should the quantity and quality of public transport be heavily weighted than the culture and environment factors? Somehow the methodological tools of the objective approach to livability allow us to delegate this decision to well-known statistical algorithms. An important shortcoming arises when subjective indicators are not taken into account which can be used to calibrate the model. Further investigations in this direction would certainly be interesting.

A major constraint for the elaboration of the proposed Spatial Livability Index in other cities is the accessibility, availability, and reliability of the data sources, especially at highly disaggregated geographical level. For example, the suggested indicators of infrastructure, Street Connectivity Index and Entropy Index, require computing metrics of street network and land usage which may be easy to obtain in developed countries but far more difficult to quantify in cities of the developing world. The suggestion is to adapt the Spatial Livability Index accordingly to the available data sources.

Concluding remarks

This work contributes to the development of a tool for assessing livability in dense urban centers. The proposed composite indicator is defined based on a literature review and considers eight dimensions of livability (public transport, infrastructure, community facilities, open space and public space, healthcare, culture and environment, education, and employment) captured through 17 objective indicators. The key feature of the research is the inclusion of the spatial configuration within the city. GWPCA is used with the aim of generating spatial insights into the livability, particularly for small or peripheral neighborhoods around big cities. The case of Singapore’s Subzones is studied and discussed. Although the findings suggest similarities between the spatial and non-spatial Livability indices, the Monte Carlo test based on 200 randomizations of the data supports the idea that eigenvalues vary significantly across Subzones and they are randomly distributed, i.e. the majority of all 17 objective indicators exhibit spatial behavior with a very high confidence level. The proposed spatial index can be further utilized to diagnose local processes, giving finer-grained information on spatial differences (as shown in Figure 3), as a first step toward guiding stakeholders to target specific causes of poor livability in specific neighborhoods. We hope this article could serve as a starting point for research and/or urban planning design that not only fully illustrates the idea of spatial interactions of livability in dense urban environments but also performs in the operational terms of robust statistical analysis.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The research leading to these results is supported by funding from the Ministry of Education, Singapore, under its Grant SGPCTRS1804. The second author would like to acknowledge CONACyT grants CB-2013-01-221676 and FC-2016-01-1938.

ORCID iD

Francisco Benita

Note

Francisco Benita is Research Fellow at Singapore University of Technology and Design. He received his Ph.D. in Engineering Sciences in 2016 from Tec de Monterrey. He is interested in urban systems and its interface with of optimization, data science and statistical learning.

Vyacheslav Kalashnikov is professor of operations research at the School of Engineering and Sciences at Tec de Monterrey. He is the author and co-author of 5 monographs and more than 90 research papers published in many prestigious and highly indexed journals in the area of Optimization and its applications to Engineering.

Bige Tunçer is an associate professor of design computation and the associate head of pillar at the Architecture and Sustainable Design Pillar of Singapore University of Technology and Design. She received her PhD from Delft University of Technology and her MSc from Carnegie Mellon University. She was an assistant professor at TU Delft, a visiting professor at the Chair of Information Architecture at ETH Zurich, and a visiting scholar at MIT. Her main research interest is evidence informed design processes.

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