# Spatiotemporal gender differences in urban vibrancy

Thomas Collins  0000-0003-1791-7002 Riccardo Di Clemente  Complex Connections
Lab, Network Science Institute,
Northeastern University London
London, E1W 1LP, United Kingdom.  The Alan Turing Institute
London, NW1 2DB, United Kingdom.  0000-0001-8005-6351 Mario Gutiérrez-Roig
Department of Mathematical Sciences
University of Essex, Colchester
CO4 3SQ, United Kingdom.  0000-0002-8488-1954 Federico Botta  Department of
Computer Science
University of Exeter, Exeter
EX4 4QF, United Kingdom.  Complex Connections Lab, Network Science Institute,
Northeastern University London
London, E1W 1LP, United Kingdom.  0000-0002-5681-4535

Urban vibrancy is the dynamic activity of humans in urban locations. It can
vary with urban features and the opportunities for human interactions, but it
might also differ according to the underlying social conditions of city
inhabitants across and within social surroundings. Such heterogeneity in how
different demographic groups may experience cities has the potential to cause
gender segregation because of differences in the preferences of inhabitants,
their accessibility and opportunities, and large-scale mobility behaviours.
However, traditional studies have failed to capture fully a high-frequency
understanding of how urban vibrancy is linked to urban features, how this
might differ for different genders, and how this might affect segregation in
cities. Our results show that (1) there are differences between males and
females in terms of urban vibrancy, (2) the differences relate to ‘Points of
Interest‘ as well as transportation networks, and (3) there are both positive
and negative ‘spatial spillovers‘ existing across each city. To do this, we
use a quantitative approach using Call Detail Record data–taking advantage of
the near-ubiquitous use of mobile phones–to gain high-frequency observations
of spatial behaviours across Italy’s seven most prominent cities. We use a
spatial model comparison approach of the direct and ‘spillover‘ effects from
urban features on male-female differences. Our results increase our
understanding of inequality in cities and how we can make future cities
fairer.

_Keywords_ urban vibrancy $\cdot$ urban gender segregation $\cdot$ mobile
phone data $\cdot$ spatial data science

##  1 Introduction

As the world continues to urbanize at an unprecedented rate, the lives of city
inhabitants are transforming, with both unprecedented opportunities but also
growing challenges and complexities that cannot be ignored. The United Nations
reported that, by 2050, $68\%$ of the world’s population will be living in
cities (UN DESA, 2019) and that, while urban populations are increasing, rural
populations are in decline. This trend toward urban life is thought to be
related to economic development alongside changes in social organisation
(Harris, 1990; Bettencourt et al., 2007), how humans use land (Liu et al.,
2020), and the drastic changes in the patterns of collective human behaviour
(Thomas, 2008; Bettencourt et al., 2007). Rapid urban growth is thought to
make cities more innovative and generate wealth but can cause large-scale
social issues for people and communities. These include reduced housing
affordability (Nelson et al., 2002), environmental degradation (El Araby,
2002), high crime rates with negative effects on economics, education, and
health (Glaeser and Sacerdote, 1999), greater disease incidence (Connolly et
al., 2021; Santana et al., 2023) and traffic congestion (Zheng et al., 2014;
Bassolas et al., 2019; Kalila et al., 2018; Xu et al., 2021).

Tóth et al. (2021) reported that rapid city growth can increase segregation
and inequality in urban areas (Tóth et al., 2021). Indeed, in cities in the
United States, life expectancy has generally increased in the middle classes
whereas, in poorer classes, it has remained the same (Bor et al., 2017).
Within the spatial structure of cities, some neighbourhoods have become
differentially desirable. More expensive locations force lower-income
inhabitants away, and in some cases, to the fringes of cities or areas with
increased levels of criminality or poverty (Weller and van Hulten, 2012). This
can generate a powerful reinforcement loop thought to block those wishing to
move to the area and hinder social mobility further.

One way to understand and quantify socio-spatial segregation in cities has
been to use traditional data, like a census. However, by being based only on
where people live, such data only ever ‘scratch at the surface‘ regarding the
quantification of the fascinating details of urban environments and the
relationship to our social lives and our ‘quality-of-life‘ (Entwisle, 2007;
King, 2013). Thus, city planners increasingly look to new technologies to
study collective human behaviour and, especially, to characterise mobility
patterns (Steenbruggen et al., 2015). Data on broad movement behaviours are
now accessible due to widespread interaction with technological systems
(González et al., 2008) and computer technology can help to reveal patterns in
human behaviour. The world’s near-ubiquitous uptake of mobile phone technology
and social media generates huge amounts of data on our behaviour and mobility
(Lazer et al., 2009; Vespignani, 2009; Salesses et al., 2013; Botta et al.,
2015; Seresinhe et al., 2016; Preis et al., 2020). From shopping habits (Di
Clemente et al., 2018; Bannister and Botta, 2021; Xu et al., 2019) to
transportation (Su et al., 2022), there is an unlimited array of uses afforded
to us due to this new ability to track and record the movements of citizens.
This new direction has provided an extraordinary new understanding of urban
environments and cities (Batty, 2013; Pan et al., 2013; Botta et al., 2015;
Barthelemy, 2016; Botta et al., 2020).

Mobile phone data can support the study of _urban vibrancy_ or _urban
vitality_ , which measures the activity of urban environments (Sulis et al.,
2018; Botta and Gutiérrez-Roig, 2021; Wang et al., 2021). Urban vibrancy is a
concept that has been extensively theorised. Jane Jacobs was hugely
influential in highlighting how urban design could encourage urban vibrancy
and her arguments often focused on the maintenance and provision of social
interactions in cities (Jacobs, 1961). Her greatest addition to theory is an
understanding that density and diversity in the physical structure of an urban
place might affect its functional use (Moroni, 2016) and that locations that
are more diverse – or more concentrated, in terms of their street networks,
buildings, or ‘Points of Interest‘ – may be the most vibrant locations. Thus,
city planners should consider diversity and social accessibility because
diversity provides social cohesion and supplies opportunities for spontaneous
interactions, subsequently allowing high levels of creativity and activity
that are accessible to the inhabitants and also maintain the community with a
diverse socioeconomic background (Perrone, 2019).

