sustainability
Article
Spatial Distribution of Public Housing and Urban Socio-Spatial
Inequalities: An Exploratory Analysis of the Valencia Case
Alfonso Gallego-Valadés
, Francisco Ródenas-Rigla *
and Jorge Garcés-Ferrer
Polibienestar Research Institute, University of Valencia, 46022 València, Spain; alfonso.gallego@uv.es (A.G.-V.);
jordi.garces@uv.es (J.G.-F.)
* Correspondence: francisco.rodenas@uv.es
Abstract: The urban spatial distribution of public housing is not a widely addressed issue in Spain,
from a geographical perspective. This paper analyses the spatial distribution of public housing
in the city of Valencia (Spain), as well as to identify its relationship with other socio-residential
characteristics of the urban environment. Different techniques of spatial point pattern analysis,
exploratory spatial data analysis (ESDA) and clustering methods are implemented. We analyse both
the univariate spatial patterns of public housing and its relationship with two variables: a low-income
population and median monthly rent. Analysis has revealed that public housing follows a pattern of
partial agglomeration and mostly peripheral dispersion in its spatial distribution. However, there
does not seem to be a univocal and immanent relationship between such distribution patterns and the
characteristics of the socio-residential environment. Conversely, it is possible to point to the existence
of multiple local forms of association. The lack of a clear pattern may be due to many reasons: the
heterogeneity of profiles eligible for public housing, the size of the projects and the spatial dispersion
in their location.
Citation: Gallego-Valadés, A.;
Ródenas-Rigla, F.; Garcés-Ferrer, J.
Spatial Distribution of Public
Keywords: spatial distribution; socio-spatial inequalities; public housing; urban vulnerability;
urban policies
Housing and Urban Socio-Spatial
Inequalities: An Exploratory Analysis
of the Valencia Case. Sustainability
2021, 13, 11381. https://doi.org/
10.3390/su132011381
Academic Editor: Brian Deal
Received: 2 September 2021
Accepted: 13 October 2021
Published: 15 October 2021
Publisher’s Note: MDPI stays neutral
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Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1. Introduction
The housing regime in Spain is characterised by the widespread predominance of
home ownership versus renting [1–6]. Public housing provision has adopted this general
trend (Figure 1) and is mainly oriented towards promoting access to ownership through
financial demand-side financial support [3,5]. The heterogeneity of rules on the access and
allocation of social housing between regional governments and housing typologies [7],
the temporary protection of the subsidization arrangement [4,8], and the predominance of
private promotion of new public housing [8], are the most remarkable features that public
housing policies have shown throughout a long-term trajectory.
Public housing provision can contribute to mitigate some of the negative impacts
generated by the free housing market in urban areas, such as the difficulty of access to
housing for certain population groups [9–13] or the increase in prices in the real estate
market [14,15], linked to gentrification processes [16–19]. However, the way public housing
is located also shapes the spatial segregation patterns [20]. The experience of several U.S.
cities in the second half of the 20th century shows clear trends: public housing produced
a “poverty concentration effect” in host neighbourhoods [21–24]. The argument is also
plausible the other way round: it is well reported that former public housing residents
relocated with vouchers end up in neighbourhoods with slightly lower poverty rates than
those in public housing, suggesting a modest “poverty deconcentration effect” [25]. It is
a fact that cuts across the vast majority of cases that there is a greater presence of public
housing in disadvantaged neighbourhoods. However, most of the available literature
proposes that the way in which public housing is distributed in the urban environment can
Sustainability 2021, 13, 11381. https://doi.org/10.3390/su132011381
https://www.mdpi.com/journal/sustainability
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drive different types of socio-spatial equilibria and segregation processes, not necessarily
homogeneous.
Figure 1. Number of definitive qualifications by housing tenure regime. State and regional plans.
Source: Own elaboration from Ministry of Transport, Mobility and Urban Agenda [26].
The case of Montreal illustrates how a heterogeneous spatial insertion of housing
in the socio-residential environment can discourage the formation of strong segregation
patterns and even favour social mixing [27–29]. Different studies applied to this city point
to the variety of ways in which public housing is inserted in the urban area and highlight
that only a small proportion of public housing tenants (7%) live in residual spaces [29].
The case of New York [30] reveals the existence of a varied casuistry in the spatial distribution of public housing. On the one hand, the authors show the presence of significant
local spatial correlations between the share of conventional public housing and extreme
poverty rates in neighbouring census tracts. However, they also identify several clusters
where the share of public housing correlates inversely with poverty rates, suggesting that
there is no immanent relationship between these two characteristics.
Why, in some contexts, does the presence of public housing shape highly marked
patterns of segregation and in others it does not? The sizes of public housing stock and
projects, their spatial distribution or the degree of social heterogeneity of the beneficiary
profiles may be some of the key drivers. The experience of French cities (1982–2012) shows
how, while large housing projects built before the 1980s would have increased segregation, smaller projects would have favoured the “social mix”, attracting non-European
immigrants to urban areas where they did not previously reside [31].
Oslo provides a clear example of how a small and spatially dispersed social housing sector makes a minor contribution to ethnic segregation [32]. A similar underlying
logic is found in Montreal, where larger projects are spatially dispersed in neighbourhoods with varying socio-economic profiles [28]. In Hong Kong, mechanisms to avoid
the “poverty concentration effect” have focused on maintaining social heterogeneity and
spatial homogeneity in the location of public housing, with successful outcomes [33].
In Spain, with a low stock of public housing and a wide heterogeneity in the socioeconomic profiles of the population eligible for public housing [7], it is plausible to argue
that its location is not one of the main factors in shaping spatial segregation patterns. The
urban development that began in the 1960s, with the construction of large blocks of mass
social housing had important consequences for the urban fabric in terms of social segregation, insecurity and progressive degradation of the environment and housing [34–38];
but these policies were responsive to the widespread housing need at the time and are not
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largely representative of public housing policies today. Rather, national land legislation
provides mechanisms to foster tenure heterogeneity.
