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Immigration flows and social inequalities reflect increased social and multi-ethnic segregation in contemporary urban Europe. For a better understanding of these processes, the present study investigates the main strengths of the multi-group residential indices, testing sensitivity and reliability under different metropolitan contexts in five European countries. These indices focus on different research dimensions and approach multi-group residential segregation conceptually and mathematically in a different way. A multivariate exploratory data analysis was adopted to classify the observed segregation patterns into a few homogeneous types and to delineate the multivariate relationship between the indices. The results of principal component analysis demonstrate that the indices assessing uniformity and disproportionality of the social groups analysed (H and D) contribute largely to the diversification in today's multi-ethnic communities, clarifying the importance of the dimension of evenness. Our results highlight how segregation is more evident in economically disadvantaged metropolitan regions with high levels of social vulnerability.
International Migration. 2022;00:1–21.
Received: 6 September 2021 
  Revised: 13 February 2022 
  Accepted: 12 April 2022
DOI: 10.1111/imig.13018
Measuring residential segregation in multi- ethnic
and unequal European cities
Federico Benassi1| Alessia Naccarato2| Ricardo Iglesias- Pascual3|
Luca Salvati4| Salvatore Strozza5
© 2022 The Authors. International Migration published by John Wiley & Sons Ltd on behalf of International Organization for
1Italian National Institute of Statistics (Istat),
Rome, Italy
2Roma Tre University, Rome, Italy
3Universidad Pablo de Olavide, Sevilla,
4Sapienza University of Rome, Rome, Italy
5University of Naples Federico II, Naples,
Ricardo Iglesias- Pascual, Universidad Pablo
de Olavide, Edificio nº 2, Ctra. de Utrera,
km. 1, 41013 Sevilla, Spain.
Funding information
Ministry of Economy, Industry and
Competitiveness of the Spanish
Government, Grant/Award Number:
RTI2018- 095325- B- I00; Universidad Pablo
de Olavide/CBUA
Immigration flows and social inequalities reflect increased
social and multi- ethnic segregation in contemporary urban
Europe. For a better understanding of these processes, the
present study investigates the main strengths of the multi-
group residential indices, testing sensitivity and reliability
under different metropolitan contexts in five European
countries. These indices focus on different research di-
mensions and approach multi- group residential segrega-
tion conceptually and mathematically in a different way. A
multivariate exploratory data analysis was adopted to clas-
sify the observed segregation patterns into a few homoge-
neous types and to delineate the multivariate relationship
between the indices. The results of principal component
analysis demonstrate that the indices assessing uniform-
ity and disproportionality of the social groups analysed (H
and D) contribute largely to the diversification in today's
multi- ethnic communities, clarifying the importance of the
dimension of evenness. Our results highlight how segrega-
tion is more evident in economically disadvantaged metro-
politan regions with high levels of social vulnerability.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which
permit s use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no
modifications or adaptations are made.
    BEN ASSI E t Al.
The social integration of the growing immigrant flows and promotion of more cohesive and inclusive societies
are major challenges facing Europe today (Smith, 2019). Earlier studies have analysed how recent inequalities in
wealth and income within advanced societies (Malmberg & Clark, 2021; Yao et al., 2019), increasing ethnic diversity
(Catney, 2016; Logan & Zhang, 2010; Zwiers et al., 2018), and unbalanced international and interregional migra-
tion flows (Ciommi et al., 2018; Cuadrado- Ciuraneta et al., 2017; Di Feliciantonio et al., 2018), all play key roles in
metropolitan transformations (Czaika & De Haas, 2014; Panori et al., 2019; Portes, 2000). These challenges have
brought the relationship between integration, social and ethnic segregation, and their intrinsic measurement, to the
forefront of the political and social agendas in European countries (Coulter & Clark, 2019; Piekut et al., 2019). Earlie r
studies on the social repercussions of living in segregated social settings (e.g. Badanta et al., 2021; Casey, 2016)
delineate the importance of class and ethnic segregation. They also point out the intrinsic association of social seg-
regation with economic advantages (Kaplan, 1998; Peach, 1996; Portes & Manning, 1986; van Kemp en & Ozue kre n,
1998). More recent works have documented the negative impact of residential segregation, arguing how the resi-
dential segregation of minority groups leads to a set of negative effects (i.e. Charles, 2003; Sampson et al., 2008). In
particular, a high level of residential segregation reinforces the social exclusion of certain groups, and is detrimental
to social cohesion (Amin, 2002; Peterson, 2 017; Putnam, 2007; Sturgis at al., 2014; van Ham & Manley, 2010).
Additional studies argue that geographical dispersion, and thus less segregation, does not ensure a broader
(cultural or social) integration, nor a greater sense of belonging to the host society (Wright & Ellis, 2000). Assuming
that segregation reflects social inequalities (Yao et al., 2019), the notions of segregation and integration largely
depend on the particular social group under investigation (Kr ysan et al., 2017). A refined analysis of social changes
in specific economic contexts will contribute towards delineating the relationship between ethnic segregation and
the design of inclusive policies (Allen et al., 20 04; Hochstenbach & Musterd, 2018; Iglesias- Pascual et al., 2019;
Johnston et al., 2014). In this regard, expanding immigration flows and rising economic inequalities have produced
a generalized increase in social segregation in European cities (Lymperopoulou & Finney, 2017; Monkkonen et al.,
2018; Tammaru et al., 2016, 2017). Earlier studies have pointed out the limitations of classical residential segre-
gation approaches since they do not usually consider the background context (Bolt et al., 2010). However, mea-
surement tools that allow for a more accurate analysis of the multi- ethnic dimension of society (Kramer & Kramer,
2019; Reardon & Firebaugh, 2002; Yao et al., 2019) and its relationship with the demographic and socio- economic
dimensions (Benassi, Iglesias- Pascual, et al., 2020; Finney et al., 2015) will help to provide us with the necessary
knowledge about the current ethnic segregation in European societies.