We follow on from previous work by Botta and Gutiérrez-Roig (2021) that found
that _third places_ – i.e., places that humans use, that are neither home
(_first places_) or work (_second places_) places and are specific in that
they are used for social interactions – are important predictors of urban
vibrancy levels across age groups. Here, we study gender segregation and urban
inequality through the lens of urban vibrancy. We explore the link between
urban features and urban vibrancy and whether this differs for different
genders, resulting in spatial segregation. We use a large data set that
contains the presence of males and females in urban spaces, as measured via
mobile phone activity data, as well as _OpenStreetMap_ geographical data, and
residential census data. We use mobile phone activity data as a proxy
measurement for urban vibrancy and analyse which urban features contribute to
urban vibrancy for different social groups, particularly males and females. We
find that there are differences between males and females in terms of urban
vibrancy. Indeed, the differences relate to ‘Points of Interest‘ and
transportation networks; however, there are both positive and negative spatial
‘spillovers‘ that exist across each city. We discuss how these differences
could be accounted for in urban planning and design, and how human interaction
with large technological systems provides a wealth of data that can complement
that derived from more traditional methods of monitoring populations. This
could allow social problems, such as spatial segregation, to be measured more
accurately, and at faster rates, so that social problems might be solved more
easily by policymakers and urban planners for the cities of the future. We aim
to further the understanding of gender differences (Vaitla et al., 2017) and
segregation in urban spaces.

##  2 Data

We use three main data sources: (1) Italian census data that contains detailed
information on where people live, (2) Call Detail Records data (CDR), derived
from mobile phones, containing information on where people are at a high
temporal granularity, and (3) _OpenStreetMap_ (OSM, 2017). We use OSM data
because it provides measurable features of urban environments. For each data
type, we gather data for only the ‘metropolitan areas‘ of each city because
these areas are the most densely populated areas of cities (see Supplementary
Materials for summary statistics Table SI 1). Metropolitan cities are areas
that are linked to the city in terms of its culture and economy as well as its
geographic proximity. Data for the metropolitan area boundary were gathered
from the Italian Office for National Statistics (‘ISTAT‘) (ISTAT, 2023). Data
can be made available on request. We outline the data sources below.

###  2.1 Italian census data

The _ISTAT_ census (ISTAT, 2023) is conducted every decade in Italy. Census
sections are small, typically with 250 households, and provide total
population and gender counts per section. We use 2011 census data downloaded
from the ISTAT to confirm resident locations during key times of the day.

###  2.2 Call Detail Record data

We use mobile phone Call Detail Record (CDR) data from _Gruppo TIM_ (formerly
_Telecom Italia_) that was made available as part of their ‘ _Big Data
Challenge 2015_ ‘ (described in GruppoTIM (2015)). The CDR data is available
for seven different cities: _Milan_ , _Rome_ , _Turin_ , _Naples_ , _Venice_ ,
_Palermo_ , and _Bari_ , covering approximately two months (from 23:00 GMT on
2015-02-28 to 21:45 GMT on 2015-04-30). Each CDR data set has a corresponding
grid designed by _Telecom Italia_ (GruppoTIM, 2015). Each grid takes into
account the topology of each city and the potential communication load. Each
spatial grid was also designed to maintain the privacy of the inhabitants of
each city. Subsequently, the grid polygons change shape in relation to the
underlying mobile cells: cells typically get smaller the closer they are to
the centre of each city. The activity of the data has a granularity of
fifteen-minute intervals; however, there are time points in the CDR data that
contain no records; this may occur because the number of users drops below
three, and no data is recorded to preserve privacy, but there may also be
further issues such as cutouts or problems in the collection of the data. The
data contain the gender of the user who generated the CDR within the network
(see CDR summary statistics Table SI 2). The data contain a value for each
gender and the gender is derived from the registration of the SIM card of male
and female mobile phone users. Therefore, the data shows male and female use
across time.

A related data set has already been used to understand how different age
groups interact with cities (Botta and Gutiérrez-Roig, 2021). This is possible
because this type of data allows us to analyse and investigate the existence
of differences across social groups instead of aggregating across a
population, where information concerning the differences between social groups
is neglected or reduced.

We utilize the mobile phone CDR data set as a vector-based proxy for measuring
urban vibrancy in the cities under investigation because prior research
findings demonstrate consistent effectiveness in studying urban vibrancy
(Sulis et al., 2018; Wang et al., 2021; Botta and Gutiérrez-Roig, 2021).
Though graph-based metrics are also used to measure urban vibrancy (Wang et
al., 2018), we approximate urban vibrancy in a vector-based way because the
method allows fine temporal and spatial granularity and because we can
separate the data according to gender. We intend to use these data to
understand differences between social groups to understand how urban features
contribute to a vibrant environment with respect to gender. We have aggregated
the cell–user data across an array of time periods such that we get metrics
pertaining to urban vibrancy in each grid cell.

###  2.3 _OpenStreetMap_ data

To understand cities, we must first create representations of their
characteristics. Creating such representations has only recently been made
easier thanks to collaborative projects such as _OpenStreetMap_ (OSM, 2017).
OSM is an open-source data repository generated and collected by volunteer
collaborators. The data that is formed consists of large-scale geographic data
that is made freely available to users. It is possible to download data on an
array of city attributes including the networks, systems, and features of
urban landscapes. Here, we retrieve data for each study area; however, it is
important to note that the data that was downloaded was the most up-to-date
version of the urban features. What we derive from these data is explained
systematically in the next section.

##  3 Methods

###  3.1 A proxy for urban vibrancy: Call Detail Records

As a proxy measure for urban vibrancy, we use CDR data as it indicates the
presence of inhabitants throughout the day. We calculate gender differences by
subtracting the male value from the female value:

$\displaystyle\Delta_{i}=M_{i}-F_{i}$ (1)

where $\Delta_{i}$ represents the vector of differences, $M_{i}$ is the vector
of male users, and $F_{i}$ is the female users.

Gender identity was only available for users who disclosed it when acquiring
their SIM cards. Users who did not disclose their gender were excluded from
the analysis. As described in Section 2.2, gaps in the data occur when the
number of users falls below three to protect their anonymity. To fill in these
gaps, we assumed a value of zero for these time points. The grid consists of
cells of varying sizes, so we normalized the raw data by the area of each grid
cell to obtain a population density that accounts for the usage and topology
of each cell in relation to the city.