In the international context, the study of public housing is approached from multiple
perspectives. However, although there are some notable contributions of international
scope on the spatial distribution patterns of public housing in the urban environment,
this field of study has not occupied a prominent place in Spain. Analysis using explicitly
geographical techniques is an issue that has not been examined much before, largely as
a consequence of the scarcity of available official statistical sources. This study aims to
contribute to narrowing this gap. We argue that, from a cross-sectional approach, the
relationship between the spatial distribution pattern of public housing and the socioresidential characteristics of the urban environment reveals the type of impact that the
location decision has had on the socio-spatial structure of the population. Thus, this paper
addresses these key issues: what is the spatial distribution pattern of the location of public
housing in Valencia? How does this pattern relate to socio-spatial inequalities? What
factors drive this relationship? With these objectives, different techniques of spatial point
pattern analysis and exploratory spatial data analysis (ESDA) are implemented.
2. Materials and Methods
2.1. Data Set
Valencia is the capital city of the Valencian community. Its urban area includes a total
of 45 municipalities [39]. In 2020, it had a population size of 800,215 inhabitants and a
surface area of 134.65 km2 , being the third largest municipality in Spain in population
size. At the reference period of analysis (2017), the municipality was spatially structured
through 19 districts, 88 neighbourhoods (Figure S1) and 596 census sections (Figure 2).
From the second half of the 20th century, at the start of the developmentalist period
until the present day, Valencia has undergone a considerable process of social and urban
transformation. Over this period, the city has gone from having an agricultural sector with
an extensive weight in the productive structure to becoming a metropolis of services and
a cultural and tourist enclave with international scope [40,41]. This shift has been linked,
since the 1990s, to several processes of tourist and commercial gentrification in declining
neighbourhoods, driven by the urban planning policies of local governments [42–45].
Figure 3 shows some key points of urban and residential development patterns in
the city of Valencia. On the top left, functional buildings predominantly destined for
residential use are represented by year of construction. On the right is the average year
of construction, aggregated at census tract level. The delimitation of intervals follows
the criteria established by the author [46] in the definition of the different phases of the
urbanisation process in Spain.
Below left is the map of quintiles of the standard deviation of the year of construction,
also aggregated at census tract level. As can be seen, historical and older areas tend to
present more segmented patterns of urban development over time than more recently
developed areas, as suggested by the presence of a moderate–high negative correlation
(r = −0.64, p < 0.01) between the average year of construction of residential buildings and
their respective standard deviation.
The land use map (bottom right) allows for a more detailed identification of the spatiotemporal trends in urban and residential development in the city. The map is coherent
with the spatial distribution of the descriptive statistics: the old city occupies a central
position, together with the first urban extensions. On the periphery, a large part of the
old nuclei is located, which present continuity with the urban fabric as a consequence of
later developments.
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Figure 2. Valencia: census districts.
Figure 3. Maps of: (top left) building year (excluding rehabilitation, reform or conservation actions) of residential buildings;
(top right) average building year of residential buildings; (bottom left) building year standard deviation of residential
buildings, in quintiles; (bottom right) land occupation [47].
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2.2. Variables
In this study we use open data from public sources. The variables obtained from the
processing of these data are shown in Table 1.
Table 1. Description of variables, data sources and specified years.
Variable
Description
Aggregation
Source
Year
Low-income population
Population with income per
unit of consumption 1 below
40% of the median
Census tract
NSI: Atlas of Household
Income Distribution [48]
2017
Rent
Median monthly rent of the
predominant type of housing
(euros/m2 )
Census tract
Ministry of Transport,
Mobility and Urban Agenda:
Housing Rental Index [49]
2018
Average construction year
Average year of construction
of functional buildings for
residential use (excluding
rehabilitation, reform or
conservation actions)
Census tract
Ministry of Finance
Cadastre—INSPIRE [50]
2017
Construction year
standard deviation
Standard deviation of the year
of construction of functional
buildings intended for
residential use (excluding
rehabilitation, reform or
conservation actions)
Census tract
Ministry of Finance.
Cadastre—INSPIRE [50]
2017
Public housing
Geolocation of public housing
Spatial points
Valencia City Council:
Transparency and Open Data
Portal [51]
2015
1
The concept of consumption unit is used for a better comparison of incomes of different types of households. The number of equivalent
household consumption units is calculated using the modified OECD equivalence scale.
A large part of the analysis developed took the census tract as the basic unit of
statistical aggregation of data. The vector layer used with the census tracts corresponds
to the period 2017 and was obtained from the National Statistics Institute (NSI). The data
on low-income population were also obtained from the NSI and are specified at census
tract level.
Data on median monthly rent were obtained from the Ministry of Transport, Mobility
and Urban Agenda, and are specified for the year 2018. The vector layer, on the other hand,
contains the census tracts corresponding to the year 2011, coinciding with the population
and housing census, so the limits of some tracts differ with respect to the limits in 2017. To
address this problem, the values of the missing census tracts were assigned to the tracts
that totally or partially occupy the territory of the previous one. Similarly, the values of the
new census tracts were taken from the value of the old tracts that occupied that territory.
The vector layer of Valencia City Council contained the delimitations of the plots
intended for public housing, including both those with building permits and those that
were built. To obtain a sample of the locations of public housing built before 2017, we
intersected the vector layer with the cadastral cartography of the municipality.
The cadastral cartography contains information on all properties according to year of
construction, functional status and use, among others. First of all, we removed all buildings
that are not mainly used for residential purposes. Next, we excluded all properties whose
year of construction ended after 2017. Finally, we filtered the properties by functional status,
deleting all those in ruin or declined condition. After the screening process, we intersected
the clean cadastral cartography with the vector layer of public housing, obtaining a sample
of 124 functional buildings of residential use, totally or partially destined to public housing.
In Spain, the configuration of public housing blocks tends to be heterogeneous. In
many cases, the buildings are entirely intended for public housing, but in others they
coexist with free market tenure housing, in varying proportions. However, as a proxy for
the capacity of the blocks to host public housing beneficiaries, we use cadastral information
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on the number of dwellings per building. In total, we refer to n = 3643 dwellings located in
buildings totally or partially intended for public housing.
The software used for cartographic representation and mapping was QGIS 3.16, with
base map © Stamen Terrain.
2.3. Methods
2.3.1. Spatial Autocorrelation Analysis
The socio-residential composition of the census tracts can be characterised according
to the presence of a low-income population and the median monthly rent. In Valencia, 12%
of the population has an income, per consumption unit, below 40% of the median. The rent
for collective housing is 6 euros, while that for single-family housing is 5.5.
However, these levels may vary widely across census tracts. To assess the degree to
which the relative weight of each population group is distributed following a pattern of spatial clustering, dispersion or randomness, we use Moran’s index (see seminal work [52,53]).