The present study contributes to such challenging issues with a refined analysis of statistical data derived from D4I
- Integration of m igrants in cities (Ti nto r i et al., 2018), a data ch all e nge init iat i ve promo ted by the Euro pean Commi ssi on.
More specifically, our work investigates (and compares the fit of) multi- group segregation indices at the level of
metropolitan Functional Urban Areas (hereafter ‘FUA’) on regular lattice data (grid) for selected European countries
(Germany, Ireland, Spain, the Netherlands and United Kingdom). These are a subset of the countries involved in the
D4I da ta challen ge that def ine their mi gra nt popu latio ns with the same criterion (i.e. coun try of bir th). We be lieve that
by selecting these countries, we can analyse the main models of welfare regimes and housing systems that have been
prominent in the academic debate on the residential segregation of immigrants in Europe (Arbaci, 2019).
Two- group indices assess phenomena occurring when a given group (usually the minority group) is not distrib-
uted spatially in a similar way with respect to another (usually the majority group). In contrast, multi- group indices
approach residential segregation as a phenomenon which concerns all the population groups which reside in a
given area simultaneously (Reardon & Firebaugh, 2002). According to the most rec ent literat ure, two- grou p in dices
are ineffective in representing contemporary societies with multiple population groups (identified through eth-
nicity, race, religion and citizenship) which coexist within the same context (Benassi, Iglesias- Pascual, et al., 2020).
Based on these premises, our study has three main aims. The first is to identify apparent and latent information
from a comprehensive set of multi- group residential indices using a multivariate analysis to classify segregation
patterns. Secondly, we aim to delineate the relationship between the above indices, each of which pertains to dif-
ferent dimensions and which were derived by approaching multi- group residential segregation conceptually and
mathematically in a different way (Reardon & Firebaugh, 2002). Finally, we test the sensitivity and responsiveness
of multi- group segregation indices by comparing metropolitan contexts defined with the same functional logic
(“FUA”), using the same base geography (grid) and input data (2011 census). By following these steps, our study
can infer the existence of common patterns of residential segregation among FUAs from the latent relationship
between multi- group indices and background variables.
The present paper is organized as follows: in the next section, we offer some reflections on how residential
segregation is measured. Next, we describe data and methods, focusing on the characteristics and properties of
the multi- group indices. In the penultimate section, we present our results, and this is followed by a discussion and
our conclusions in the final section.
Tools used to assess residential segregation should be adapted to the objectives, scales, and units of analysis on
which social science is built (de Bézenac et al., 2021; Morrill, 1991). Earlier studies, such as the seminal contribu-
tions of Duncan and Duncan (1955) and, later, Massey and Denton (1988), conceptualize residential segregation
as the degree of spatial separation between two or more population groups in a given context (Yao et al., 2019). In
the past, the two study groups used to be blacks and whites (e.g. Farley, 1977), while in recent times, they consist
of an immigrant (foreign) nationality and the host society (e.g. Kauppinen & Van Ham, 2019; Wessel et al., 2018).
These indices are traditionally based on single- value results (i.e. global indices), and are descriptive in nature and
intrinsically a- spatial, relying only on the numerical values in each observation unit without taking into account
the situation in the surrounding areas or the spatial patterns in rates (Jones et al., 2015). Instead, they are easy-
to- interpret indices that investigate dissimilarity, isolation and exposure – among other dimensions of residential
segregation – and allow for a comparative analysis across metropolitan areas (Arcaya et al., 2018; Reardon et al.,
2008). Nevertheless, these indices typically do not capture complex residential patterns across racial and social
groups (de Bézenac et al., 2021; Clark et al., 2015).
The increasing ethnic diversity of Western societies (Long & Zhang, 2010 ; Zwiers et al., 2018) has generated
an important academic debate regarding the importance of the idea of "super- diversity" and its social and ana-
lytical implications (Meissner & Vertovec, 2015; Vertovec, 20 07). In this context, it should be noted that the size
of the (resident) foreign population in a given city, the associated economic conditions and the migratory trajec-
tory of the surrounding region all play a key role in the degree of ethnic and cultural diversity and the residential
segregation patterns (Marcińczak et al., 2021; Pisarevskaya et al., 2021). This undeniable social reality suggests
that a dichotomous analysis of segregation (i.e. the ones typically based upon traditional two- group segregation
indices) cannot properly explain the current segregation patterns of a multi- racial society (Kramer & Kramer, 2019;
Reardon & Firebaugh, 2002). From the multi- racial perspective, the concept of residential segregation can be in-
terpreted as the extent to which individuals from different groups occupy and experience different social environ-
ments (Reardon & O’Sullivan, 2004). Research using multi- group segregation indices is based either on traditional
a- spatial indices (Reardon & Firebaugh, 2002; Reardon & O’Sullivan, 2004), such as Theil's entropy index (H) or the
dissimilarity index (D), or on spatially explicit indices (Wong, 1997, 2005).
Another key factor is the role of the geographical scale of analysis and its effect on segregation indices (Clark &
Östh, 2018; Jones et al., 2015; Marcińczak et al., 2021; Olteanu at al., 2019). No one scale can be considered more
appropriate than others when studying segregation, especially when it comes to intra- urban studies (Duvernoy
et al., 2018; Salvati et al., 2018; Zambon et al., 2018). In fact, the relationship between the degree of segregation
and the spatial scale adopted often differs from one city to another (Lan et al., 2020). Even multi- scale studies
have shown that residential segregation can vary according to the ethnic group analysed in the same city (Catney,
    BEN ASSI E t Al.