###  3.2 Cities as networks: Independent variables

We downloaded for each static grid cell of each city a range of features shown
to be related to urban vibrancy by previous research (Sung et al., 2013; Botta
and Gutiérrez-Roig, 2021; Yu et al., 2022; Chen et al., 2022). We processed
these features in two ways as outlined below.

####  3.2.1 _Density_ in urban features

By Jacobs (Jacobs, 1961), increased feature density was a promoting factor in
urban vibrancy because of the increased activity. The density of buildings,
highways, networks, intersections, or ‘Points of Interest‘ in a place, all
have the potential to provide more opportunities for activities because of the
increased number of users of those locations, or the increased vehicular or
pedestrian access; however, importantly, these might differ across genders.
Here, we define density as the concentration of a feature type within a given
area. To arrive at the density value, we first download features from the free
geographical database: _OpenStreetMap_ (OSM; see Section 2). We construct
feature collections of the buildings, transport networks, and ‘Points of
Interest‘ found in each cell of each city. We took the total count per cell
and divided it by the total area of that cell to give a value of the feature
density. For the networks, we calculated the average length of transport
networks or the average number of intersections, that are accessible for (1)
pedestrians, (2) cyclists, and (3) drivers. We used the following calculation
to determine feature density:

$\displaystyle\rho=\frac{N}{A}$ (2)

where $\rho$ is the density, $N$ is the total number of features in the
geometry, and $A$ is the area of the geometry. The values were added to the
grid cells for each city (see Figure SI 2).

####  3.2.2 _Diversity_ in urban features

According to Jacobs, it is the diversity in features that increases and
encourages a location’s vibrancy (Jacobs, 1961). Similarly to above, in a
place, the diversity of buildings, highways, or ‘Points of Interest‘ all have
the potential to provide more opportunities for activities because of the
increased usage of those locations; however, these might differ across
genders. To gather data on urban feature diversity we use the same downloaded
OSM feature collections. We use the Shannon-Wiener diversity index (Shannon,
1948) to calculate the diversity of features. The diversity index is
calculated as follows:

$\displaystyle H=-\sum_{i=1}^{M}P_{i}\,log_{2}\,P_{i}$ (3)

where $H$ is the diversity index, $M$ is the total number of categories in the
geometry feature, and $P_{i}$ is the frequency of the $i\textsuperscript{th}$
category. The values were added to the grid cells for each city (see Figure SI
2). We detail the ‘Points of Interest‘ variables below.

##### ‘Points of Interest‘:

‘Points of Interest‘ are important features that directly relate to urban
vibrancy. We collected all ‘Points of Interest‘ from OSM found under the
amenity, building, leisure, shop, and sport tags in the OSM database to
construct a ‘Points of Interest‘ collection for each city. We manually labeled
the points using the same label collection as Moro et al. (2021) and Fan et
al. (2022), based on the Foursquare classification system, which includes 14
categories. This taxonomy of labels is as follows: (1) _Arts / Museum_ , (2)
_City / Outdoors_ , (3) _Coffee / Tea_ , (4) _College_ , (5) _Entertainment_ ,
(6) _Food_ , (7) _Grocery_ , (8) _Health_ , (9) _Residential_ , (10) _Service_
, (11) _Shopping_ , (12) _Sports_ , (13) _Transportation_ , and (14) _Work_.
We considered these labels because they represent the most frequently visited
locations and are likely to be important for segregation (Moro et al., 2021).

##### ‘Third Places‘:

We constructed a collection of ‘ _Third Places_ ‘ (Oldenburg and Brissett,
1982). Third Places are locations that are neither home nor workplaces and are
considered to be vitally important in terms of urban vibrancy because they
allow for impromptu everyday gatherings in urban locations that result in
positive effects for communities (Jeffres et al., 2009; Botta and Gutiérrez-
Roig, 2021) and because people spend a significant fraction of their free time
in third places. For this analysis, we considered that there may be
differences between genders in how they use amenities like shops, pubs, cafés,
or community centres. And that this was likely to be used differently
depending on general discrepancies in urban mobility diversities and, amongst
others, related to socioeconomic characteristics.
Here, using the same ‘Points of Interest‘ tags used in OSM (i.e., ‘amenity‘,
‘building‘, ‘leisure‘, ‘shop‘, and ‘sport‘), we calculated density and
diversity for third places (as defined in Section 3.2.1 and 3.2.2) across all
grid cells and cities. We manually labeled third places based on Jeffres et
al. (2009)’s categorization of (1) _eating and drinking_ , (2) _organized
activities_ , (3) _outdoor_ , and (4) _commercial venues_ , and added a fifth
label of _commercial services_. Commercial services are based on the locations
where people might receive a service or go with the intent of buying
something, but where you may also have opportunities for social interactions
that might be brief compared to the other groupings. We included this label to
capture the potential for brief social interactions in locations like banks
and pharmacies that would have otherwise been removed due to Jeffres et al.
(2009) definition. Only those locations that fit within these categories were
considered third places.

###  3.3 Statistical approach

In this analysis, the Call Detail Record (CDR) data and census data have
different spatial grids. We use the geometry of CDR data as our main reference
and extract OSM data for each cell. We interpolate census data to the same
spatial grid using areal interpolation (Comber and Zeng, 2019; Bergroth et
al., 2022) to enable correlation analysis and spatial linear regression at the
grid cell level (for an overview of the methodology, see SI 1).

We perform a correlation analysis to test the data’s representativeness by
comparing the CDR data (we used the nighttime values only) with census counts
that have been converted to density estimates, matching the CDR data in terms
of spatial scale and intensive property. We compare both male and female
nighttime CDR values with their respective interpolated census data and use
Kendall’s correlation coefficient as it is distribution-free and more suitable
for spatial data (Hamed, 2011). We carry out this analysis in all cities.

We aim to model male-female differences for each city while also building an
aggregated model to identify common trends. We refer to this aggregated model
in many of the analyses below for clarity. To ensure comparability, we
standardize all variables. We then construct an ordinary least squares (OLS)
model as a baseline method for estimating the regression $\beta$ coefficients
and evaluating the importance of spatial extensions to OLS. We use the
following linear function to explain male-female differences as a function of
a set of separate features denoted by $X$ (See Section 3.1):

$\displaystyle Y=\beta_{i}X_{i}+\epsilon$ (4)

where $Y$ represents the male-female differences as a response variable
consisting of a value proportional to the users per gender used here as a
proxy for activity and a measure of vibrancy (see Section 3.1), $\beta_{i}$
are the regression coefficients, $X_{i}$ is the independent variables, and
$\epsilon$ is the error.

