# Understanding the interplay
between social and spatial behaviour

Laura Alessandretti  Technical University of Denmark, DK-2800 Kgs. Lyngby,
Denmark  Sune Lehmann  Technical University of Denmark, DK-2800 Kgs. Lyngby,
Denmark  Niels Bohr Institute, University of Copenhagen, DK-2100 København Ø,
Denmark
<EMAIL_ADDRESS>Andrea Baronchelli  City, University of London, London EC1V 0HB, United Kingdom

###### Abstract

According to personality psychology, personality traits determine many aspects
of human behaviour. However, validating this insight in large groups has been
challenging so far, due to the scarcity of multi-channel data. Here, we focus
on the relationship between mobility and social behaviour by analysing
trajectories and mobile phone interactions of $\sim 1,000$ individuals from
two high-resolution longitudinal datasets. We identify a connection between
the way in which individuals explore new resources and exploit known assets in
the social and spatial spheres. We show that different individuals balance the
exploration-exploitation trade-off in different ways and we explain part of
the variability in the data by the big five personality traits. We point out
that, in both realms, extraversion correlates with the attitude towards
exploration and routine diversity, while neuroticism and openness account for
the tendency to evolve routine over long time-scales. We find no evidence for
the existence of classes of individuals across the spatio-social domains. Our
results bridge the fields of human geography, sociology and personality
psychology and can help improve current models of mobility and tie formation.

## Introduction

Our social and spatial behaviour are shaped by both internal and external
constraints. On one hand, external factors [1] such as time, cognition, age or
the need for food constrain our possibilities. On the other hand, we are
driven by internal needs, purposes and preferences. Specifically, within
personality psychology, it has been conjectured that personality traits play a
key role in shaping our choices across various situations [2, 3].

In the social realm, individuals cope with cognitive and temporal constraints
by establishing and maintaining connections in a distinctive [4, 5] and
persistent [4] manner. For example, the size of an individual’s social circle
is bounded under $\sim 150$, the so-called Dunbar number [6], but varies among
individuals around this limit [7]. These differences result from an interplay
between physical and extrinsic factors such as gender [8], age [9] and socio-
economic status [10] as well as from stable individual dispositions underlying
personality [11].

Spatially, individuals are characterised by an _activity space_ of repeatedly
visited locations within which they move during their daily activities [12],
but this geo-spatial signature varies in size [13] and spatial shape [14].
However, unlike the social case, the conjecture that individuals’ spatial
behaviour is persistent in time [15] had not been verified until recently.

Here, we capitalise on the recent discovery that the size of the activity
space is conserved and correlates with the social circle size [16] to test the
conjecture that the same personality dispositions in part determine social and
spatial behaviour. We test this theory by analysing two long-term datasets
consisting of $\sim 1000$ individuals mobility trajectories and their phone
interactions (for previous studies see section ‘State of the art’ below).

First, we test the hypothesis that the strategies individuals adopt in order
to choose where to go and with whom to interact are similar. Then, we identify
and characterise the prevailing socio-spatial profiles appearing in the
datasets. Finally, we show that socio-spatial profiles can be partially
explained by the widely adopted big-five personality trait model, often used
to describe aspects of the social and emotional life [17, 18, 11, 7, 19, 20,
21, 22]. In the section ‘State of the art’, we review the relevant literature;
in ‘Methods’ we describe data collection and pre-processing, and we provide
details of the methods implemented; in ‘Results’ we present our findings.

## State of the art

Individual-level variability in social and spatial behaviour has mostly been
investigated in isolation so far, with few notable efforts to reconcile the
two. Here, we briefly review the empirical findings in the two domains.

### The social domain

Individuals deal with limited time and cognitive capacity resulting in finite
social networks [6, 23] by distributing time unevenly across their social
circle [24, 25, 26, 4, 27, 28]. While this is a shared strategy, there is
clear evidence for individual-level variation. First, social circles vary in
terms of diversity: they differ in size [7] \- within a maximum upper-bound of
$\sim 150$ individuals [6] \- and in structure [4, 29]. Second, individuals
display different attitudes towards exploration of social opportunities as
they are more or less keen on creating new connections [30, 31, 32, 33].
Finally, individuals manage social interactions over time in different ways.
Some are characterised by high level of stability as they maintain a very
stable social circle, while others renew their social ties at high pace [5].

These heterogeneities can be partially explained by factors including gender
[34, 8], age [9, 35, 36], socio-economic status [37, 10] and physical
attractiveness [38]. Moreover, as conjectured by personality psychologists
[39, 2], differences in personalities partially explain the variability in
social circle composition [11, 7, 40, 17, 41, 42, 43, 44], and the different
attitudes towards forming [30, 45], developing [46, 20] and replacing [29]
social connections. It is worth noticing that many of these findings are
recent, resulting from the analysis of digital communication traces.