2018; Lee et al., 2008). This means that communities can be highly segregated at the macro- scale level and yet
much less segregated at the micro- scale level (Simpson & Jivraj, 2015), because racial/ethnic and economic segre-
gation at the metropolitan scale may be lower, and yet it may increase when analysed within smaller geographical
areas, either at the district or census tracts level (Arcaya et al., 2018). This aspect has led recent studies to develop
a multi- scale approach when analysing residential segregation and designing bespoke/egocentric neighbourhoods
according to different measurements of radius or areas based on population size (e.g. de Bézenac et al., 2021;
Manley et al., 2019; Marcińczak et al., 2021; Östh et al., 2015; Petrović, et al., 2018; Wright et al., 2011). However,
in the studies that address the relationship between segregation and the spatial scale, there is little reflection
that goes beyond the merely spatial dimension. Deciding which scale is the most suitable for analysing the social
consequences of the different degrees of segregation is an important outcome of this reflection.
Finally, it should be highlighted that, if a comparative analysis is to be developed to detect the existence of
common comparative patterns or different behaviours at the level of large and middle urban areas, it is advis-
able to use a broader scale that allows for comparison across different types of urban centres (Benassi, Iglesias-
Pascual, et al., 2020; Rey et al., 2021). This is where the use of FUAs, as a commuting space and daily living space,
makes the most sense (Dijkstra et al., 2019). In fact, these macro analyses between large regional models should
prevent us from concentrating exclusively on the study of the most important (or populated) urban centres, and
focus rather on the considerable number of cases that permit a refined investigation of the existence of common
(or divergent) patterns of segregation at the regional level (Benassi, Iglesias- Pascual, et al., 2020; Marcińczak et al.,
2021; Pisarevskaya et al., 2021).
The data used in this contribution were provided by the Data Challenge on “Integration of Migrants in Cities” (D4I).
D4I is an initiative launched at the end of 2017 by the Joint Research Center (JRC) – Knowledge Centre on
Migration and Demography (KMCD) of the European Commission to disseminate scholars and researchers with
a data set of population estimates for grids which permit the analysis of concentrations of migrants in selected
European Union cities with a high spatial resolution.1
This data set was based on ad hoc extractions of the 2011 Population and Housing Census data provided
by the National Statistical Institute of 8 EU member states (France, Germany, Ireland, Italy, Portugal, Spain, The
Netherland s an d the United Kingdom). The result s of the spatial pro ce ssing of the original data are an est imat ion of
population by place of birth or citizenship (depending on the country), for a uniform grid (cells of 100 by 100 me-
ters) in the countries involved in the initiative (Tintori et al., 2018). This means that data are comparable from a
geographical point of view. Grid data are ver y useful when it comes to measuring specific processes like residential
segregation, where spatial pattern alterations produced by tract level analysis tend to be highly localized (Catney
& Lloyd, 2020; Lee et al., 2008; Mazza, 2020). In the last few years, scholars worldwide have been involved in
several initiatives to produce grid data on population attributes (Batista e Silva et al., 2013; Deichmann et al., 2001;
Leyk et al., 2019; Lloyd, Catney, et al., 2017; Lloyd, Sorichetta, et al., 2017). Grid data are particularly suitable for
between- country comparisons, and are also useful when compiling official statistics, especially when studying
the causes and effects of socio- economic and environmental phenomena. Eurostat, for instance, stresses the
importance of using grid data in these kinds of studies because same- sized grid cells (i) allow an easy comparison
between any kind of quantitative population attribute which is stable over time; (ii) can be easily integrated with
other scientific data; (iii) can be constructed hierarchically in terms of cell size to match the study area and, finally,
(iv) can be assembled to create areas for specific purposes and study2. The production and availability of grid data
on population depend on the type of data available from official statistics. As clearly explained by Catney and
Lloyd (2020), in countries where geo- referenced household- specific data are normally available, grid population
counts ar e easil y pro duced by agg regat ing elementary data. In ot her case s, or for othe r populati on variabl es, wher e
gridded data are not provided, estimation procedures can be used, although these can lead to minor or even major
errors. The different follow- up methods range from the simplest (e.g. weighting approaches) to the most sophis-
ticated, which are based on the use of ancillary data source, such as land use (Catney & Lloyd, 2020). For an over-
view of methods for producing grid data, see, among others, Leyk et al. (2019), Lloyd, Catney, et al. (2017), Lloyd,
Sorichetta, et al. (2017 ), and Batista e Silva et al. (2013). In this paper, we used the grid data of population counts
produced by the Joint Research Center, focusing on the input data of the 2011 Population Censuses produced
by the National Statistical Institute of the countries involved in the D4I initiative through a complex estimation
procedure. Details about the methods applied for processing the original data and for technicalities regarding es-
timation of the data used here can be found in the JRC Technical Report (Alessandrini et al., 2017). It is important
to underline that we have chosen to work only with micro- level grid data, because this spatial scale allows us to
measure not only the level of segregation but also other social variables, such as the degree of inter- ethnic contact
at the local level or discrimination in the residential market (Catney & Lloyd, 2020; Imeraj et al., 2020; Vogiazides,
2018). In turn, this contact bet ween the host society and the foreign population has been shown to be a key fac tor
in constructing the social integration process (Layton & Latham, 2021; Peterson, 2017; Vertovec, 2021). We hope
that, by the end of the 2021 census round, other gr id dat a based on migrant populations will be released so th at we
can address the study of residential segregation across time and using comparable geographical areas.
However, it is important to underline that the D4I data are drawn from two different statistical concepts as
far as the origin of migrants is concerned: the country of citizenship (Italy and France) and the country of birth
(Germany, Ireland, Portugal, Spain, The Netherlands and the United Kingdom). Both approaches are based on
information provided by the 2011 general population censuses (Benassi, Bonifazi, et al., 2020). However, the
two criteria to identify the target population determine aggregates that are also significantly different from each
other (Bonifazi & Strozza, 20 06). For a better comparison between different urban contexts, we have selected a
subset of countries: Spain, the Netherlands, the United Kingdom, Ireland and Germany. We chose these countries
because all of them used the same criterion to identify their migrant populations (country of birth), which provides
with an explicit distribution of single country of birth broken down by grid level.3
Our analysis takes as its analysis domain the major Functional Urban Areas (FUAs) of the five countries. The FUAs
are functional partitions proposed by the OECD on the basis of a clearly defined methodology that refers to daily
people's job- related movements. The FUAs provide a functional definition of cities and their area of influence
(commuting zone), maximizing international comparability and overcoming the limitations and drawbacks of the
administrative approaches, thereby ensuring a minimum link to the government levels of the city or metropolitan
area at large (OECD, 2012).