Our data may have spatial autocorrelation, which violates some assumptions of
a basic regression model. We address this issue in the following sections.

We diagnosed spatial dependence by analyzing OLS model residuals. The error
terms may not be independent due to a spatial relationship, so we checked for
spatial structure and the need for spatial models using Moran’s _I_ analyses
from Ward and Gleditsch (2019). Spatial clustering implies spatial dependence,
and so requires spatial models.

We use maximum likelihood estimation to create spatial lag and spatial error
models (Anselin et al., 2006; Ward and Gleditsch, 2019). The Lagrange
multiplier and AIC difference from OLS were calculated. We utilized _Queen’s
contiguity_ based on grid-cell geometry for spatial weights’ matrix,
connecting centroids of observations to those with shared vertices (Rey and
Anselin, 2010). We used row transformation to normalize the weights’ values to
achieve an average of variable values in each observation’s neighbourhood. We
chose Queen’s contiguity due to the irregular grid size. To assess the
sensitivity of the choice of spatial weights, we replicate the same analysis
using both Rook’s contiguity and k-nearest neighbours’ distance as weighting
schemes, and we find qualitatively similar results (see SI 3).

We consider the spatial error model (SEM) as our first model, which
incorporates spatial dependence using a spatially lagged error term:

$\displaystyle Y=X_{i}\beta_{i}+u,u=\rho Wu+\epsilon$ (5)

where $Y$ is the male-female differences as a response variable, $X_{i}$
represents the explanatory variables, $\beta_{i}$ are the regression
coefficients, $u$ is the first error term, $\rho$ is a scalar of the spatial
lag parameter, $W$ is the weights’ matrix (Queen’s contiguity), and $\epsilon$
is the spatially independent error term.
We also utilized spatial lag models (SAR) where dependent variables were
spatially lagged, providing coefficients for both _direct_ and _indirect_
effects of independent variables on the response and mean activity of
neighbouring grid cells (Lesage and Fischer, 2008). The SAR model terms are as
follows:

$\displaystyle Y=X_{i}\beta_{i}+\rho WYu+\epsilon$ (6)

where $Y$ is the vector of the response variable, $X$ represents the
explanatory variables, $\beta$ is the regression coefficients, $\rho$ is a
scalar of the spatial lag parameter, $WY$ is the weights’ matrix (Queen’s
contiguity), and $\epsilon$ is the spatially independent error term.

For each model, we calculated the direct effect, indirect effects, and total
effects due to the challenges associated with interpreting predictors unit
change under ‘spillover’ effects (Anselin and Rey, 2014). Spatial spillover
effects are indirect effects and refer to secondary impacts that result from
the direct effects. To compute these values, we first derived estimated
coefficients for exogenous variables in the model, which yielded the direct
effect that shows the influence of one spatial unit on another (Lesage and
Fischer, 2008). Direct effects are calculated as:

$\displaystyle DE=\beta$ (7)

where $DE$ are the direct effects, $\beta$ are the coefficients of the SAR
model without the spatial lag term.

Contained within the direct effects are both the indirect effects and the
total effects (GuoMeng et al., 2021). To split these apart, we extract the
spatial lag term from the coefficients and divide the coefficients by 1 minus
the spatial lag term multiplied by the largest eigenvalue of the spatial
weights’ matrix which effectively normalizes the coefficients (Lesage and
Fischer, 2008; Bivand and Piras, 2015). Total effects take into account the
full range of impacts that a particular change may have on the spatial system
as a whole (Lesage and Fischer, 2008). Total effects are calculated as:

$\displaystyle TE=\beta/(1-\rho*\lambda)$ (8)

where $TE$ are the total effects, $\beta$ are the coefficients of the
exogenous variable in the spatial lag model, $\rho$ is the spatial lag term,
and $\lambda$ is the maximum eigenvalue from the spatial weights’ matrix.

Finally, we calculate the indirect effects. These refer to the secondary
impacts that result from the direct effects. Indirect effects are a measure of
any spillover effects that occur beyond the immediate spatial units (Lesage
and Fischer, 2008). Indirect effects are calculated as:

$\displaystyle IE=DE-TE$ (9)

where $IE$ are the indirect effects, $DE$ are the direct effect and $TE$ are
the total effects.

Using the above methods and data, we created a hierarchy of models that
aggregated CDR data at different time periods. These included: (i) All daytime
data (08:00-20:00), (ii) Weekdays (Monday-Thursday) versus Weekends (Friday-
Sunday) within the all-day time period, and (iii) Twenty-four-hour day data
divided into Morning (06:00-12:00), Afternoon (12:00-18:00), Evening
(18:00-00:00), and Night (00:00-06:00) categories. Models were run for
individual cities and for all cities combined. This approach enabled us to
study how vibrancy relates to gender and urban features at different times and
investigate variations over time.

##  4 Results

First, we use Kendall’s rank correlation coefficient (Kendall, 1938) to
compare the census and the Call Detail Record (CDR) data to check
representativeness. Across all cities, we find results were positive and
significant at the $5\%$ level (see Figure SI 5). The lowest $\tau$ for
females is 0.55 (Bari) whereas the highest $\tau$ for females is 0.72
(Torino). For males, the lowest $\tau$ is 0.56 (Bari) whereas the highest
$\tau$ for males is 0.7 (Torino). These strong correlations between the
CDR–when selecting only the nighttime values–and census data show that the CDR
data are broadly representative of the census data. This suggests that the
values of the daytime should also be representative of the movements of the
general population.

Next, we use Kendall’s rank correlation coefficient to compare each urban
feature with the male-female differences. We adjust our results using false
discovery-rated detection to correct for the rate of type I errors in the null
hypothesis. We found that, except for a few instances, all of our results were
positive and were highly significant at the $5\%$ level (_P_ $<$ 0.05). Also,
between density and diversity metrics, diversity often had a smaller
association contrasting with previous work on age groups (Botta and Gutiérrez-
Roig, 2021), we found that smaller cities had larger associations with male-
female differences. See Table 1 for the full correlation analysis results.