### The spatial domain

Constraints including physical capabilities, the distribution of resources,
and the need to coordinate with others limit our possibilities to move in
space [1]. Individuals cope with these limitations by allocating their time
within an activity space of repeatedly visited locations [47], whose size is
conserved over several years according to a recent study based on high-
resolution trajectories [16], and previous ones based on unevenly sampled and
low spatial resolution data [48, 49]. The activity space varies across
individuals in terms of size [16] and shape [14]: it was shown that two
distinct classes of individuals, _returners_ and _explorers_ , can be
identified based on their propensity to visit new locations, similarly to the
social domain [5]. Heterogeneities in spatial behaviour can be explained in
terms of gender [50], age [51, 52], socio-economic [53, 35] and ethnic [54]
differences. There has only been sporadic efforts to include personality
measures in geographic research, despite the strong connections between the
two [55]. Recent works [56, 44] suggest that spatial behaviour can be
partially explained from personality traits. However, in [56], this
understanding is based on biased data collected from location-based social
networks. In [44], the connection between spatial behaviour and personality is
not investigated extensively, as it is not the main focus of the study.

### Social and spatial connection

Recently, connections between the social and spatial behaviour of pairs [57,
58, 59, 60, 61, 62] and groups [63] of individuals have been demonstrated, and
used to design predictive models of mobility [58, 64, 65] or social ties [66,
59, 67, 68]. Shifting the attention to the individual level, recent works
based on online social network data [69, 70], mobile phone calls data [62] and
evenly sampled high resolution mobility trajectories [16] have shown
correlations between the activity space size and the ego network structure,
calling for further research to more closely examine the connections between
social and spatial behaviour at the individual level.

## Methods

### Data description and pre-processing

Our study is based on $850$ high resolution trajectories and call records of
participants in a $24$ months longitudinal experiment, the Copenhagen Networks
Study (CNS) [71]. Results on the connections between social and spatial
behaviour were corroborated with data from another experiment with fixed rate
temporal sampling, but lower spatial resolution and sample size: the Lausanne
Mobile Data Challenge (MDC) [72, 73], lasted for $19$ months (see Table 1).

| N | $\delta t$ | $T$ | $\delta x$ | $TC$
---|---|---|---|---|---
CNS | 850 | 16 s | 24 months | 10 m | 0.84
MDC | 185 | 60 s | 19 months | 100-200 m | 0.73
Table 1: Characteristics of the mobility datasets considered. $N$ is the
number of individuals, $\delta t$ the temporal resolution, $T$ the duration of
data collection, $\delta x$ the spatial resolution, $TC$ the median weekly
time coverage, defined as the fraction of time an individual’s location is
known.

#### CNS dataset

The Copenhagen Networks Study (CNS) experiment took place between September
2013 and September 2015 [71] and involved $\sim 1000$ Technical University of
Denmark students ($\sim 22\%$ female, $\sim 78\%$ male) typically aged between
19 and 21 years old. Participants’ position over time was estimated combining
their smart-phones WiFi and GPS data using the method described in [74, 16].
The location estimation error is below 50 meters in 95% of the cases.
Participants’ calls and sms activity was also collected as part of the
experiment. Individuals’ background information were obtained through a 310
questions survey including the Big Five Inventory [75], which measures how
individuals score on five broad domains of human personality traits: openness,
conscientiousness, extraversion, agreeableness, neuroticism. The personality
questionnaire used in the study is a version of the Big Five Inventory [75],
translated from English into Danish. It contains 44 individual items and each
trait is computed as the average of 7-10 items. Data collection was approved
by the Danish Data Protection Agency. All participants provided individual
informed consent. Mobility patterns of participants in the CNS experiment
display statistical properties consistent with previous literature [13], as
shown in [16].

#### MDC dataset

Data was collected by the Lausanne Data Collection Campaign between October
2009 and March 2011. The campaign involved an heterogeneous sample of $\sim
185$ volunteers with mixed backgrounds from the Lake Geneva region
(Switzerland), who were allocated smart-phones [73]. In this work we used GSM
data, that has the highest temporal sampling. Following Nokia’s privacy
policy, individuals participating in the study provided informed consent [73].
The Lausanne Mobile Data Challenge experiment involves 62% male and 38% female
participants, where the age range 22-33 year-old accounts for roughly 2/3 of
the population [76].

### Metrics

In this section, we define the concepts and metrics used to quantify the
social and spatial behaviour of an individual $i$.

Exploration behaviour is characterised by the following quantities:

Number of new locations/week: $n_{loc}(i,t)$ is the number of locations
discovered by $i$ in the week preceding $t$.

Number of new ties/week: $n_{tie}(i,t)$ is the number of individuals who had
contact with $i$ (by sms or call) for the first time in the week preceding
$t$.

Note that locations/ties are considered ‘new’ only if discovered after $20$
weeks from the beginning of data collection.