The FUAs were classified according to their demographic size into 4 categories: small urban areas (50,000–
100,000 inhabitants); medium- sized urban areas (100,000– 250,000 inhabitants); metropolitan areas (250,000–
1.5 million inhabitants) and large metropolitan areas with over 1.5 million inhabitants. Here, we focus our attention
on the last two categories of FUAs: metropolitan and large metropolitan areas (Table 1). These are the territorial
contexts in which the presence of foreigners is comparatively higher and where ethnic diversity is more intense
(Benassi, Bonifazi, et al., 2020; Feitosa et al., 2007).
The population size of each selected FUA varies from a minimum of (at least) 500,000 inhabitants (e.g. in the case
of Freiburg (529,806 residents), the smallest of the 53 FUAs) to a maximum of approximately 12 million residents
(London, the densest FUA in the sample). The top 15 FUAs with the largest populations, which together represent
well over 50% of the total population of the 53 metropolitan areas, include three Spanish FUAs (Madrid, Barcelona
and Valencia), six German FUAs (Berlin, Hamburg, Munich, Frankfurt, Cologne and Essen), Dublin for Ireland, two
Dutch FUAs (Amsterdam and Rotterdam) and two English FUAs, in addition to London, (Birmingham and Manchester).
    BEN ASSI E t Al.
The multi- group residential segregation indices used in this paper are listed and described in Table 2. The indices
have been computed using the OasisR package (Tivadar, 2019). In some cases, they are an evolution of well- known
two- group indices (in the case of D and P), while in other cases, they rely on other well- known indices (H and R) or,
alternatively, they have been constructed directly as a multi- group measure (C). Each of them is calculated follow-
ing a precise conceptual and mathematical approach to segregation, which makes it possible to highlight aspects
of the phenomenon that can change radically from one context to another (Reardon & Firebaugh, 2002). European
cities identified here through a functional (gravitation) approach do not in fact differ from one another only
TAB LE 2 Multi- group residential segregation indices computed for the major FUAs of selected European
countries: brief description, types and bibliographic references
Index Description Types References
Information theory (H) The multi- group version of Theil's
entropy index (H Theil)
diversity ratio
Theil, 1972; Theil & Finizza,
Dissimilarity (D) Multi- group dissimilarity index
- a multi- group version of
Duncan's dissimilarity index (D)
Disproportionality Morgan, 1975; Sakoda, 1981
exposure (P)
Multi- group normalized exposure
index - a multi- group version
of the Bell's exposure index
Weighted average James, 1986
Squared Coefficient of
Variation (C)
Can be interpreted as a measure
of the variance of the spatial
representation of the groups
across spatial units, or as
a normalized chi- squared
measure of association
between groups and units.
Reardon & Firebaugh,
Relative Diversity (R) Multi- group relative diversity
index - a multi- group
index based on Simpson's
interaction index (I)
Diversity ratio Carlson, 1992; Goodman
& Kruskal, 1954;
Reardon, 1998
Source: authors’ own work, based on Reardon and Firebaugh (2002).
TAB LE 1 Selected characteristics of the Functional Urban Areas under research
Number of
metropolitan and
large metropolitan
(A .V. )
Incidence of total
population of
selected FUAs
Incidence on total
resident population in
Germany 24 31,685,013 38.7 39.5
Ireland 11,690,947 2.1 36 .9
Spain 816,744,726 20.5 35.8
The Netherlands 56,172, 23 4 7. 5 36.9
United Kingdom 15 25,538,350 31.2 40.3
Tot a l 53 81,831,270 100.0 37. 4
Source: OECD city and region data base.
in terms of migration history, integration and housing policies and the foreign- born communities involved; they
also vary in terms of urban morphology. As a matter of fact, compact and mono- centric settlements in Europe
alternate with less dense and moderately polycentric urban systems (Benassi, Bonifazi, et al., 2020; Pili et al., 2017;
Salvati & Serra, 2 016).
As described in Reardon and Firebaugh (2002), each multi- group index is classifiable into basic types, in rela-
tion to how it addresses the issue of social segregation. These categories correspond to the approaches used here
to derive multi- group indices. Following Reardon and Firebaugh (2002), there are basically four ways of viewing
residential segregation, and, therefore, of measuring it through the indices derived from these approaches:
(i) Segregation as a function of non- proportionality (disproportionality) in the proportions of groups in elemen-
tary territorial units (Firebaugh, 1998, 1999; Reardon & Firebaugh, 2002).
(ii) Segregation as an association between population groups and elementary territorial units (Reardon &
Firebaugh, 2002).
(iii) Segregation as variability in the diversity of units (e.g. variation in the composition of ethnic groups in a census
section: Reardon & Firebaugh, 2002).
(iv) Segregation measured through indices that are constructed as weighted averages of dichotomous residential
segregation indices (Reardon & Firebaugh, 2002).
With reference to these indices, in Table 2, we report details provided in Reardon and Firebaugh (2002), from
which we have adopted the same notation to formalize the indicators. In particular,
denotes size and π denotes
proportion; subscripts i and j index territorial units; and subscripts m and n index group. Hence,
= number of
cases in territorial unit j; T = total number of cases;
= propor tion in group m;
= propor tion in group m, of
those in unit j.