Table 1: Correlation between male-female differences and all urban features. For each city and the aggregation of all cities, we calculate the correlation coefficient and associated $p$-value. We have separated the variables into categories of density and diversity. We use Kendall’s tau ($\tau$) rank correlation coefficient because of its particular suitability for spatial data (Hamed, 2011). We can see both the associational strength and directionality of each correlation. We also calculated the average for each variable based on each city but not the aggregation of all cities. $p$-values are shown using their significance stars, where [0 - 0.001] is ’***’, [0.001 - 0.01] is ’**’, [0.01 - 0.05] is ’*’, [0.05 - 0.1] is ’.’, and [0.1 - 1.0] has no symbol. Cities are ordered by the number of grid cells.  Variable | Aggregated | Milano | Roma | Torino | Napoli | Venezia | Palermo | Bari | Average
---|---|---|---|---|---|---|---|---|---
| $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ | $\tau$ | $p$ |
Density
Building | 0.41 | *** | 0.25 | *** | 0.49 | *** | 0.42 | *** | 0.40 | *** | 0.60 | *** | 0.64 | *** | 0.62 | *** | 0.53
Road network length | 0.37 | *** | 0.19 | *** | 0.46 | *** | 0.48 | *** | 0.41 | *** | 0.51 | *** | 0.58 | *** | 0.51 | *** | 0.49
Cycling network length | 0.36 | *** | 0.21 | *** | 0.52 | *** | 0.47 | *** | 0.43 | *** | 0.53 | *** | 0.53 | *** | 0.46 | *** | 0.49
Walking network length | 0.36 | *** | 0.27 | *** | 0.55 | *** | 0.48 | *** | 0.45 | *** | 0.53 | *** | 0.55 | *** | 0.44 | *** | 0.5
Highway | 0.41 | *** | 0.34 | *** | 0.65 | *** | 0.57 | *** | 0.65 | *** | 0.74 | *** | 0.71 | *** | 0.62 | *** | 0.66
Road network node | 0.40 | *** | 0.20 | *** | 0.51 | *** | 0.52 | *** | 0.51 | *** | 0.54 | *** | 0.62 | *** | 0.55 | *** | 0.54
Cycling network node | 0.39 | *** | 0.25 | *** | 0.55 | *** | 0.52 | *** | 0.53 | *** | 0.56 | *** | 0.62 | *** | 0.54 | *** | 0.56
Walking network node | 0.38 | *** | 0.29 | *** | 0.58 | *** | 0.52 | *** | 0.51 | *** | 0.57 | *** | 0.63 | *** | 0.53 | *** | 0.56
Point of interest | 0.42 | *** | 0.29 | *** | 0.58 | *** | 0.50 | *** | 0.13 | * | 0.65 | *** | 0.61 | *** | 0.66 | *** | 0.52
Third place | 0.36 | *** | 0.28 | *** | 0.55 | *** | 0.51 | *** | 0.45 | *** | 0.65 | *** | 0.61 | *** | 0.49 | *** | 0.54
Diversity
Building | 0.08 | *** | 0.14 | *** | 0.29 | *** | 0.32 | *** | -0.04 |  | -0.23 | ** | -0.16 | . | 0.42 | *** | 0.1
Highway | 0.00 |  | -0.10 | ** | 0.19 | *** | 0.02 |  | 0.01 |  | 0.04 |  | -0.02 |  | 0.35 | *** | 0.1
Point of interest | 0.10 | *** | 0.11 | ** | 0.32 | *** | 0.03 |  | 0.44 | *** | 0.44 | *** | 0.13 |  | 0.10 |  | 0.24
Third place | 0.06 | ** | -0.04 |  | 0.27 | *** | -0.04 |  | 0.06 |  | 0.22 | ** | 0.12 |  | 0.20 | * | 0.14
Commercial venue (third place) | 0.30 | *** | 0.27 | *** | 0.42 | *** | 0.46 | *** | 0.27 | *** | 0.54 | *** | 0.48 | *** | 0.34 | *** | 0.42
Organised activity (third place) | 0.20 | *** | 0.10 | ** | 0.40 | *** | 0.15 | *** | 0.20 | ** | 0.46 | *** | 0.22 | * | 0.46 | *** | 0.31
Outdoor (third place) | 0.26 | *** | 0.17 | *** | 0.46 | *** | 0.38 | *** | 0.29 | *** | 0.57 | *** | 0.32 | *** | 0.31 | *** | 0.39
Eating drinking (third place) | 0.31 | *** | 0.26 | *** | 0.50 | *** | 0.41 | *** | 0.22 | *** | 0.53 | *** | 0.36 | *** | 0.33 | *** | 0.39
Commercial service (third place) | 0.27 | *** | 0.24 | *** | 0.45 | *** | 0.40 | *** | 0.24 | *** | 0.46 | *** | 0.42 | *** | 0.37 | *** | 0.39

We use Moran’s spatial autocorrelation analysis to determine the global
Moran’s _I_ of the data and to further understand the data in terms of its
spatial dependence. We extract residuals of an ordinary least squares (OLS)
model at each level of the model hierarchy. We calculate Moran’s _I_
statistics for the male-female differences in each city. For clarity, we
report only the minimum and maximum in the lowest level of the hierarchy (this
does not include the aggregated model which is excluded from this analysis due
to its obvious spatial clustering in different cities), i.e. the daytime data
(08:00-20:00; see Section 3.3). The lowest value for Moran’s _I_ was 0.013,
the maximum was 0.8, and the mean was 0.2. Of the seven cities in the
analysis, two were non-significant at the $5\%$ level, these were Bari and
Napoli; all the rest were significant (_P_ $<$ 0.05). These values confirm the
presence of spatial clustering and spatial dependence; however, these values
alone cannot provide a full account of the presence or absence of spatial
clustering or fully understand the spatial structure of the data; this,
however, provides evidence that spatial models may be more appropriate. See
Supplementary Materials Figure SI 4 and Table SI 3 for full Moran’s _I_
analysis results.