This spatial autocorrelation statistic is particularly suitable for assessing the similarity of
the socio-residential composition of each census tract with respect to neighbouring tracts
and is more sensitive to the degree of clustering rather than to other dimensions of spatial
segregation (see [54]). The values obtained by the indicator range from −1 (maximum
negative autocorrelation) to 1 (maximum positive autocorrelation), where 0 indicates the
absence of autocorrelation or spatial randomness.
This autocorrelation, by contrast, is global in scope and does not provide information
on the spatial heterogeneity present between territorial units. Thus, we also use the local
version of this indicator: local Moran’s I [55]. For a better interpretation, statistically
significant clusters are represented in the Local Indicators of Spatial Association’s (LISA)
maps. Census tract clusters with the highest value for each variable are labelled with the
typology High-High; clusters with the lowest value are labelled Low-Low, and the types
Low-High and High-Low indicate that the statistical association between the values of the
reference tract and the neighbouring tracts is negative. Statistically non-significant results
are represented in white. This family of methods has become highly popular over the last
decades to study the spatial distribution patterns of a wide variety of phenomena and is
also used to analyse the bivariate relationship between poverty rate and public housing
share [30].
The use of the above methods is appropriate in the case of continuous variables.
However, to detect the presence of spatial autocorrelation between census tracts according
to whether or not they contain public housing buildings, we employ the local join count
statistic [56], particularly designed for binary variables coded as 0 or 1. Local spatial
autocorrelation is assessed in this case through the identification of clusters of neighbouring
census tracts where the co-presence of public housing does not respond to a random pattern.
The mentioned techniques were implemented using the free spatial analysis software
GeoDa 1.18 [57].
2.3.2. Spatial Point Pattern Analysis
Aggregation of statistical data to a territorial unit has potential advantages for ESDA,
particularly when downscaling analysis is tedious or does not add value. However, this
approach has some limitations in the case of data whose main interest lies in geolocation,
such as the impossibility of observing specific and disaggregated patterns within and
across boundaries. The analysis of spatial points consists in the study of events location
and the identification of the ways in which these locations are distributed, namely whether
they follow a clustered, random or uniform pattern [58]. In our case, the set of spatial
points under analysis corresponds to the location of public housing buildings.
The intensity function (u) of the point process can be calculated non-parametrically
by Kernel density estimation (KDE), obtaining for each spatial location u contained in
the analysis region W (whose locations u are spatially structured as a grid) a value of the
magnitude of the intensity with which public housing buildings are located, weighted by
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the number of dwellings. KDE makes it possible to observe local variations at a much
higher level of detail than estimates based on territorial units. Although this is one of the
most common techniques for the visual identification of geolocated event hotspots, its
application in the analysis of the spatial distribution of public housing is not widespread.
However, a case study can be cited [59].
The second option, focused on identifying statistically significant patterns of spatial
clustering, is to look for evidence of high intensity in the distribution within a circle of
fixed radius, r, centred on each location, u. Under the assumption of complete spatial
randomness (CSR), we hypothesise the null hypothesis that the intensity is homogeneous
versus the alternative that the intensity is different inside the circle, as opposed to outside.
We employ the likelihood ratio test statistic Λ(u) [60] to obtain a test of homogeneity or
heterogeneity in the spatial distribution of public housing buildings, for all locations u in
the municipality. The χ2 distribution function allowed us to identify statistically significant
patterns of clustering.
We used the ‘spatstat’ package [61,62], embedded in R statistical software, to implement the techniques described in this section.
2.3.3. Quadrant Map Analysis
The levels of low-income population and median monthly rent are negatively correlated, albeit with low intensity (r = −0.35, p < 0.01). For this reason, we classify the sections
according to the type of interaction between the two variables and represent them in a
quadrant map (Figure 6).
A quadrant map is an exploratory analysis method that allows us to visualise the
association of two variables in space. It separates the cases into four groups, whose
boundaries can be set according to a defined criterion and maps the cases according to the
group in which they fall. In this paper, we take the overall value of each variable, for the
entire municipality, as a reference. In the case of rent, this corresponds to that of collective
housing, as this is the predominant housing typology in general. In the labelling of the
clusters, the first term corresponds to the classification of the low-income population, and
the second term to the rent. Areas where high values coincide are represented in red, low
values in blue and the others in light blue (Low-High) and orange (High-Low).
3. Results
3.1. The Spatial Distribution of Public Housing
Figure 3 presents a visual summary of the main characteristics of the spatial distribution of public housing in Valencia. In total, 47 census tracts contain at least one public
housing building, which represents 7.9% of the total (Figure 3 top left). In dark green
(Figure 4 top right), we show the tracts with a pseudo p-value < 0.05 of the local join count
statistic, based on 999 permutations. In total, we identify nine tracts, of which eight are
located in the Ciutat Vella district, mainly in the neighbourhoods of El Carmen (n = 4) and
El Pilar (n = 3), and one in the neighbourhood of El Mercat. The remaining tract is located
in Poble Nou (Benicalap).
A total of 38 public housing buildings (31%) are located in historic areas, according to
the SIOSE classification on land occupation [47], despite the fact that these areas only represent 9.6% of the total surface area of the residential fabric. The presence of public housing
presents a positive point-biserial correlation (rpb ), although of low intensity, with respect
to the standard deviation of the year of construction of residential buildings (rpb = 0.24,
p < 0.01), while it barely correlates with the average year of construction (rpb = −0.11,
p < 0.01). This trend may be mainly due to the high concentration of buildings in the
neighbourhoods of the Ciutat Vella district. It should, however, be stated that the capacity
of these buildings to host a large number of dwellings for public housing and, therefore, the
beneficiary population, is limited by urban planning regulations in an area that is declared
a protected historical site and is of great heritage interest.
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Figure 4. Maps of: (top left) Census tracts with Public Housing; (top right) pseudo p-value of Local
Join Count statistic; (bottom left) Gaussian KDE (σ = 600 m) of public housing locations, weighted
by number of dwellings; (bottom right) p-values of Λ(u) statistic (radius = 2σ m), with natural
logarithmic colour scale.
Global Moran’s I of the percentage of public housing over total housing is 0.021,
which indicates that, aggregating the data at the census tract level, the variable presents
practically zero spatial autocorrelation. Alternatively, to assess the spatial distribution of
public housing buildings from their geolocation, we employ two spatial point analysis
techniques: Gaussian KDE and the Λ(u) statistic [60]. Figure 4 (bottom left) presents the
results of the KDE, weighted by the number of dwellings and with an isotropic standard
deviation of 600 m. The colour scale ranges from dark red (indicating maximum location
density) to bluish yellow (indicating lower density). Areas in blue correspond to the lower
interval, where values are close to 0.