The multi- group version of the Theil's entropy group index can be written as:
The second index, the multi- group version of the Duncan's dissimilarity index, can be written as:
The third index, the normalized exposure index is:
The last two indices are:
TE 𝜋jmln 𝜋
𝜋jm 𝜋m
𝜋jm 𝜋m
𝜋jm 𝜋m
𝜋jm 𝜋m
    BEN ASSI E t Al.
In the above equations,
deno tes The i l's Entrop y Index (T hei l, 1972) and
represents the Simpson's Interaction
Index (Lieberson, 1969; White, 1986):
As Table 2 shows, belonging to a type of index is not a mutually exclusive condition. The meaning of the dif-
ferent indices is as follows:
Multi- group H is the multi- group version of the popular entropy index H (Theil, 1972; Theil & Finizza, 1971) It
is related to the dimension of evenness but, unlike D, it addresses the social diversity characterizing a given
territor y.
Multi- group D is a multi- group version of the dissimilarity index of Duncan and Duncan (1955). From the
theoretical point of view, this index belongs to the dimension of evenness (Massey & Denton, 1988) and
measures the degree of dissimilarity that exists between different groups that reside simultaneously in a
given territory.
Multi- group P is de ri ved from exposure indices (Bell, 1954; Farley, 1984). It indicates the degree of isolation (low
exposure) that exists between groups, and is relative to the size of the exposure (isolation) according to the
conceptual scheme produced by Massey and Denton (1988).
Multi- group C, which is not derived directly from any bi- group index, was proposed by Reardon and Firebaugh
(2002). It can be interpreted as "as a measure of the variance of the rjm's or "as a normalized chi- squared measure of
association between groups and units" (Reardon & Firebaugh, 2002: 42).
Multi- group R, assumed to be the equivalent of Goodman and Kruskal's τb (Reardon & Firebaugh, 2002),
can be interpreted as “one minus the ratio of the probability that two individuals from the same unit are mem-
bers of different groups to the probability that any two individuals are members of different groups(Reardon &
Firebaugh, 2002: 46).
From a mathematical (Reardon & Firebaugh, 2002) and operational (Lee et al., 2008) perspective, multi- group
H index has the most desirable properties and gives the best performance in empirical terms. However, it should
be remembered that the aim here is not so much to establish the goodness of fit as to understand their behaviour
in different urban contexts, and to try to measure their reciprocal relationship and latent dimensions.
We used a M(c,v) data matrix, where the cases (i.e. statistical units) were the 53 FUAs and the variables were the
five multi- group segregation indices. The statistical analysis described in the following section aims to investi-
gate the relationship between multi- group indices, evaluating a significant part of shared variability by extract-
ing latent factors that reproduce the maximum par t of the variability of the M(c,v) matrix (Di Feliciantonio et al.,
2018; Gavalas et al., 2014; Morelli et al., 2 014). To achieve this, we first calculated a series of linear correlation
coefficients and then performed a principal component analysis (PCA). In addition, we aimed to understand the
relationship between contextual (demographic and socio- economic) variables and multi- group segregation indi-
ces. In this regard, we used a synthesis of all the multi- group segregation measures to consider all the dimensions
of segregation together. To do this, we introduced an ad hoc indicator based on Gismondi and Russo (2004) to
summarize the loadings of the first two components extracted and assume the independence of the components
by construction. The composite indicator is obtained in the following way:
1. Extracting the principal components from the statistical matrix M (c,v);
2. Standardizing the v indices, taking into account the respective average (μ) and standard deviation (σ):
3. Computing the final index (PC index) for each FUA (i) as the weighted arithmetic mean of the standard-
ized indicators (point 2), calculated using the coordinates of the factorial axes and the variance of the
components derived from the PCA (point 1) as weights.
Formally, in the case of the two principal components, the PC index (point 3) is calculated as follows:
where z are the standardized indicators for each variable (i.e. multi- group segregation indices) v and territorial unit
(FUA) i, a represents the coordinates of the factorial axes relative to the two principal components (I and II) and λ ex-
presses the variance of the principal components. This method is based on uncorrelated factors and takes more than
one component into account. Moreover, the weight of the variables in computing the PC index reflects the variance
explained by each factor; in this way, the variables with higher component loadings have greater weights. The index
obtained has been standardized by a linear transformation based on the equation:
thus producing elementary scores ranging between 0 and 1. The index was then used in relation to a key variable in
the labour market (the unemployment rate) to shed lights on its behaviour.
Levels and types of multi- group residential segregation
Before presenting and discussing the results, it is useful to focus on the different composition in terms of foreign-
born population that characterize each country analysed. Table 3 shows some basic population data from 2011.
There is a quite high level of heterogeneity between the countries selected here in terms of the size of the
foreign- born population and the main foreign country of birth recorded in the 2011 census. The highest figure
is from Ireland, where the foreign- born population accounts for about 17% of the total population, while the
lowest (11.2%) is observed in The Netherlands. In Ireland, 72.3% of the foreign- born population came from other
European Union countries. In The Netherlands, United Kingdom and Spain, the vast majority (between 65% and
75%) of the foreign- born population originated from outside the European Union. Germany showed an interme-
diate pattern, with those born outside the European Union slightly exceeding those born in another EU country.
Turkey is one of the two main countries of birth both in Germany and in The Netherlands. Poland is the main
country of birth in 3 countries: the United Kingdom, Ireland and Germany. In Spain, Morocco and Romania are
PC index
v=1zviaIv +𝜆II
PC index
PC Index
PC Index
PC Index
PC Index
    BEN ASSI E t Al.
the main foreign- born countries, while in the United Kingdom, it is India and Poland. Suriname is the second main
foreign- born country in The Netherlands.