Exploitation behaviour can be quantified by considering:

Activity space: The set
$AS(i,t)=\\{\ell_{1},\ell_{2},...,\ell_{j},...\ell_{C}\\}$ of locations
$\ell_{j}$ that individual $i$ visited at least twice and where she spent a
time $\tau_{j}$ larger than $200min$ during a time-window of $T=20$ weeks
preceding time $t$ (see Supplementary Material for the analysis with $T=30$
weeks). Among the locations in the activity space, $i$ visited $\ell_{j}$ with
probability $p(\ell_{j})=\tau_{j}/\sum\tau_{j}$. (It is worth noting that this
time-based definition of activity space includes all significant locations
independently of their spatial position and it is only loosely connected with
space-oriented definitions widespread in the geography literature such as the
“standard deviational ellipse” and the “road network buffer” [77]).

Social circle:  The set $SC(i,t)=\\{u_{1},u_{2},...,u_{j},...u_{k}\\}$ of
individuals $u_{j}$ with whom individual $i$ had a number of contacts
$n_{j}>5$ by sms or call during a time-window of $T=20$ consecutive weeks
preceding time $t$ (see Supplementary Material for the analysis with $T=30$
weeks). The probability that $i$ has contact with a given member $u_{j}$ of
her social circle is $p(u_{j})=n_{j}/\sum n_{j}$.

For these two sets $AS(i,t)$ and $SC(i,t)$, we consider their sizes $C(i,t)$
and $k(i,t)$, quantifying the number of favoured locations and social ties,
respectively; their entropies $H_{AS}(i,t)$ and $H_{SC}(i,t)$, measuring how
time is allocated among locations and ties; their stabilities $J_{AS}(i,t)$
and $J_{SC}(i,t)$, quantifying the fraction of conserved locations and ties,
respectively, across consecutive non-overlapping windows of $T=20$ weeks (see
Supplementary Material for $T=30$); their rank turnovers $R_{AS}(i,t)$ and
$R_{SC}(i,t)$ measuring the average absolute change in rank of an element in
the set between consecutive windows. The mathematical definition of these
quantities is provided in Table 2

|  Activity space | Social circle
---|---|---
1) Size |  $C(i,t)=|AS_{i}(t)|$ | $k(i,t)=|SC(i,t)|$
2) Entropy |  $H_{AS}(i,t)=-\sum\limits_{j=1}^{C(i,t)}{p(j)\log p(j)}$ | $H_{SC}(i,t)=-\sum\limits_{j=1}^{k(i,t)}{p(j)\log p(j)}$
3) Stability |  $J_{SC}(i,t)=\dfrac{|SC(i,t)\cap SC(i,t-T)|}{|SC(i,t)\cup SC(i,t-T)|}^{*}$ | $J_{AS}(i,t)=\dfrac{|AS(i,t)\cap AS(i,t-T)|}{|AS(i,t)\cup AS(i,t-T)|}^{*}$
4) Rank Turnover |  $R_{AS}(i,t)=\sum\limits_{j=1}^{N}\dfrac{|r(j,t)-r(j,t-T)|^{**}}{N}$ | $R_{SC}(i,t)=\sum\limits_{j=1}^{N}\dfrac{|r(j,t)-r(j,t-T)|^{**}}{N}$
∗ Here $T=20$ weeks, see Supplementary Material for the analysis with $T=30$
weeks
∗∗ $r(\ell_{k},t)$ and $r(u_{k},t)$ denote the rank of a location $\ell_{k}$
and individual $u_{k}$ at $t$, respectively

Table 2: Definition of the metrics characterising the activity space and the
social circle. 1) The size of a set is the number of elements in the set 2) We
compute the entropy of a set considering the probability $p(j)$ associated to
each element $j$ of the set. 3) We measure the stability $J_{AS}$ by computing
the Jaccard similarity between the activity space at $t$ and at $t-T$, with
$T=20$ weeks. $J_{SC}$ is computed in the same way for the social circle. 4)
We compute the rank turnover of a set by measuring for each of its elements
$j$ the absolute change in rank between two consecutive time windows of length
$T=20$ weeks. The rank is attributed based on the probability $p(j)$. The
average absolute change in rank across all elements corresponds to the rank
turnover.

.

#### Other metrics

In order to compare the difference in entropy between two different sets, we
compute their Jensen-Shannon divergence (JSD). The JSD between two sets
$P_{1}$ and $P_{2}$ is computed as
$JSD(P_{1},P_{2})=H(\frac{1}{2}(P_{1}+P_{2}))-\frac{1}{2}[H(P_{1})+H(P_{2})]$
(see also [4]).

## Results

Both in their spatial and social behaviour, individuals are constantly
balancing a trade-off between the exploitation of familiar options (such as
returning to a favourite restaurant or spending time with an old friend) and
the exploration of new opportunities (such as visiting a new bar or going on a
first date) [78]. We adopt this exploration-exploitation perspective to
analyse the relationship between social and spatial strategies in our dataset
[16].

We quantify the propensity for exploration and exploitation within each
individual, $i$, using the metrics reported in Table 3, Fig. 1 and described
in section ‘Methods’. We focus on two aspects of exploitation, (i) diversity,
characterising how individuals allocate time among their set of familiar
locations and friends, and (ii) evolution, characterising the tendency to
change exploited locations and friends over time.