The Λ(u) statistic assesses the contrast in the spatial distribution of housing inside
and outside a circle of fixed radius centred on each location u of a centroid grid, assuming
conditions of CSR (see [60]). Figure 4 (bottom right) presents the p-value associated with
the statistic, in natural logarithmic colour scale. The deep blue areas indicate a lower
probability that the highest locational intensity within each circle is a random event.
These spatial point analysis techniques allow us to identify a pattern of partial agglomeration and mostly peripheral dispersion of public housing in Valencia. Partial agglomeration, because several clusters of public housing blocks stand out. The one with the
greatest weight is located in Benicalap, in the northern peripheral crown. The second one is
located in Faitanar, on the southern boundary of the municipality. Amongst the secondary
sites, the one located in the Patraix district, particularly in the Safranar neighbourhood,
stands out; as well as the peripheral axis formed by the La Punta neighbourhood, located
in the Cuatro Caminos district, and the Poblados Marítimos district.
Peripheral dispersion does not seem obvious when taking into account only the
presence or absence of public housing or the probability of randomness in locational
intensity of the blocks. However, when weighting by the number of dwellings, the KDE
reveals that the central district (Ciutat Vella) loses weight as a location for public housing.
The urban characteristics of the district do not allow for large blocks of collective housing,
so the projects located in the area are mainly of small and medium size. On the other hand,
the blocks are larger in size in the case of the peripheral partial agglomerations in the north
and south of the municipality.
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3.2. Spatial Patterns of Insertion of Public Housing in the Socio-Residential Environment
The analysis in the previous section shows the existence of a pattern of partial agglomeration and mostly peripheral dispersion of public housing in the municipality. In
general, the existence of an association between the presence of public housing in the
urban space and its urban and residential development trajectory could be stated: public
housing blocks tend slightly to be located in sections with a more staggered development
over time. However, the spatial distribution patterns of public housing according to the
socio-economic characteristics of the environment in which it is located are not taken into
account. In the following sections, we analyse this association.
3.2.1. Spatial Distribution of Socio-Residential Characteristics
Global Moran’s I points to the existence of positive spatial autocorrelation patterns
in both cases, with I = 0.36 for the low-income population, and I = 0.56 for the median
monthly rent. Next, we will analyse how this autocorrelation manifests locally.
As in the case of public housing, the spatial distribution of the low-income population
(Figure 5 left) is characterised by the formation of scattered High-High clusters (10.6%
of the total census tracts) mainly in peripheral areas, covering core areas of the districts
of Benicalap, Rascanya and L’Olivereta, and several sections of the districts of Quatre
Carreres, Poblats Marítims (particularly in the neighbourhoods of Cabanyal—Canyamelar
and Nazaret) and Pobles de l’Oest. Low-Low clusters (15.1%) are distributed in large areas
belonging to the districts of Ciutat Vella, L’Eixample, Extramurs and Pla del Real, as well
as in the neighbourhoods of Penya-Roja (Camins al Grau district), Trinitat (La Saïdia),
Benimaclet, Sant Pau—Campanar and La Carrasca (Algirós).
Figure 5. Top. Quintile maps of: (left) low-income population; (right) median monthly rent. Bottom. LISA Cluster maps of:
(left) low-income population (I = 0.36); (right) median monthly rent (I = 0.56).
The spatial distribution of the median monthly rent follows a far clearer pattern of
clustering than in the previous case. It is characterised by the formation of an extensive
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Low-Low cluster (18%) in the south-western area of the last peripheral crown, and in Pobles
del Nord and Pobles de l’Oest. The High-High clusters (17.3%), on the other hand, follow a
very similar spatial distribution to the Low-Low clusters of the low-income population,
but have a greater presence in the Camins al Grau district.
Table 2 shows how public housing is located in these census tracts. In the case of the
low-income population, the vast majority of buildings (64.5%) are located in tracts that
do not form clusters. Of the remaining buildings, 25% are located in High-High clusters,
although they would only account for 16.1% of the dwellings. The rest are distributed
between Low-Low (6.5%) and Low-High (4%) clusters.
Table 2. Public housing buildings and dwellings located in LISA Clusters.
Census Tracts
LISA Clusters
Low-income population
Not significant
High-High
Low-Low
Low-High
High-Low
Median monthly rent
Not significant
High-High
Low-Low
Low-High
High-Low
General
Buildings
Dwellings
n
%
n
%
n
%
423
63
90
15
5
70.97
10.57
15.1
2.52
0.84
80
31
8
5
0
64.52
25.00
6.45
4.03
0
2618
586
324
115
0
71.86
16.09
8.89
3.16
0
372
103
107
5
9
62.42
17.28
17.95
0.84
1.51
53
37
34
0
0
42.74
29.84
27.42
0
0
1712
506
1425
0
0
46.99
13.89
39.12
0
0
596
100
124
100
3643
100
These patterns differ markedly in the case of monthly rent. Buildings located in census
tracts that do not form statistically significant clusters account for 42.7%. The remaining
buildings are distributed between the High-High (29.8%) and Low-Low (27.4%) clusters,
indicating the lack of an unambiguous form of insertion in the environment. The capacity
of blocks located in Low-Low clusters (39.1% of dwellings), however, is significantly higher
than in High-High clusters (13.9%).
3.2.2. Association Patterns between Socio-Residential Characteristics and Public Housing
The effect sizes between census tracts with public housing and census tracts without
public housing in median monthly rent and percentage of low-income population is hardly
remarkable (Table 3). The point-biserial correlation coefficient between the presence of
public housing and both variables (rpb = 0.02 with respect to low-income population;
rpb = 0.05 with respect to rent) does not reveal a significant overall association either.
Table 3. Effect sizes between the census tracts with public housing and without public housing.