The intrinsic ranking of the first 30 FUAs for multi- group indices H, P, D, C and R is illustrated in Table 4, together
wit h the descriptive statistic s for each indicator. As ca n be seen, there is a clea r distinction between the Spa nish FUAs
and the other European FUAs analysed here. The first group shows comparatively higher values of H, D, C and R,
systematically occupying the highest positions in the ranking of these indices. For P, the situation is somewhat differ-
ent, with Leicester coming first, and another two non- Spanish FUA , Bradford and Rotterdam in the top ten positions.
The FUAs of the other countries are relatively scattered in the ranking, with German cities ranking bottom,
on average. In terms of the statistical distribution, we can observe how the min- max and mean values for D are
comparatively high, especially compared to H, since they are two indices of the same dimension of segregation
(evenness). The dimension of isolation (P) is relatively low in all the FUAs here analysed, as are the values delineat-
ing the statistical distribution of C and R.
The relationship between multi- group segregation indices and latent components
All multi- group indices present positive and a relatively high level of linear correlation (from 0.64 to 0.97). This
means that all the indicators are biased in the same direction as regards the concept of residential segregation,
and that there is a significant amount of common variance. This underlines the need for PCA, whose results are
reported in Tables 5 and 6 and Figure 1.
The first two components account, together, for 0.97 of the initial variance (85% the first component and 12%
the second). Component 1 alone accounts for about 0.85 of that variance and assigns positive loadings to all the
multi- group indices analysed here. The highest loadings were assigned to H (0.458) and D (0.461). Based on load-
ings, component 1 can be seen as a latent dimension directly correlated with multi- group segregation (from com-
paratively low- to- negative values on the first axis of Figure 1 to comparatively high- to- positive values on the first
axis in the same figure) and particularly in the dimension of evenness. The second component re cords both positive
and negative component loadings. The highest positive correlation is recorded for P (0.672); the highest negative
correlation is recorded for H (−0.386). This component is more closely related to the dimension of isolation, and
diversity. From Figure 1, we can see clearly the difference between Spanish FUAs and the other urban agglomera-
tio ns . German cit ie s ar e clus tered separately from the rest of conti ne nt al cit ie s in Europe, while Dutc h an d UK cities
are more heterogeneous and substantially concentrated on positive values of both axes 1 and 2.
TAB LE 3 Basic population data for the selected European countries in the analysis, 2011
Population born
(A .V. in 1, 000)
% of total
N o n - E U 2 7
Germany 10,906 13.6 47.9 52 .1 Poland, Turkey
Ireland 767 16.8 72.3 2 7. 7 United Kingdom
Spain 5649 12.1 33.5 66.5 Morocco, Romania
The Netherlands 1869 11.2 24.2 75.8 Turkey, Suriname
United Kingdom 7986 12.6 33.5 66.5 India, Poland
aCroatia was not yet an EU member country in 2011.
bInformation on the main countries from The Netherlands is based on “Dutch Census 2011. Analysis and Methodology
Statistics Netherlands, The Hague/Heerlen 2014 and refers to top 10 immigrant groups in non- EU/EFTA countries by
duration of stay, 2011 (p. 53).
Source: partially based on Benassi, Bonifazi, et al. (2020) on Eurostat 2011 Census Hub data.
TAB LE 4 Ranking of the top 30 FUAs. H, P, D, C and R
Ranking HRanking PRanking DRanking CRanking R
Seville 0.6130 Leicester 0.1929 Seville 0.9498 Barcelona 0.124 0 Zaragoza 0.1777
Bilbao 0.5 426 Zaragoza 0.1817 Las Palmas 0.9114 Madrid 0.1188 Màlaga 0.1694
Valencia 0.5333 Màlaga 0.176 4 Bilbao 0.9071 Màlaga 0.10 41 Barcelona 0.1505
Las Palmas 0.5316 Bradford 0.1590 Valencia 0.8549 Zaragoza 0.1041 Madrid 0.150 1
Màlaga 0.52 55 Madrid 0.1582 Màlaga 0.8404 Valencia 0.1026 Leicester 0.1498
Barcelona 0. 5191 Barcelona 0.1534 Barcelona 0.8005 Seville 0.0953 Valencia 0.1366
Zaragoza 0.48 41 Sheffield 0.1494 Zaragoza 0.7989 Bilbao 0.0901 Seville 0.1364
Madrid 0.4818 Seville 0 .1417 Madrid 0.7660 Las Palmas 0.0885 Bradford 0.1295
Amsterdam 0.2565 Rotterdam 0 .1414 Sheffield 0.5135 Eindhoven 0.0540 Sheffield 0.116 0
Sheffield 0.2531 Valencia 0.140 3 Bradford 0 . 5074 Dublin 0.0514 Bilbao 0.1147
Rotterdam 0.2468 Birmingham 0.1328 Leicester 0.50 07 Essen 0.0458 Rotterdam 0.1 076
The Hague 0.2429 London 0.1239 New Castle 0. 4762 Bochum 0.0441 Birmingham 0.1042
Glasgow 0.2359 The Hague 0.120 9 Birmingham 0.4730 Glasgow 0.0429 London 0.1019
Leicester 0. 23 41 Amsterdam 0.1192 Rotterdam 0. 4726 London 0.0427 Las Palmas 0.1015
Saarbrücken 0.2336 Manchester 0.1189 Leeds 0.4718 Amsterdam 0.0401 The Hague 0.0987
Bradford 0.2327 Bilbao 0.115 7 Saarbrücken 0.4662 The Hague 0.0386 Amsterdam 0.0977
New Castle 0.2302 Leeds 0 .1112 Glasgow 0.4640 Leicester 0.0376 Manchester 0.0904
Eindhoven 0.2286 Las Palmas 0.1105 Manchester 0.4523 Augsburg 0.0370 Dublin 0.0882
Leeds 0.2238 Glasgow 0.1096 Liverpool 0. 4519 Sheffield 0.0368 Glasgow 0.0879
Birmingham 0.2225 New Castle 0.1080 Nottingham 0.4497 Hamburg 0.0368 Leeds 0.0851
Liverpool 0.2153 Nottingham 0.1053 Amsterdam 0.4367 Duisburg 0.0367 Liverpool 0.0808
Essen 0. 2151 Augsburg 0 .1027 Cardiff 0.4338 Leipzig 0.0362 New Castle 0.0781
Freiburg 0. 21 51 Dublin 0.1020 Nuremberg 0.4278 Utrecht 0.0359 Nottingham 0.0778
Utrecht 0. 214 4 Liverpool 0.1012 Augsburg 0.4271 Edinburgh 0.0358 Eindhoven 0.0774
Manchester 0.2135 Nuremberg 0.0937 Freiburg 0.4271 Birmingham 0.0353 Edinburgh 0.0735
    BEN ASSI E t Al.