To further test the presence of spatial clustering, we calculate the Lagrange
multiplier test statistic (both non-robust and robust) for the OLS model of
each city and at each level of the analysis. We did this to identify the type
of model most suitable for the analysis. This provides a measure to inform us
whether to use a simple linear model or use either the spatial lag models
(SAR) or the spatial error models (SER) (LeSage and Pace, 2009). At the same
time, we calculate the Akaike information criterion (AIC) of each of the
models. We find that the SAR models most often contain the highest values
(Minimum LMerr = 0.062, _P_ is NS, Maximum LMerr = 410.104; Minimum LMlag =
9.56, _P_ $<$ 0.001, Maximum LMlag = 539.642). The same relationship is also
found for the robust methods. The differences between the AIC of the OLS and
the AIC of the spatial models were consistently greater for the SAR models.
Because these tests consistently pointed toward using the SAR models, and we
observe spatial clustering, we continue the rest of our analysis with SAR
models.

We find fairly consistent results across this hierarchy. Firstly, we find that
smaller cities had larger amounts of error in the estimates than larger cities
and with more variation in the coefficients, most likely due to the size and
number of cells in the smaller cities. Secondly, there are no strong gender
differences between the night and day (see Figures 1, SI 6 and SI 7). In the
larger cities, we find a significant positive indirect effect between male-
female differences and third-place density (see Figure 1); this relationship
is consistent across the three largest cities and the aggregated model. We
also found a significant negative indirect effect between male-female
differences and the density of ‘Points of Interest‘ (see Figure 1). The
pattern was again similar across, this time, the four largest cities and the
aggregated model. We also find a relationship between highway density and all
three of the intersection variables; however, they did not share the
direction. Both cycling and walking intersection density were significant with
positive indirect effects; however, for road intersections, though there was a
negative indirect effect, this was not significant. The highway density was
only significant in the aggregate model (see Figure 1). We found that
diversity metrics generally were not significant; however, we found that the
‘organised activity‘ and ‘outdoor‘ third place categories were significant;
this was not the case for third places generally (see Figures SI 6 and SI 7).
We find that the strongest effect, which was also the most consistent, was the
positive indirect effect of the third place density. We consider this an
interesting finding when coupled with the significant negative indirect effect
found in the ‘Points of Interest‘ variable because the directionality of the
‘Points of Interest‘ variable – without accounting for the social aspect of
the third places – are opposing one another. This could suggest that locations
that fall under our five categories for third places are not equally used by
each gender whereas, the ‘Points of Interest‘ as a whole are used more
equally.

For each level of the nested hierarchy, we report the results of the pseudo-r-
squared values from the models. The pseudo-r-squared is the squared
correlation between the dependent variable and the predictions of the
dependent variable (Anselin, 1988). These values are a measure of goodness-of-
fit and are used to understand the relationship between the model variables.
Our models exhibited relatively high values consistently across cities and
across the hierarchy of models highlighting a good relationship between
independent and dependent variables (see Figures 1, SI 6, and SI 7).

Figure 1: The relationship between density in features and male-female
differences for the spatial model aggregating all cities. The plot shows the
significance of the direct effect; however, the $\beta$ coefficients represent
the indirect effect (see 3.3 for definitions). The plot displays all density
variables, with the y-axis showing the variables for each model and the colour
representing each variable. Panel (A) shows all daytime data between 08:00 and
20:00; Panel (B) displays weekday (Monday-Thursday) versus weekend (Friday-
Sunday) data within the same time period; Panel (C) shows data averaged into
four categories: Morning (06:00-12:00), afternoon (12:00-18:00), Evening
(18:00-00:00), and Night (00:00-06:00). To aid comparison, shapes denote
categories in Panels (B) and (C). Significance is indicated by closed and open
shapes (_P_ $<$ 0.05 and _P_ $>$ 0.05, respectively), and each shape shows the
error bars as a horizontal line. The pseudo-r-squared is reported for each
panel.

##  5 Discussion

In this study, we have focused on modelling _urban vibrancy_ –a measure of the
dynamic activity of human beings in urban environments. For this, we have
considered seven of the largest cities in Italy. We asked how urban features
might contribute to a vibrant environment and how they might vary across
social groups, especially concerning gender. We hypothesised that there would
be differences for different genders because, firstly, heterogeneity exists
generally in how people interact with urban environments (De Palma and
Papageorgiou, 1988) but, secondly, that similarities might correlate most
closely with groups such as gender due to similarity in socioeconomic
characteristics or general behaviours. We used a computational approach to
reveal any potential socio-spatial segregation across our study areas, and we
used a range of relevant urban features taken from urban vibrancy theory (Sung
et al., 2013; Botta and Gutiérrez-Roig, 2021; Yu et al., 2022; Chen et al.,
2022). To model urban vibrancy, we used data showing the presence of mobile
phone users as a proxy–another established methodology (Jia et al., 2019;
Botta and Gutiérrez-Roig, 2021).

We have uncovered a variety of findings. First, we have been able to study
urban vibrancy–and potential segregation in urban vibrancy–by using high-
frequency Call Detail Record (CDR) data and open-source geographical data. We
show that it is possible to do this with high predictive power and goodness-
of-fit, and we do this across a model hierarchy that accounts for movement
behaviours in order to reflect the reality of life in cities. Second, we have
furthered discussions from previous works that focused on the importance of
third places in cities: we found significant evidence that an increase in the
density of third places in a given area is associated with larger male-female
differences in urban vibrancy whereas an increase in the density of ‘Points of
Interest‘ overall (i.e., without specifically considering third places) is
associated with smaller male-female differences. The evidence that third
places are associated with larger differences could suggest that locations
that we have defined as third places, i.e., locations that fall under our
five-category system (see Section 3), are not equally used by each gender.
This evidence does not necessarily mean that increases in the density of third
places increase differences; however, it may be that certain types of third
places are unequally used across genders. Reasons for this could be based on
cultural differences or socioeconomic factors. Another part to consider is the
clustered nature of third places in cities: a positive indirect effect
indicates increases in male-female differences but also that the variable is
positively correlated with the neighbouring values of male-female differences.
It is important to consider that third places are places that are likely to
cluster geographically with other factors such as economic activity or
environmental conditions. More evidence would be needed to uncover further
details but a similar methodology could be used with extensions and additional
analyses. One such methodological adaptation could be the use of a
Geographically Weighted Regression. This would help to understand the
predictive power across cities whilst exploring potential spatial biases in
the data.