Census Tracts
Has Public Housing
Variables
Low-income
population (%)
Median monthly
rent (euros/m2 )
n
%
47
7.9
47
7.9
Mean
(SD)
12.66
(5.83)
5.98
(1.53)
No Public Housing
n
%
549
92.1
549
92.1
Cohen’s d [95% CI]
Mean
(SD)
12.21
(6.14)
5.78
(1.12)
0.07 [−0.23, 0.37]
0.17 [−0.13, 0.47]
Taking the census tract as a statistical unit, and estimating for each district, however,
the situation changes: the patterns of association appear to be heterogeneous across census
districts (Table 4). In Ciutat Vella, where 27.4% of public housing buildings (n = 34) and
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8.7% of dwellings (n = 317) are located, the coefficient is 0.66 (p < 0.01). As highlighted
in the previous section, the buildings are predominantly located in the neighbourhoods
of El Carmen and El Pilar, where the levels of low-income population are higher than in
the rest of the district. However, it should be noted that these levels are not particularly
high compared to other neighbourhoods in the city where no public housing buildings
are located.
Table 4. Point-biserial correlation coefficient between presence of public housing buildings and:
(3) low-income population; (4) median monthly rent (in each census districts).
Census District
(1) n Buildings
(2) %
(3)
(4)
Ciutat Vella
Eixample
Extramurs
Campanar
La Saïdia
El Pla del Real
L’Olivereta
Patraix
Jesús
Quatre Carreres
Poblats Marítims
Camins al Grau
Algirós
Benimaclet
Rascanya
Benicalap
Pobles del Nord
Pobles de l’Oest
Pobles del Sud
34
0
0
2
0
0
0
18
2
22
11
2
0
1
2
15
2
5
8
27.42
0.00
0.00
1.61
0.00
0.00
0.00
14.52
1.61
17.74
8.87
1.61
0.00
0.81
1.61
12.10
1.61
4.03
6.45
0.66 **
−0.19
−0.02
−0.01
−0.12
0.01
0.06
0.16
−0.01
−0.21
−0.63
−0.20
0.23
−0.03
0.32
−0.21
−0.16
0.08
−0.16
0.02
0.00
0.01
0.34 *
0.63
0.29
0.05
** p < 0.01, * p < 0.1.
In the rest of the districts, the association of public housing with both variables returns
highly variable coefficient sizes, ranging from −0.63 to 0.63, although in no other case are
they statistically significant at p < 0.05.
3.2.3. Socio-Residential Categories
Figure 6 presents the quadrant map of the variables corresponding to the median
monthly rent and the low-income population. Table 5 presents a detailed summary of
the results. As can be seen, most public housing buildings are located in High-High
tracts (38.71%), although they belong to an atypical category of interaction (only 9.7% of
the sections fall into this group). The High-High clusters do not show as clear a spatial
clustering pattern as the other clusters and can be identified as areas with a certain level
of social segmentation, where there occurs simultaneously an above-average presence of
low-income population and higher rental prices.
The remaining buildings are located, to a lesser extent, in the High-Low cluster
(24.19%), which corresponds mostly to socially vulnerable urban areas and deprived
neighbourhoods; the Low-High cluster (19.35%), which corresponds predominantly to
socio-residentially advantaged areas; and in the Low-Low cluster (17.74%). The location of
dwellings in public housing blocks, on the other hand, is notably higher in the High-Low
cluster (35.85%). The rest of the dwellings are located, in this order, in the Low-High cluster
(25.89%), the Low-Low cluster (21.63%) and the High-High cluster (16.63%).
Table S1 systematically reports the differences between clusters, based on several
hypothesis tests. Only the ANOVA test does detect significant differences in the absolute
number of public housing buildings at p < 0.01, with F (3, 592) = 5.862. The post-hoc Tukey’s
test shows that statistically significant pair differences (p < 0.01) occur between the HL-HH,
LH-HH and LL-HH clusters, i.e., between the High-High cluster and each of the other
Sustainability 2021, 13, 11381
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cluster typologies. This fact could suggest that the location of public housing has produced
a slight “poverty concentration effect” on socially segmented neighbourhoods, although, in
any case, of a very limited and spatially heterogeneous scope. None of the other ANOVA
tests could find significant differences between clusters for any of the variables related to
the presence of public housing. At p < 0.1, only t-tests found significant differences in the
total number of blocks between H low-income and L low-income clusters (t = 1.709); and
H Rent and L Rent clusters (t = 1.697), which is consistent with the rest of the findings.
Figure 6. Quadrant map of low-income population and median monthly rent.
Table 5. Public housing buildings and dwellings located in quadrant clusters.
Census Tracts
Clusters
H Lowincome
L Lowincome
H Rent
L Rent
HH
HL
LH
LL
General
Buildings
Dwellings
n
%
n
%
n
%
256
42.95
78
62.9
1912
52.48
340
57.05
46
37.1
1731
47.52
230
366
58
198
172
168
596
38.59
61.41
9.73
33.22
28.86
28.19
100
72
52
48
30
24
22
124
41.94
41.56
38.71
24.19
19.35
17.74
100
1549
2094
606
1306
943
788
3643
42.52
57.48
16.63
35.85
25.89
21.63
100
Sustainability 2021, 13, 11381
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4. Discussion
This study has revealed that public housing in Valencia (Spain) follows a spatial distribution pattern of partial agglomeration and mostly peripheral dispersion, thus providing
an answer to the first question. However, this pattern does not seem to be univocally
related to the socio-spatial inequalities characteristics of the environment. In the same
direction as other studies applied to cities such as Montreal [27–29], our analysis shows
that in Valencia there does not seem to be a single trend in terms of the spatial insertion of
public housing. Rather, it could be noted the existence of multiple local casuistries, which
vary according to the socio-economic characteristics of the neighbourhood and its patterns
of urban and residential development.
As shown above, a large percentage of the blocks (38.7%) is located in sections where
there is a simultaneous above-average presence of low-income population and higher rent
prices (High-High cluster), even though this typology accounts for only 9.7% of the total
number of census tracts. The simultaneous coexistence of two inversely correlated characteristics (r = −0.35, p < 0.01), together with a relatively high presence of public housing
buildings, suggests that its location may have driven a slight “poverty concentration effect”
in these neighbourhoods. Indeed, the fact that a census tract has a high percentage of
low-income population and above-average median monthly rent is an atypical form of
interaction between the two variables. However, this would be a narrow and spatially
heterogeneous effect. Public housing blocks are present, to a greater or lesser degree, in all
socio-residential neighbourhood profiles.
The key factors for this not being a generalised and wide-ranging trend would lie
in the heterogeneity of profiles eligible for public housing, the size of the projects and
the spatial dispersion in their location. As stated by Alberdi [7], in Spain some 80% of
households have an income below the ceiling for access to some form of public housing.