Ranking HRanking PRanking DRanking CRanking R
London 0.2064 Freiburg 0.0936 Eindhoven 0.4211 Munich 0.0350 Augsburg 0.0732
Nottingham 0.2031 Cardiff 0.0929 The Hague 0.4203 Bradford 0.0342 Utrecht 0.0731
Augsburg 0.2006 Eindhoven 0.0906 London 0 .4195 Manchester 0.0339 Cardiff 0.0705
Munster 0.2002 Utrecht 0.0905 Edinburgh 0.4138 Leeds 0.0331 Freiburg 0.0688
Frankfurt 0.1993 Edinburgh 0.0889 Munster 0. 4106 Bremen 0.0329 Essen 0.0685
Min 0.12 Min 0.04 Min 0.31 Min 0.01 Min 0.03
Max 0. 61 Max 0.19 Max 0.95 Max 0.12 Max 0.18
Mean 0.25 Mean 0.10 Mean 0.48 Mean 0.04 Mean 0.08
Sd 0.12 Sd 0.04 Sd 0 .17 Sd 0.03 Sd 0.04
CV 49.19 CV 35.07 CV 35.28 CV 66.82 CV 42.36
N53 N53 N53 N53 N53
Source: authors’ own work based on D4I data.
TAB LE 4 (Continued)
PC index and inequalities in the labour market
Th e PC ind ex al low s us to create a unique rank ing of all the FUAs he re an aly sed. We can rank th e FUA s (Figure 2)
from the one in which the multi- group segregation is the highest (PC index = 1.0 ,laga) to the one in wh ich th e
multi- group segregation is the lowest (PC index = 0.0, Port smouth). It should be noted that here the meaning of
TAB LE 5 Analysis of the eigenvalues of the correlation matrix
Factors Eigen value Proportion Cumulate
14.2348 0.8 470 0.8 470
20.6161 0.1232 0.970 2
30.134 3 0.0269 0.9970
40.0094 0.0019 0.9989
50.0055 0.0011 1.0000
Source: authors’ own work based on D4I data.
TAB LE 6 Component loadings
Multigroup segregation
indices 1st comp 2nd comp 3rd comp 4th comp 5th comp
H0.458 −0.386 0.317 0.644 0.353
P0.412 0. 672 −0 .104 0. 245 0. 555
D0.461 −0.320 −0.490 −0.592 −0.309
C0.4 47 −0.332 0.795 0.199 0.133
R0.456 0.431 0.129 0.368 0. 674
Source: authors’ own work based on D4I data.
FIGURE 1Factorial plane and statistical unitsa.
Source: Authors' own work based on D4I data. (a) Red: Spain, blue: UK, orange: The Netherlands, black:
Germany, green: Ireland
-6 -4 -2 0246
PC 2
PC 1
    BEN ASSI E t Al.
“highest” and “lowest” refers to the empirical distribution of PC index based on the standardized version of the
index (Equation 8). The distinction between Spanish FUAs and the other FUAs is evident. Only 10 FUAs record
a standardized PC index value over 0.5: all the 8 Spanish FUAs plus two UK FUAs (Leicester and Bradford). In
terms of statistical dis tribution, the standardized PC index has a mean value of 0.35, a median value of 0. 25 and
a coefficient of variation of 76.3%.
In this perspective, it is clear that the Spanish FUAs, belonging to Southern Europe, and all the other FUAs an-
alysed here, belonging to Central and Northern Europe, differ greatly. These two ‘blocks’— that is, two areas within
the same main economic areas— are characterized by different levels of economic development and wealth and by
different dynamics of the labour market. Typically, the level of unemployment is much higher in Southern Europe
compared with Northern Europe. Moreover, the economies of the former are characterized by a comparatively
high level of informal sector dynamics and low labour productivity.
One way to test whether the PC index behaviour is coherent with this evidence is to compare its distribution
with the unemployment rate in the FUAs here selected. The results are clear (Figure 3): the relationship between
the unemployment rate and PC index in the selected FUAs – that is, between unemployment and multi- group
segregation – is positive, with a linear correlation coefficient of 0.81. In metropolitan contexts where the unem-
ployment rate is low, the PC index of multi- group segregation is low, and the opposite holds for contexts with high
unemployment rates.
As Piketty recently argued (Piketty, 2020), in an increasingly unequal society, where accumulation has become
the key to the social system, we can consider the residential market and all its social dimensions as one of the
variables that best reflects the growing inequalities and inconsistencies of the neoliberal economic model. In
FIGURE 2PC index (standardized). Selected FUAs.
Source: Authors' own work based on D4I data
this context, given the growing ethnic and cultural diversity of European societies, it is more necessary than
ever to generate flexible and useful tools to analyse processes of integration and segregation in the foreign
population (Auspurg et al., 2017 ) to develop effective policies to build a more cohesive European society
(Piekut et al., 2019).