Figure 1: Schematic description of our framework.

|  Exploration | Exploitation: Diversity | Exploitation: Evolution
---|---|---|---
Spatial |  New loc./week, $n_{loc}$ | Activity space size, $C$ | Activity space stability, $J_{AS}$
|  | Activity space entropy, $H_{AS}$ | Activity space rank turnover, $R_{AS}$
Social |  New ties/week, $n_{tie}$ | Social circle size, $k$ | Social circle stability, $J_{SC}$
|  | Social circle entropy, $H_{SC}$ | Social circle rank turnover, $R_{SC}$

Table 3: Metrics characterising social and spatial behaviour. The metrics are
defined in section Methods

.

Exploration and exploitation are persistent in time. First, we verify that
individual behaviour is persistent in time. For all the aforementioned
measures, we compare the individual self-variation across time $d_{self}(i)$
with a reference difference $d_{ref}(i,j)$ between individuals $i$ and $j$. In
the case of the activity space size, for example, self-variation is measured
as $d_{self}=\langle|C(i,t)-C(i,t-T)|\rangle$, where $\langle\cdot\rangle$ is
the average across time and $T=20$ weeks (see Supplementary Material for
$T=30$) ; the reference difference is computed as $d_{ref}(i,j)=|\langle
C(i,t)\rangle-\langle C(j,t)\rangle|$. If $d_{self}(i)<d_{ref}(i,j)$ for most
$j$, we can conclude that for individual $i$, fluctuations of the activity
space size are negligible compared to the difference with other individuals.
The same procedure is followed for all metrics with an adjustment in the case
of entropies: The persistence of the entropy $H_{AS}$ is verified by comparing
the Janson-Shannon divergences $d_{self}=JSD(AS(i,t),AS(i,t-T))$ and
$d_{ref}=JSD(AS(i,t),AS(j,t))$. The same method was used for $H_{SC}$ (see
Methods and [4]).

Results from the CNS dataset reported in Table S3 show that for all metrics
$d_{self}(i)<d_{ref}(i,j)$ holds in more than $99\%$ of cases on average (MDC:
$97\%$, see Supplementary Material Table S1). Moreover, the average self-
variation across the population $\overline{d_{self}}$ is consistent with
$\overline{d_{self}}=0$ within errors, and $\overline{d_{self}}$ significantly
smaller than the average reference difference $\overline{d_{ref}}$ (see Tables
S3 and S1 in Supplementary Material).

| $\overline{d_{self}}$ | $\overline{d_{ref}}$ | $\overline{d_{self}(i)<d_{ref}(i,j)}$
---|---|---|---
Social circle size, $k$ | $0.04\pm 0.09$ | $12\pm 5$ |  $99$%
Activity space size, $C$ | $0.04\pm 0.07$ | $7\pm 3$ |  $99$%
New ties/week, $n_{tie}$ | $0.05\pm 0.10$ | $0.9\pm 0.5$ |  $96$%
New locations/week, $n_{loc}$ | $0.10\pm 0.17$ | $1\pm 1$ |  $95$%
Social circle entropy, $H_{SC}$ | $0.002\pm 0.007$ | $0.7\pm 0.2$ |  $99$%
Activity space entropy, $H_{AS}$ | $0.002\pm 0.005$ | $0.4\pm 0.1$ |  $99$%
Social circle stability, $J_{SC}$ | $({9}\pm{22})\cdot 10^{-4}$ | $0.13\pm 0.05$ |  $100$%
Activity space stability, $J_{AS}$ | $({9}\pm{26})\cdot 10^{-4}$ | $0.10\pm 0.04$ |  $99$%
Social circle rank turnover, $R_{SC}$ | $0.05\pm 0.39$ | $2\pm 1$ |  $99$%
Activity space rank turnover, $R_{AS}$ | $0.04\pm 0.10$ | $2\pm 1$ |  $99$%
Table 4: CNS dataset: Persistence of social and spatial behaviour.For each of
the social and spatial metrics, $\overline{d_{self}}$ is the average self-
distance and $\overline{d_{ref}}$ is the reference distance between an
individual and all others, averaged across individuals. The third column
reports the fraction of cases where $\overline{d_{self}(i)<d_{ref}(i,j)}$,
averaged across the population.

These results extend previous findings [4, 16] and suggest that each
individual is characterised by a distinctive socio-spatial behaviour captured
by the ensemble of these metrics averaged across time. In fact, these averages
are heterogeneously distributed across the samples considered (see Fig. S2).

Figure 2: Distribution of social (above line) and spatial (bottom line)
metrics for the CNS and MDC datasets.

Exploration and exploitation are correlated in the social and spatial domain.
A natural way to test the interdependency between social and spatial
behaviours is measuring the correlation between a given social metric and a
corresponding spatial one. We find positive and significant correlations for
all metrics and datasets (see Figs. S3 and S1 in Supplementary Material).