This represents a wide range of potential beneficiaries and thus a great variability in
their socio-economic profiles. Due to the availability of data, the different typologies of
arrangements are not considered in this study, so it would not be difficult to accept that
low-income beneficiaries have been located to a greater extent in the High-High clusters.
When the size of the blocks (number of dwellings) is taken into account, the location
pattern becomes less obvious. Most of the buildings located in the High-High clusters are of
small or medium size, which would have contributed to reduce this “poverty concentration
effect”. It is reported that this is the case of Montreal, where, in addition, larger projects are
scattered throughout the neighbourhoods, especially in the middle and upper-middle class
sectors, where they are over-represented [28]. The experience of French cities also supports
the idea that small projects are more likely to drive “social mixing” [31].
The spatial distribution pattern of public housing in the municipality, closer to dispersion than clustering, may have discouraged the formation of large low-income population
hotspots. Although, in general, the predominant trend is towards peripheralisation, the
case of the central district Ciutat Vella should be noted, as it presents some characteristics
that differentiate it from the rest. As a whole, it has the highest spatial clustering of public
housing buildings, but these are mainly located in the El Carmen and El Pilar neighbourhoods, which also have comparatively higher levels of low-income population than the
rest of the old city neighbourhoods. Urban policies designed in the 1990s faced the need
to protect part of the social structure of a physically and socially degraded area in the
initial stages of a transformation process [40]. An example of this would be the provision
of public housing formulated in a broader urban planning instrument, such as the Special
Plan for the Protection and Interior Reform (PEPRI) Barrio del Carmen, approved in 1991.
Considering the impacts on urban space of the location of public housing, and in
relation to the above, it is possible that the clustering of public housing in this area has
contributed to mitigating some of the worst effects of the social structure reconfiguration,
although it is methodologically complicated to establish what the real extent is. As can be
seen in the previous section, the “local” district-level relationship between the presence
of public housing and low-income population is positive and statistically significant, in
Sustainability 2021, 13, 11381
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contrast to the vast majority of districts. The effects on housing rental prices, on the
other hand, might have been very limited, or counteracted by the intense processes of
touristification of traditionally residential urban areas. However, it should be noted that,
although the district contains 27.4% of the public housing buildings (n = 34) of the entire
municipality, it would only contain 8.7% of the dwellings (n = 317). This is mainly due to
the particular urban configuration of the district, which concentrates most of the historic
centre of the city and is mostly composed of low and medium-rise buildings with little
surface area.
5. Conclusions
Our study aimed to carry out an exploratory analysis of the main characteristics of
the spatial distribution of public housing in the city of Valencia. In general, although the
study reveals that public housing follows certain patterns in its spatial distribution, the
results show that there is no single trend in terms of the insertion of public housing in the
socio-residential environment.
The implemented analysis faces some limitations, mainly derived from the availability
of data. Firstly, this study constitutes a “snapshot” of the main characteristics of the
spatial distribution of public housing buildings at a given point in time. However, as
Apparicio et al. [29] stated, public housing environments are not frozen in time and may
have changed, due to filtering or gentrification, or to spatial and urban transformation
processes. The study could be complemented with the use of methods to automatically
generate urban growth boundaries [63].
Secondly, and related to the previous limitation, causal mechanisms and the localised
impact of the spatial distribution of housing are not assessed in more detail. At this
point, it is worth noting the methodological difficulties of undertaking this task with only
cross-sectional information.
Finally, we have analysed data at the aggregate level, but the absence of micro-data or
aggregated data at a lower scale (e.g., at the block level) hampers the purpose of drawing
concrete conclusions about the population benefiting from public housing. The dynamics
analysed in this study are essentially ecological.
Moreover, in Spain there are hardly any recent studies on the spatial distribution
of public housing with an intrinsically geographical focus. In any case, it is advisable
to improve the availability and scope of data on public housing and to promote applied
research on the causes and socio-spatial impacts derived from its location in urban space,
in order to adequately inform policy-making processes.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/
10.3390/su132011381/s1, Figure S1. Territorial boundaries of Valencia: neighbourhoods; Table S1.
Hypothesis testing. Comparisons between clusters.
Author Contributions: Conceptualization, A.G.-V. and F.R.-R.; methodology, A.G.-V.; software,
A.G.-V.; validation, A.G.-V.; formal analysis, A.G.-V.; investigation, A.G.-V. and F.R.-R.; resources,
A.G.-V.; data curation, A.G.-V.; writing—original draft preparation, A.G.-V. and F.R.-R.; writing—
review and editing, F.R.-R. and J.G.-F.; visualization, A.G.-V.; supervision, F.R.-R. and J.G.-F.; project
administration, F.R.-R. and J.G.-F. All authors have read and agreed to the published version of
the manuscript.
Funding: This research was funded by the Valencian Regional Government (Generalitat Valenciana);
Cod. Exped: OTR2021-22062SUBDI, Cod. CC: 31726.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
Sustainability 2021, 13, 11381
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References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
Eastaway, M.P.; Martin, I.S. General Trends in Financing Social Housing in Spain. Urban Stud. 1999, 36, 699–714. [CrossRef]
Eastaway, M.P.; Varo, I.S.M. The Tenure Imbalance in Spain: The Need for Social Housing Policy. Urban Stud. 2002, 39, 283–295.
[CrossRef]
Hoekstra, J.; Saizarbitoria, I.H.; Etxarri, A.E. Recent changes in Spanish housing policies: Subsidized owner-occupancy dwellings
as a new tenure sector? J. Hous. Built Environ. 2010, 25, 125–138. [CrossRef]
Pareja-Eastaway, M.; Sánchez-Martínez, M.T. El alquiler: Una asignatura pendiente de la Política de Vivienda en España. Ciudad.
Y Territ. Estud. Territ. 2011, 43, 53–70.
Pareja-Eastaway, M.; Sánchez-Martínez, T. More social housing? A critical analysis of social housing provision in Spain. Crit.
Hous. Anal. 2017, 4, 124–131. [CrossRef]
Echaves-García, A.; Navarro-Yañez, C.J. Regímenes De provisión De Vivienda Y emancipación Residencial: Análisis Del Esfuerzo
Público En Vivienda En España Y Efecto En Las Oportunidades De emancipación Desde Una Perspectiva autonómica Comparada.