Based on these assumptions, our study set out to answer two main research issues: (i) first, from a method-
ological/technical point of view, we looked at the validity and interrelation of the multi- group indices for analysing
segregation patterns and (ii) second, from a socio- territorial approach, we tested the usefulness of these indices
when relating them to the main social variables that account for segregation. In this perspective, our study in-
cludes, for the first time as far as we know, an in- depth reflection about multi- group segregation levels using
comparative data, functional and standardized geographies (Functional Urban Areas) and a unique indicator (PC
index) that summarizes several dimensions of multi- group segregation simultaneously.
From a me thodolo gical poi nt of vi ew, the em pi rical result s of thi s study provi de new eviden ce for analysing re s-
idential segregation in multi- ethnic settings. We can see how H and D, as indices that show the uniformity and dis-
propor tionalit y of the groups anal ysed, are the most sui table scales for measuring th e degree of diver sity in tod ay 's
multi- ethnic societies. We can therefore consider them of special importance when analysing the degree of ethnic
diversity of a society and its territorial impact. It is also a valid socio- territorial indicator to relate to other socio-
economic variables, and allows us to arrive at a better diagnosis of the levels of socio- territorial cohesion. In turn,
similar values of P and R reflect their contribution to the analysis of the potential social interaction of the foreign
popula tion with the native populati on. The P and R indices, by estim ating the possibilit y of sharing common spa ces,
can therefore play a fundamental role in helping us to understand the spatial dimension of interethnic relations, as
different theoretical approaches have shown (e.g. Allport, 1954; Blalock, 1967; Iglesias- Pascual et al., 2019).
The analysis of the relationship of multi- group segregation indices with social variables shows how a com-
prehensive understanding of urban segregation is only possible if they are intended as a spatial result of (urban)
inequalities (van Ham et al., 2021). Our macro- scale findings, in line with recent studies at a micro- local level
(Marcińczak et al., 2021), show that segregation is higher in the urban areas of Europe with a less stable economy
FIGURE 3Scatterplot between PC index standardized (y axe), and unemployment rate as a share of labour
force (%). 2011a.
Source: authors’ own work based on D4I data and on data from OECD city and region data base. aRed: Spanish
FUAs. y = 0.0333x + 0.0284; R2 = 0.66; r = +0.81 (for all FUAs). y = 0.0159x+0.132; R2 = 0.10; r = +0.33 (for
non- Spanish FUAs)
    BEN ASSI E t Al.
and a high level of social vulnerability (e.g. Spain) than in its Central and Northern counterparts. Intense multi-
group segregation in Spanish metropolitan areas, an aspect that has already been partially analysed (Benassi,
Iglesias- Pascual, et al., 2020), confirms the importance of carrying out a comparative analysis of the real estate
markets in each country. In areas of growing multi- culturalism and greater social vulnerability, a relevant aspect
that deserves further investigation is the inherent difficulty for migrants to access the housing market (Farley
et al., 2000; Iglesias- Pascual, 2019; Van der Bracht et al., 2015).
Moreover, intense multi- group segregation allows us to relativize the idea that Spanish attitudes towards im-
migration have been an exception within Europe (Rinken and Trujillo- Carmona, 2018). In fact, so far, there have
been no major social reactions against migrants, nor can the recent rise of the extreme right in Spain be linked
to the presence of a migrant population as clearly as in other European countries (Iglesias- Pascual et al., 2021).
However, it is evident that these high values of residential segregation can be understood as a sign of the low
degree of prejudice felt by the Spanish population towards their migrant population.
One clear indication of this emerges from the analysis of the PC index in relation to unemployment: the
higher the unemployment rate, the higher the PC index values. Many recent studies have gained important in-
sights into the relationship between urban segregation and economic inequalities (van Ham et al., 2021) and the
importance of the labour market in defining residential segregation (Benassi, Bonifazi, et al., 2020). Conversely,
when the unemployment rate is low, multi- group segregation is low. The vicious circle of marginality has been
clearly highlighted in a recent study (Benassi, Iglesias- Pascual, et al., 2020). This evidence demonstrates how
multi- group segregation rates increase in contexts of high unemployment, with more saturated housing markets
in places where migrants are more segregated, due to the greater difficulty in accessing housing.
Our results indicate how, to reduce the level of urban segregation, it is necessary to reduce inequalities between
urban Europe in terms of unemployment and to help local public institutions to develop more active housing poli-
cies that do not leave housing management exclusively in the hands of the real estate market. As we have seen
since the economic crisis of 2008, the housing market seeks efficiency and profit, not social equity. By reshaping
the foundations for inclusive societies and more cohesive local contexts, new forms of active intervention are
needed to reduce social segregation and economic divides. The current pandemic, naturally poses an added health
threat as well as socio- economic inequalities. It would not be reckless to assume that these effects are greater in
the most fragile and, above all, less socially cohesive contexts, affecting especially the most vulnerable popula-
tions. New avenues for research are also opening up on the basis of our results, which we hope can be followed.
On the one hand, the current census round will produce new population counts, also in relation to foreigners.
These new data, if processed and made available on regular grids consistent with those used in the study, may
provide an oppor tunit y to assess the spatial and temporal evolution of the level of residential segregation in
European metropolitan areas. On the other hand, hopefully, the recovery of the economy thanks in part to the
post- pandemic investment plans will lead to a recovery in the labour markets, which could in turn result in lower
unemployment rates and a corresponding decrease in the level of multi- group residential segregation, given the
negative correlation between the two quantities. To be able to design spatially and territorially appropriate poli-
cies, it is therefore necessary to invest in refined population statistics based on regular grids.
This work was supported by grants from the Ministry of Economy, Industry and Competitiveness of the
Spanish Government (RTI2018- 095325- B- I00), funding for open access publishing: Universidad Pablo de
Olavide/CBUA. The opinions expressed in the paper are the ones of the authors and do not necessarily reflect
the ones of their institutions.
The peer review history for this article is available at https://publo blo n/10 .1111/imig.13018.
Federico Benassi
Alessia Naccarato
Ricardo Iglesias- Pascual
Luca Salvati
Salvatore Strozza
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