Figure 3: CNS dataset: correlation between the four dimensions of social and
spatial behaviour. (A) Activity space vs social circle size. (B) Activity
space vs social circle composition measured as their entropy. (C) Average
number of new locations vs new ties per week. (D) Stability of the activity
space vs the stability of the social circle measured as the Jaccard similarity
between their composition in consecutive time-windows. (E) Rank turnover of
the activity space vs the rank turnover of the social circle. Coloured filled
areas correspond to cumulative probabilities estimated via Gaussian Kernel
Density estimations. Grey lines correspond to linear fit with angular
coefficient $b$ reported in the legend. The Pearson correlation coefficient,
with corresponding p-value, is reported in the legend.

We find that individuals with high propensity to explore new locations are
also more keen on exploring social opportunities (see Fig. S3A). Those with
diverse mobility routine are also likely to have a correspondingly large
social circle (see Fig. S3B), and those that often replace social ties, have
also an unstable set of favourite locations (see Fig. S3C and D).

We verify that the observed correlations are not spurious by performing
multiple regression analyses that control for other possible sources of
variation: gender, age, and time coverage (the average time an individual
position is known). We implement five multiple linear regression models M1,
M2, M3, M4 and M5. Each regression model predicts a given spatial metric (the
activity space size $C$, the activity space entropy $H_{AS}$, the number of
new locations/week $n_{loc}$, the activity space stability $J_{AS}$ and the
rank turnover $R_{AS}$) using the corresponding social metric and the control
variables (age, gender and time coverage) as regressors. The relative
importance of each regressor is assessed using the Lindeman, Merenda and Gold
($LMG$) [79] method.

Results obtained via weighted least square regression (see Tables S4 for the
CNS dataset and S2 in Supplementary Material for the MDC dataset) reveal that
the social metrics are significant predictors for spatial metrics (p
value$<0.01$ in all cases except for M4 in the MDC dataset), and they
typically have more importance than factors such as gender, time, coverage and
age group (see Fig. S4).

Model M1: Activity space size, $C$ | coeff | p val | LMG
---|---|---|---
Social circle size, $k$ | $4\pm 0$ | $<10^{-50}$ | 0.94
gender | $-0.4\pm 0.2$ | 0.05 | 0.05
time coverage | $0.4\pm 0.2$ | 0.06 | 0.01
[$R^{2}=0.32$, $F=100.44$, $p_{F}=0.0$ ] |  |  |
Model M2: Activity space entropy, $H_{AS}$ |  |  |
Social circle entropy, $H_{SC}$ | $0.07\pm 0.01$ | $<10^{-6}$ | 0.42
gender | $-0.06\pm 0.01$ | $<10^{-4}$ | 0.22
time coverage | $-0.07\pm 0.01$ | $<10^{-5}$ | 0.36
[$R^{2}=0.11$, $F=27.30$, $p_{F}=0.0$] |  |  |
Model M3: New locations/week, $n_{loc}$ |  |  |
New ties/week, $n_{tie}$ | $0.60\pm 0.05$ | $<10^{-32}$ | 0.9
gender | $-0.16\pm 0.05$ | $<10^{-3}$ | 0.08
time coverage | $0.001\pm 0.047$ | 1.0 | 0.01
[$R^{2}=0.22$, $F=61.99$, $p_{F}=0.0$] |  |  |
Model M4: Activity space stability, $J_{AS}$ |  |  |
Social circle stability, $J_{SC}$ | $0.024\pm 0.004$ | $<10^{-10}$ | 0.6
gender | $0.007\pm 0.003$ | 0.05 | 0.04
time coverage | $0.017\pm 0.004$ | $<10^{-5}$ | 0.36
[$R^{2}=0.16$, $F=33.36$, $p_{F}=0.0$] |  |  |
Model M5: Activity space rank turnover, $R_{AS}$ |  |  |
Social circle rank turnover, $R_{SC}$ | $1\pm 0$ | $<10^{-56}$ | 0.98
gender | $0.12\pm 0.07$ | 0.06 | 0.01
time coverage | $-0.12\pm 0.07$ | 0.07 | 0.01
[$R^{2}=0.36$, $F=108.31$, $p_{F}=0.0$] |  |  |
Table 5: Linear regression models for the CNS dataset. For each model, we show
the coefficients (coeff) calculated by the regression model, the probability
(p val) that the variable is not relevant, and the relative importance (LMG)
of each regressor computed using the Lindeman, Merenda and Gold method [79].
Gender is a binary variable taking value 1 for females and 2 for males. For
this dataset, age is not relevant as all participants have similar age. For
each model, we report the $R^{2}$ goodness of fit, the $F-test$ statistics
with the corresponding p-value $p_{F}$.  Figure 4: Relative importance of
regressors LMG of each regressor computed using the Lindeman, Merenda and Gold
method [79] for models M1 (A), M2 (B), M3 (C), M4 (D) and M5 (D). Plain bars
show results for the CNS dataset, dashed bars for the MDC dataset. Variables
that are not significant in the regression model are marked with *.