POSO 2018, 55, 615–638. [CrossRef]
Alberdi, B. Social housing in Spain. In Social Housing in Europe; Scanlon, K., Whitehead, C.M., Arrigoitia, M.F., Eds.; John Wiley
and Sons: Chichester, UK, 2014; pp. 223–237. [CrossRef]
Sánchez, A.B.; Plandiura, R. La provisionalidad del régimen de protección oficial de la vivienda pública en España. Scr. Nova. Rev.
Electrónica Geogr. Cienc. Soc. 2003. Available online: http://www.ub.es/geocrit/sn/sn-146(090).htm (accessed on 1 August 2003).
Gutiérrez, A.; Delclòs, X. The uneven distribution of evictions as new evidence of urban inequality: A spatial analysis approach
in two Catalan cities. Cities 2016, 56, 101–108. [CrossRef]
Gutiérrez, A.; Delclòs, X. Geography of the housing crisis in Catalonia: An overview from the point of view evictions due to
foreclosures. Scr. Nova. Rev. Electrónica Geogr. Cienc. Soc. 2017, 21, 1–33. [CrossRef]
Gutiérrez, A.; Arauzo-Carod, J.-M. Spatial analysis of clustering of foreclosures in the poorest-quality housing urban areas:
Evidence from catalan cities. ISPRS Int. J. Geo-Inf. 2018, 7, 23. [CrossRef]
Gutiérrez, A.; Domènech, A. The mortgage crisis and evictions in Barcelona: Identifying the determinants of the spatial clustering
of foreclosures. Eur. Plan. Stud. 2018, 26, 1939–1960. [CrossRef]
Gonzalez-Perez, J.M.; Vives-Miro, S.; Rullan, O. Evictions for unpaid rent in the judicial district of Palma (Majorca, Spain): A
metropolitan perspective. Cities 2020, 97, 102466. [CrossRef]
Liang, C.; Hui, E.C.; Yip, T.L.; Huang, Y. Private land use for public housing projects: The Influence of a Government Announcement on Housing Markets in Hong Kong. Land Use Policy 2020, 99, 105067. [CrossRef]
Zheng, W. Critical issues in spatial distribution of public housing estates and their implications on urban renewal in Hong Kong.
Smart Sustain. Built Environ. 2015, 4, 172–187. [CrossRef]
Gutiérrez, J.; García-Palomares, J.C.; Romanillos, G.; Salas-Olmedo, M.H. The eruption of Airbnb in tourist cities: Comparing
spatial patterns of hotels and peer-to-peer accommodation in Barcelona. Tour. Manag. 2017, 62, 278–291. [CrossRef]
Garcia-Ayllón, S. Urban transformations as an indicator of unsustainability in the P2P mass tourism phenomenon: The Airbnb
Case in Spain through three case studies. Sustainability 2018, 10, 2933. [CrossRef]
Bockarjova, M.; Botzen, W.J.W.; van Schie, M.H.; Koetse, M.J. Property price effects of green interventions in cities: A meta-analysis
and implications for gentrification. Environ. Sci. Policy 2020, 112, 293–304. [CrossRef]
Lagonigro, R.; Martori, J.C.; Apparicio, P. Understanding Airbnb spatial distribution in a southern European city: The case of
Barcelona. Appl. Geogr. 2020, 115, 102136. [CrossRef]
Arbaci, S. Ethnic segregation, housing systems and welfare regimes in Europe. Eur. J. Hous. Policy 2007, 7, 401–433. [CrossRef]
Bickford, A.; Massey, D.S. Segregation in the second ghetto: Racial and ethnic segregation in American public housing, 1977. Soc.
Forces 1991, 69, 1011–1036. [CrossRef]
Goering, J.; Kamely, A.; Richardson, T. Recent research on racial segregation and poverty concentration in public housing in the
United States. Urban Aff. Rev. 1997, 32, 723–745. [CrossRef]
Carter, W.H.; Schill, M.H.; Wachter, S.M. Polarisation, public housing and racial minorities in US cities. Urban Stud. 1998, 35,
1889–1911. [CrossRef]
Holloway, S.R.; Bryan, D.; Chabot, R.; Rogers, D.M.; Rulli, J. Exploring the effect of public housing on the concentration of poverty
in Columbus, Ohio. Urban Aff. Rev. 1998, 33, 767–789. [CrossRef]
Oakley, D.; Ward, C.; Reid, L.; Ruel, E. The poverty deconcentration imperative and public housing transformation. Sociol.
Compass 2011, 5, 824–833. [CrossRef]
Vivienda y Rehabilitación Protegidas. Available online: https://apps.fomento.gob.es/BoletinOnline2/?nivel=2&orden=31000000
(accessed on 14 September 2021).
Apparicio, P.; Séguin, A.M. Measuring the accessibility of services and facilities for residents of public housing in Montreal. Urban
Stud. 2006, 43, 187–211. [CrossRef]
Apparicio, P.; Séguin, A.M. Spatial Integration of Montreal Public Housing into the Social Environment. L’Espace Géographique
2006, 35, 63–85. [CrossRef]
Apparicio, P.; Séguin, A.M.; Naud, D. The quality of the urban environment around public housing buildings in Montréal: An
objective approach based on GIS and multivariate statistical analysis. Soc. Indic. Res. 2008, 86, 355–380. [CrossRef]
Sustainability 2021, 13, 11381
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
16 of 17
Wyly, E.; DeFilippis, J. Mapping public housing: The case of New York City. City Community 2010, 9, 61–86. [CrossRef]
Verdugo, G.; Toma, S. Can public housing decrease segregation? Lessons and challenges from non-European immigration in
France. Demography 2018, 55, 1803–1828. [CrossRef]
Skifter-Andersen, H.; Andersson, R.; Wessel, T.; Vilkama, K. The impact of housing policies and housing markets on ethnic spatial
segregation: Comparing the capital cities of four Nordic welfare states. Int. J. Hous. Policy 2016, 16, 1–30. [CrossRef]
Delang, C.O.; Lung, H.C. Public housing and poverty concentration in urban neighbourhoods: The case of Hong Kong in the
1990s. Urban Stud. 2010, 47, 1391–1413. [CrossRef]
Castellano, J.M.P. El destino social de la vivienda protegida de promoción privada: El caso de Las Palmas de Gran Canaria (1940–
1978). Scr. Nova. Rev. Electrónica Geogr. Cienc. Soc. 2003, 7. Available online: http://www.ub.es/geocrit/sn/sn-146(093).htm
(accessed on 1 August 2003).