Within our analysis, we can identify a number of limitations, and it is
important to acknowledge these and discuss them here. Firstly, our CDR data is
used as a proxy for urban vibrancy measurement; these data are from Telecom
Italia, just one provider. Though this is the largest provider in Italy, these
data do not capture the entire population and so may contain unknown biases. A
full account of the general population could be gained by using multiple
providers and may improve our overall analysis. It is also the case that the
data were only derived from phone calls; this clearly misses a breadth of
other communication methods and could potentially hide biases in the data due
to the myriad of different ways people communicate today. Furthermore, gender
information is derived from SIM purchases, but this is likely to not be an
exact representation of the gender of users. However, we also note that our
validation with the census data shows a good correlation with the mobile phone
data, suggesting that these issues may be relatively limited (see Figure SI
5). A second potential problem is that the data are from differing time
periods: we have taken census data from 2011, CDR data from 2015, and
_OpenStreetMap_ data from 2022. This undoubtedly introduces some biases in the
analysis; however, we expect them to be small and not affect the overall
results.

In this study, we have considered the modelling of _urban vibrancy_ with
respect to gender differences. We found that the density of different
collections of ‘Points of Interest‘ are simultaneously associated with both
decreases and increases in male-female differences. This was the case when we
gave a broad-scale use-category (‘Points of Interest‘) and a fine-scale use-
category that considers the social context of a place (third place). This adds
further evidence for the importance of characterising third places when
studying urban environments and urban vibrancy. This evidence also suggests
that comparing different collections of ‘Points of Interest‘ could hold
interesting avenues for further research relating to urban vibrancy. We have
shown that this could also provide details on the potential segregation we
find existing in cities today.

To conclude, our analysis provides further evidence and support for the use of
CDR and crowdsourced data to understand large-scale movement behaviours and
how we can use these data to understand the social fabric of urban life. In
turn, this could provide evidence for the design of our future urban
environments.

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## Supplemental material

Table SI 1: Summary statistics for each metropolitan study area. The table shows (i) the total resident population for both males and females, (ii) the total area of each study area, and (iii) the total grid cells taken from GruppoTIM [2015]. 2015 census data taken from ISTAT [2023]. City name | Males | Females | Total | Grid cell
---|---|---|---|---
| (thousands) | (thousands) | area ($km^{2}$) | count
Milano | 1218 | 1334 | 1128 | 794
Roma | 1477 | 1636 | 3746 | 739
Torino | 893 | 966 | 2850 | 494
Napoli | 800 | 846 | 643 | 267
Venezia | 231 | 251 | 1200 | 157
Palermo | 293 | 317 | 2294 | 130
Bari | 309 | 320 | 2363 | 110
Table SI 2: Mean activity across the day. Values are proportional to the number of males and females as an average (mean) across the day and each city. Values are derived from the Call Detail Record data taken for each metropolitan study area. The table shows the values for both males and females in each period of the day. The periods are (i) Morning (06:00-12:00), (ii) Afternoon (12:00-18:00), (iii) Evening (18:00-00:00), and (iv) Night (00:00-06:00). Data are taken from GruppoTIM [2015]. Cities are ordered by the total number of grid cells. City name | Gender | Morning | Afternoon | Evening | Night
---|---|---|---|---|---
Milano | F | 9.509 | 10.460 | 1.991 | 0.644
| M | 12.464 | 12.942 | 2.221 | 0.880
Roma | F | 17.244 | 17.325 | 3.654 | 1.183
| M | 23.020 | 21.585 | 4.134 | 1.650
Torino | F | 9.373 | 10.091 | 1.941 | 0.610
| M | 12.190 | 12.558 | 2.106 | 0.834
Napoli | F | 51.808 | 51.584 | 18.483 | 4.382
| M | 78.761 | 73.633 | 22.874 | 7.067
Venezia | F | 3.503 | 3.783 | 0.498 | 0.196
| M | 6.562 | 6.569 | 0.785 | 0.407
Palermo | F | 29.645 | 27.138 | 6.924 | 2.185
| M | 49.927 | 43.120 | 9.590 | 4.072
Bari | F | 21.804 | 20.271 | 5.867 | 1.878
| M | 38.773 | 33.843 | 8.408 | 3.745
Figure SI 1: An overview of the steps of the analysis. Figure SI 2:
OpenStreetMap (OSM) data types for Roma. OSM provides a range of different
data types, from points to lines, and geometries. These features might be
associated with male-female differences. In the image, we can see (A) ‘Points
of Interest‘, (B) buildings’ locations and geometries, and (C) road lengths
and intersections. Each of the data types contains detailed information
regarding each location. Each of the data types has been used and converted to
a density estimate in the above choropleth. OSM data are taken from OSM [2017]
and are visualised on the Telecom Italia grid for Roma [GruppoTIM, 2015].
Figure SI 3: Comparison of the impact of the spatial weights matrix on the
indirect effects of the spatial error model and spatial lag models for Roma.
The image shows the indirect effects for all variables in the analysis (V 1 –
V 19) when the spatial weights are either Queen’s (contiguity), Rook’s
(contiguity), or k-nearest neighbours (distance) with k values of 2 and 10,
respectively. Figure SI 4: Roma: Visual inspection suggests the presence of
differences between males and females. Each map of Roma shows the male-female
differences derived from the Call Detail Record (CDR) data. The data are split
into four categories for the periods of (A) Morning (06:00-12:00), (B)
Afternoon (12:00-18:00), (C) Evening (18:00-00:00), and (D) Night
(00:00-06:00). CDR data taken from GruppoTIM [2015] and OpenStreetMap data
taken from OSM [2017].  Figure SI 5: Correlation between Call Detail Record
(CDR) data and census data. Orange circles represent females and green circles
represent males. We test the correlation of the data sources following the
process of areal interpolation using Kendall’s tau within a rank correlation
analysis [Hamed, 2011]. This shows a positive relationship between CDR and
census data. Cities are presented in alphabetical order.