Among the control variables, gender is a significant predictor of spatial
behaviour in the CNS dataset: Females display higher level of routine
diversity and propensity towards exploration, in accordance with [80]. Time
coverage, measuring the fraction of time an individual position is known,
plays a significant role in explaining spatial entropy and activity space
stability, since individuals who spend long time in the same place (or leave
their phone in the same place) are more easily geo-localised. Age differences
are not present within the sample of students participating in the CNS study,
and they are not estimated to be relevant with respect to spatial behaviour in
the MDC study.

We do not identify distinct classes of individuals. A natural question is
whether or not, in the samples considered, there is evidence for distinct
classes of individuals based on their socio-spatial behaviour [14, 5]. We
approach this problem by reducing the set of metrics to a smaller number of
uncorrelated variables by applying Principal Component Analysis [81, 82]. The
principal components represent the data through linear combinations of the
original variables: In Table 6 we report the percentage of variance in the
data explained by all components; in Table 7 we report the coefficients $w$
describing how the original variables are linearly combined to obtain the
first two principal components.

In both datasets, we find that the first principal component (PC 0) explains
$\sim 40\%$ of the differences between individuals (see Table 6). For the CNS
dataset, the variables contributing the most to PC 0 (e.g. such that
$w^{2}>0.1$) are, in order, the activity space size $C$, the social circle
size $k$, the number of new locations/week $n_{loc}$, the activity space
entropy $H_{AS}$ and the number of new ties/week $n_{tie}$. $n_{loc}$ and
$n_{tie}$ characterise the attitude towards exploration. The other metrics
($C$, $k$ and $H_{AS}$) are related to routine diversity, or the tendency to
dispose of a large set of familiar locations and friends. Since the sign of
$w$ is the same for all the metrics above, we can conclude that individuals
with higher propensity towards exploration tend to have a more diverse social
and spatial routine, and vice-versa. Similar conclusions could be drawn by
looking at results obtained for the MDC dataset.

| PC 0 | PC 1 | PC 2 | PC 3 | PC 4 | PC 5 | PC 6 | PC 7 | PC 8 | PC 9
---|---|---|---|---|---|---|---|---|---|---
CNS | 0.39 | 0.17 | 0.12 | 0.08 | 0.07 | 0.06 | 0.04 | 0.03 | 0.03 | 0.01
MDC | 0.43 | 0.14 | 0.13 | 0.08 | 0.07 | 0.06 | 0.04 | 0.03 | 0.02 | 0.01
Table 6: Variance explained by principal components. The fraction of variance explained by each principal component for the CNS and MDC dataset.  | CNS | MDC
---|---|---
|  $w$ (PC 0) |  $w$ (PC 1) |  $w$ (PC 0) |  $w$ (PC 1)
Social circle size, $k$ | 0.41 | 0.16 | 0.37 | -0.15
Activity space size, $C$ | 0.42 | -0.24 | 0.42 | -0.08
New ties/week, $n_{tie}$ | 0.33 | 0.28 | 0.27 | 0.33
New locations/week, $n_{loc}$ | 0.38 | -0.05 | 0.37 | 0.19
Social circle entropy, $H_{SC}$ | 0.31 | 0.30 | 0.34 | 0.09
Activity space entropy, $H_{AS}$ | 0.38 | -0.16 | 0.30 | -0.07
Social circle stability, $J_{SC}$ | -0.16 | -0.46 | 0.07 | -0.72
Activity space stability, $J_{AS}$ | -0.10 | -0.49 | -0.12 | -0.51
Social circle rank turnover, $R_{SC}$ | -0.20 | 0.28 | -0.33 | 0.10
Activity space rank turnover, $R_{AS}$ | -0.30 | 0.44 | -0.38 | 0.17
Table 7: Contribution of the original variables to the first principal
component. The scalar projection $w$ of the first (PC 0) and second (PC 1)
principal components, along the axis defined by each of the original
variables. Each principal component has unit norm, hence the sum of $w^{2}$ is
$1$. Results are shown for the CNS and MDC datasets.

The second principal component (PC 1) accounts for $\sim 15\%$ of the total
variation (see Table 6). It is dominated by the social circle stability
$J_{SC}$ (CNS: $w^{2}=0.21$, MDC: $w^{2}=0.52$) and the activity space
stability $J_{AS}$ (CNS: $w^{2}=0.24$, MDC: $w^{2}=0.26$) for both datasets
(see Table 7). The sign of the coefficients $w$ for $J_{SC}$ and $J_{AS}$ are
the same, further confirming that these two metrics are correlated (see also
Fig. S3). We can conclude that the second principal component accounts for the
effects of routine evolution, or the tendency to change familiar locations and
friends over long time scales. We consider the first two principal components,
PC 0 and PC 1, to reduce the effects of noise and we test the hypothesis that
there exists different classes of individuals applying the gap statistic
method [83]. We apply it by looking at the gap between the within-cluster
dispersion expected under a uniform distribution of the data and the
dispersion obtained after applying K-means. For all possible choices of $K>1$,
we find that the gap is not large enough to support the existence of more than
one class of individuals.