Morales, L.N.A.; García-Almirall, P. A comparative view of social housing in Europe. The case of Barcelona and London. Archit.
City Environ. 2014, 26, 177–200. [CrossRef]
Guajardo, A. Typological analysis of H-plan social housing blocks built in Spain between 1957 and 1981. In Sustainable Development
and Renovation in Architecture, Urbanism and Engineering; Mercader-Moyano, P., Ed.; Springer: Cham, Switzerland, 2017; pp. 27–37.
[CrossRef]
Monzón, M.B. Using mappable indicators for prioritizing the refurbishment of social housing. A case study of Zaragoza (Spain).
In Sustainable Development and Renovation in Architecture, Urbanism and Engineering; Mercader-Moyano, P., Ed.; Springer: Cham,
Switzerland, 2017; pp. 215–224. [CrossRef]
Monzón, M.; López-Mesa, B. Buildings performance indicators to prioritise multi-family housing renovations. Sustain. Cities Soc.
2018, 38, 109–122. [CrossRef]
Ministry of Development. Áreas Urbanas en España. Cuarenta Años de las Ciudades Españolas; Publications Centre: Madrid, Spain,
2018.
Prytherch, D.L.; Maiques, J.V.B. City profile: Valencia. Cities 2009, 26, 103–115. [CrossRef]
Alcalá-Santaella, F.; Díaz Orueta, F.; Ginés, X.; Lourés, M.L. Valencia. In Políticas Urbanas en España: Grandes Ciudades, Actores y
Gobiernos Locales; Iglesias, M., Costa, M.M., Subirats, J., Tomàs, M., Eds.; Icaria: Barcelona, Spain, 2011; pp. 201–227.
Renau, L.d.R.; Trudelle, C. Mega events and urban conflicts in Valencia, Spain: Contesting the new urban modernity. Urban Stud.
Res. 2011, 2011, 1–13. [CrossRef]
Pérez, F.T.; Ferré, A.M.; Esteban, F.O. Crisis, Convivencia Multicultural Y «efectos De barrio». El Caso De Dos Barrios De Valencia.
Migr. Publ. Inst. Univ. Estud. Migr. 2015, 37, 217–238. [CrossRef]
Renau, L.R.; Martín, L.L. De Barrio-Problema a Barrio De Moda: Gentrificación Comercial En Russa-Fa, El “Soho” Valenciano.
An. Geogr. Univ. Complut. 2015, 35, 187–212. [CrossRef]
Esteve, A.J.B.; Arnandis-i-Agramunt, R. Touristificacion in the Central Market of Valencia: Fact or Fiction? In Handbook of Research
on the Impacts, Challenges, and Policy Responses to Overtourism; de Almeida, C.R., Quintano, A., Simancas, M., Huete, R., Breda, Z.,
Eds.; IGI Global: Hershey, PA, USA, 2020; pp. 156–175. [CrossRef]
Nel·lo, O. El proceso de urbanización: Motor y expresión de las transformaciones sociales y territoriales. In Geografía Humana de
España; Romero, J., Ed.; Tirant lo Blanch: Valencia, Spain, 2017; pp. 290–366.
SIOSE. Available online: https://www.siose.es/descargar (accessed on 14 September 2021).
Atlas de Distribución de Renta de los Hogares. Available online: https://www.ine.es/experimental/atlas/experimental_atlas.
htm (accessed on 14 September 2021).
Índice alquiler de Vivienda. Available online: https://www.mitma.gob.es/vivienda/alquiler/indice-alquiler (accessed on
14 September 2021).
Servicios INSPIRE de Cartografía Catastral. Available online: http://www.catastro.minhap.es/webinspire/index.html (accessed
on 14 September 2021).
Portal de Transparencia y Datos Abiertos Valencia. Available online: https://www.valencia.es/dadesobertes/es/dataset/?id=
vivendes-de-proteccio-publica-vpp (accessed on 14 September 2021).
Moran, P.A.P. The interpretation of statistical maps. J. R. Stat. Society. Ser. B 1948, 10, 243–251. [CrossRef]
Cliff, A.D.; Ord, J.K. Spatial Autocorrelation; Pion: London, UK, 1973.
Massey, D.S.; Denton, N.A. The dimensions of residential segregation. Soc. Forces 1988, 67, 281–315. [CrossRef]
Anselin, L. Local indicators of spatial association—LISA. Geogr. Anal. 1995, 27, 93–115. [CrossRef]
Anselin, L.; Li, X. Operational local join count statistics for cluster detection. J. Geogr. Syst. 2019, 21, 189–210. [CrossRef]
Anselin, L.; Syabri, I.; Kho, Y. GeoDa: An introduction to spatial data analysis. In Handbook of Applied Spatial Analysis; Fischer, M.,
Getis, A., Eds.; Springer: Berlin/Heidelberg, Germany, 2010; pp. 73–89. [CrossRef]
Gatrell, A.C.; Bailey, T.C.; Diggle, P.J.; Rowlingson, B.S. Spatial point pattern analysis and its application in geographical
epidemiology. Trans. Inst. Br. Geogr. 1996, 21, 256–274. [CrossRef]
Zhang, Z.; Liu, Y.; Chen, B.; Chen, K. Using gis and kde analysis spatial distribution on public housing households: A case study.
In 2013 8th International Conference on Computer Science & Education; IEEE: New York, NY, USA, 2013; pp. 925–930.
Sustainability 2021, 13, 11381
60.
61.
62.
63.
17 of 17
Kulldorff, M. A spatial scan statistic. Commun. Stat. Theory Methods 1997, 26, 1481–1496. [CrossRef]
Baddeley, A.; Turner, R. spatstat: An R Package for Analyzing Spatial Point Patterns. J. Stat. Softw. 2005, 12, 1–42. [CrossRef]
Baddeley, A.; Rubak, E.; Turner, R. Spatial Point Patterns: Methodology and Applications with R; Chapman and Hall/CRC Press:
London, UK, 2015; Available online: http://www.crcpress.com/Spatial-Point-Patterns-Methodology-and-Applications-with-R/
Baddeley-Rubak-Turner/9781482210200/ (accessed on 24 November 2015).
Harig, O.; Hecht, R.; Burghardt, D.; Meinel, G. Automatic Delineation of Urban Growth Boundaries Based on Topographic Data
Using Germany as a Case Study. ISPRS Int. J. Geo-Inf. 2021, 10, 353. [CrossRef]