Table SI 3: Moran’s I analysis of spatial dependence for each level of the model hierarchy. Model hierarchy | City | City | Moran’s I | Moran’s I (std) |  $p$-value | Sig. star
---|---|---|---|---|---|---
i | Day | Bari | 0.0138 | 0.995 | 0.3197 | ns
|  | Milano | 0.3826 | 21.0432 | 0 | (****)
|  | Napoli | 0.0364 | 1.6846 | 0.0921 | (ns)
|  | Palermo | 0.236 | 5.4222 | 0 | (****)
|  | Roma | 0.3668 | 19.2587 | 0 | (****)
|  | Torino | 0.2483 | 11.3134 | 0 | (****)
|  | Venezia | 0.1171 | 2.8606 | 0.0042 | (**)
| Night | Bari | 0.0312 | 1.3465 | 0.1781 | (ns)
|  | Milano | 0.2449 | 13.5969 | 0 | (****)
|  | Napoli | -0.0173 | 0.0219 | 0.9825 | (ns)
|  | Palermo | 0.1501 | 3.6517 | 0.0003 | (***)
|  | Roma | 0.3463 | 18.2038 | 0 | (****)
|  | Torino | 0.1526 | 7.1234 | 0 | (****)
|  | Venezia | 0.0931 | 2.3704 | 0.0178 | (*)
ii | Week | Bari | 0.0373 | 1.4701 | 0.1415 | (ns)
|  | Milano | 0.3581 | 19.7161 | 0 | (****)
|  | Napoli | 0.0418 | 1.8497 | 0.0644 | (ns)
|  | Palermo | 0.2546 | 5.8043 | 0 | (****)
|  | Roma | 0.3418 | 17.9708 | 0 | (****)
|  | Torino | 0.2356 | 10.7562 | 0 | (****)
|  | Venezia | 0.1237 | 2.996 | 0.0027 | (**)
| Weekend | Bari | -0.0064 | 0.5879 | 0.5566 | (ns)
|  | Milano | 0.3852 | 21.182 | 0 | (****)
|  | Napoli | 0.0135 | 0.9742 | 0.33 | (ns)
|  | Palermo | 0.1932 | 4.5393 | 0 | (****)
|  | Roma | 0.4012 | 21.0345 | 0 | (****)
|  | Torino | 0.2436 | 11.1083 | 0 | (****)
|  | Venezia | 0.1055 | 2.6224 | 0.0087 | (**)
iii | Morning | Bari | 0.002 | 0.7578 | 0.4486 | (ns)
|  | Milano | 0.3749 | 20.6226 | 0 | (****)
|  | Napoli | 0.0641 | 2.5403 | 0.0111 | (*)
|  | Palermo | 0.2405 | 5.5141 | 0 | (****)
|  | Roma | 0.3435 | 18.0568 | 0 | (****)
|  | Torino | 0.2341 | 10.6906 | 0 | (****)
|  | Venezia | 0.09 | 2.3067 | 0.0211 | (*)
| Afternoon | Bari | 0.034 | 1.4039 | 0.1604 | (ns)
|  | Milano | 0.3869 | 21.2759 | 0 | (****)
|  | Napoli | 0.0305 | 1.4994 | 0.1338 | (ns)
|  | Palermo | 0.2368 | 5.4373 | 0 | (****)
|  | Roma | 0.3852 | 20.2063 | 0 | (****)
|  | Torino | 0.2581 | 11.7389 | 0 | (****)
|  | Venezia | 0.1489 | 3.511 | 0.0004 | (***)
| Evening | Bari | 0.046 | 1.6445 | 0.1001 | (ns)
|  | Milano | 0.2519 | 13.9744 | 0 | (****)
|  | Napoli | -0.0157 | 0.0721 | 0.9425 | (ns)
|  | Palermo | 0.0821 | 2.2483 | 0.0246 | (*)
|  | Roma | 0.3708 | 19.4634 | 0 | (****)
|  | Torino | 0.1599 | 7.4434 | 0 | (****)
|  | Venezia | 0.1313 | 3.1517 | 0.0016 | (**)
| Night | Bari | 0.0343 | 1.4084 | 0.159 | (ns)
|  | Milano | 0.2862 | 15.8271 | 0 | (****)
|  | Napoli | 0.0444 | 1.9297 | 0.0536 | (ns)
|  | Palermo | 0.1683 | 4.0266 | 0.0001 | (****)
|  | Roma | 0.3702 | 19.433 | 0 | (****)
|  | Torino | 0.2085 | 9.5716 | 0 | (****)
|  | Venezia | 0.1145 | 2.8076 | 0.005 | (**)

Figure SI 6: The relationship between diversity in features excluding (‘third
place‘ variables–see below) and male-female differences for the spatial model
aggregating all cities. The plot shows the significance of the direct effect;
however, the $\beta$ coefficients represent the indirect effect (see Section
3.3 for definitions). The plot displays all diversity variables, with the
y-axis showing the variables for each model and the colour representing each
variable. Panel (A) shows all daytime data between 08:00 and 20:00; Panel (B)
displays weekday (Monday-Thursday) versus weekend (Friday-Sunday) data within
the same time period; Panel (C) shows data averaged into four categories:
morning (06:00-12:00), afternoon (12:00-18:00), evening (18:00-00:00), and
night (00:00-06:00). To aid comparison, shapes denote categories in Panels (B)
and (C). Significance is indicated by closed and open shapes (_P_ $<$ 0.05 and
_P_ $>$ 0.05, respectively), and each shape shows the error bars as a
horizontal line. The pseudo-r-squared is reported for each panel. Figure SI 7:
The relationship between diversity in ‘third place‘ features and male-female
differences for the spatial model aggregating all cities. The plot shows the
significance of the direct effect; however, the $\beta$ coefficients represent
the indirect effect (see Section 3.3 for definitions). The plot displays all
diversity variables, with the y-axis showing the variables for each model and
the colour representing each variable. Panel (A) shows all daytime data
between 08:00 and 20:00; Panel (B) displays weekday (Monday-Thursday) versus
weekend (Friday-Sunday) data within the same time period; Panel (C) shows data
averaged into four categories: morning (06:00-12:00), afternoon (12:00-18:00),
evening (18:00-00:00), and night (00:00-06:00). To aid comparison, shapes
denote categories in Panels (B) and (C). Significance is indicated by closed
and open shapes (_P_ $<$ 0.05 and _P_ $>$ 0.05, respectively), and each shape
shows the error bars as a horizontal line. The pseudo-r-squared is reported
for each panel.