The big-five personality traits partly explain spatial and social behaviour.
We verify if the differences between individuals can be explained by the Big
five personality traits model [75], typically used to describe social and
emotional life (see Table 8). We build two multiple linear regression models
that use the Big five personality traits as regressors and one of the
principal components describing socio-spatial behaviour as target. Results,
shown in Table 9, show that three personality traits, neuroticism, openness
and extraversion, are relevant predictors for socio-spatial behaviour. In
particular, extraversion is the most important predictor of the first
principal component: it positively correlates with the tendency to diversify
routine and to explore opportunities. Neuroticism and openness explain instead
the second principal component, since it correlates with the tendency to
change routine over time (see also Fig. S5).

Finally, we perform all analyses considering only spatial metrics. Results are
in line with those obtained considering all metrics: The first two principal
components account for a large fraction of the variability in the data (see
Table 10); The first component is dominated by the activity space size $C$,
the number of new locations/week $n_{loc}$ and the activity space entropy
$H_{AS}$, while the second is mostly controlled by the activity space
stability $J_{AS}$ (Table 11). For the CNS dataset, extraversion is the most
important predictor of the first principal component, while openness,
extraversion and neuroticism account for the second component (see Table 12
and Fig. S6). The result presented above hold when choosing a time-window with
length $T=30$ weeks (see Supplementary Material, section 2).

Trait | Related Adjectives
---|---
Extraversion | Active, Assertive, Energetic, Enthusiastic, Outgoing, Talkative
Agreeableness | Appreciative, Forgiving, Generous, Kind, Sympathetic
Conscientiousness | Efficient, Organised, Planful, Reliable, Responsible, Thorough
Neuroticism | Anxious, Self-pitying, Tense, Touchy, Unstable, Worrying
Openness to Experience | Artistic, Curious, Imaginative, Insightful, Original, Wide Interests
Table 8: The Big-Five traits and examples of adjectives describing them [84] |  PC 0 $R^{2}=0.17$, $F=21.40$, $p_{F}=0.0$ |  PC 1 $R^{2}=0.03$, $F=3.64$, $p_{F}=0.0$
---|---|---
| coeff | p val | LMG | coeff | p val | LMG
extraversion | $0.85\pm 0.09$ | $<10^{-19}$ | 0.85 | $0.12\pm 0.06$ | 0.05 | 0.14
openness | $-0.17\pm 0.08$ | 0.03 | 0.02 | $0.13\pm 0.06$ | 0.02 | 0.33
neuroticism | $0.25\pm 0.09$ | 0.004 | 0.04 | $0.15\pm 0.06$ | 0.02 | 0.3
agreeableness | $0.11\pm 0.08$ | 0.2 | 0.04 | $-0.07\pm 0.06$ | 0.2 | 0.12
conscientiousness | $0.06\pm 0.08$ | 0.4 | 0.04 | $-0.07\pm 0.06$ | 0.2 | 0.11
Table 9: Extraversion, openness, and neuroticism explain socio-spatial behaviour. The result of a multiple linear regression explaining principal components of socio-spatial data (see Table 7). The value of each coefficient (coeff) is reported together with the probability (p val) that the coefficient is not relevant for the model. The relative importance of each coefficient (LMG) is computed using the LMG method [79].  Figure 5: Relative importance of personality traits for socio-spatial behaviour LMG of each regressor computed using the Lindeman, Merenda and Gold method [79] for the multiple regression model of the principal components (see also Table 9). Figure 6: Relative importance of personality traits for spatial behaviour LMG of each regressor computed using the Lindeman, Merenda and Gold method [79] for the multiple regression model of the principal components (see also Table 12). | PC 0 | PC 1 | PC 2 | PC 3 | PC 4
---|---|---|---|---|---
CNS | 0.53 | 0.21 | 0.13 | 0.10 | 0.04
MDC | 0.56 | 0.19 | 0.13 | 0.07 | 0.04
Table 10: Variance explained by principal components (only spatial data). The fraction of variance explained by each principal component for the CNS and MDC dataset.  | CNS | MDC
---|---|---
| PC 0 | PC 1 | PC 0 | PC 1
Activity space size, $C$ | -0.58 | 0.02 | 0.55 | 0.12
New locations/week, $n_{loc}$ | -0.48 | -0.19 | 0.51 | -0.09
Activity space entropy, $H_{AS}$ | -0.50 | -0.08 | 0.43 | 0.20
Activity space stability, $J_{AS}$ | -0.02 | 0.94 | -0.19 | 0.95
Activity space rank turnover, $R_{AS}$ | 0.43 | -0.25 | -0.47 | -0.16
Table 11: Principal Components (only spatial data). The weight of each metric in the first two principal components, for both datasets.  |  PC 0 $R^{2}=0.10$, $F=12.83$, $p_{F}=0.0$ |  PC 1 $R^{2}=0.03$, $F=3.50$, $p_{F}=0.0$
---|---|---
| coeff | p val | LMG | coeff | p val | LMG
extraversion | $-0.50\pm 0.07$ | $<10^{-10}$ | 0.77 | $-0.11\pm 0.05$ | 0.02 | 0.3
openness | $0.19\pm 0.07$ | 0.004 | 0.08 | $-0.11\pm 0.04$ | 0.009 | 0.45
neuroticism | $-0.07\pm 0.07$ | 0.4 | 0.03 | $-0.10\pm 0.05$ | 0.03 | 0.21
agreeableness | $-0.10\pm 0.07$ | 0.2 | 0.07 | $0.01\pm 0.05$ | 0.8 | 0.01
conscientiousness | $-0.05\pm 0.07$ | 0.5 | 0.05 | $0.03\pm 0.04$ | 0.4 | 0.03
Table 12: Extraversion, openness, and neuroticism explain spatial behaviour.
The result of a multiple linear regression explaining principal components of
spatial data (see Table 7). The value of each coefficient (coeff) is reported
together with the probability (p val) that the coefficient is not relevant for
the model. The relative importance of each coefficient (LMG) is computed using
the LMG method [79].

## Discussion

Using high resolution data from two large scale studies, we have investigated
the connection between social and spatial behaviour for the first time. We
have shown that, in both domains, individuals balance the trade-off between
exploring new opportunities and exploiting known options in a distinctive and
persistent manner. We have found that, to a significant extent, individuals
adopt a similar strategy in the social and spatial sphere. These strategies
are heterogeneous across the two samples considered, and there is no evidence
suggesting that there exist distinct classes of individuals. Finally, we have
shown that the big five personality traits explain related aspects of both
social and spatial behaviour. In particular, we have found that extraverted
individuals are more explorative and have diverse routines in both the social
and the spatial sphere while neuroticism and openness associate with high
level of routine instability in the social and spatial domain.

Our findings confirm the usefulness of mobile phone data to study the
connections between behaviour and personality [85, 86, 40, 29, 44, 87]. The
results are in line with previous findings on the relation between personality
and social behaviour: extraversion correlates with ego-network size [43, 41,
18] and diverse composition [88], openness to experience to social network
turnover [29] and neuroticism does not correlate with social network size
[11]. Furthermore, our findings establish a relation between personality and
spatial behaviour, validating the theories suggesting that spatial choices are
partially dictated by personality dispositions [15] and that a single set of
personality traits underlies many aspects of a person’s behaviour [2, 3].

Our findings on the connection between spatial behaviour and personality are
consistent with the existing literature on personality. The correlation
between exploration and extraversion could be explained by the fact that
extraverted individuals are more likely to be risk-takers in various domains
of life [89]. Extraverted individuals are also generally more likely to engage
in social activities [90], which could partially explain why they allocate
time among a larger set of locations. Furthermore, the key finding that
individuals who score high in neuroticism and openness display a tendency to
change familiar locations, and friends, over time fits well within the
existing picture. In the case of neuroticism, it is well known that this trait
is closely related with ‘stability’ [91], such that the trait of neuroticism
is sometimes referred to as (low) ‘emotional stability’ [92]. Also, at the
core of neuroticism is the tendency to experience negative emotions [93]
including dissatisfaction [94], which in turn can lead into desire for change
[95, 96]. Finally, it is known that people scoring high in neuroticism have a
larger number of weak ties [42] and perceive that they tend to have less
social support [97, 98], in line with our observation that they dispose of an
unstable ego-network. Openness to experience has been shown to correlate with
‘disloyal’ behaviour also in other contexts such as politics [99] and shopping
[100]. Our results, in agreement with previous studies on social [85, 86, 40,
29, 44, 87] and online [101, 102, 103, 104] behaviour, show that personality
traits explain only partially how individuals behave in specific situations
[105].

As a final point, we emphasize that the individual characterisation of spatial
behaviour and connections with personality are fundamental to develop
conceptual [55] and predictive [106] models of travel behaviour accounting for
individual-level differences.

## Competing interests

The authors declare that they have no competing interests.

## Author’s contributions

LA, SL and AB designed the study; LA performed the analysis; LA, SL and AB
analysed the results; LA, SL and AB wrote the paper.

## Acknowledgements

This work was supported by the Danish Council for Independent Research
(“Microdynamics of influence in social systems”, grant id. 4184-00556, SL is
PI). Portions of the research in this paper used the MDC Database made
available by Idiap Research Institute, Switzerland and owned by Nokia.

## List of Abbreviations

CNS: Copenhagen Networks Study
MDC: (Lausanne) Mobile Data Challenge
GSM: Global System for Mobile Communications
JSD: Jensen-Shannon divergence
LMG: Lindeman, Merenda and Gold

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Supplementary Material for
Understanding the interplay between social and spatial behaviour

##  1 Results obtained with the MDC dataset

Tables S1, S2 and Fig. S1 report the results of the persistence analysis, the
multiple regression analysis, and the correlation analysis for the MDC
dataset.

| $\overline{d_{self}}$ | $\overline{d_{ref}}$ | $\overline{d_{self}(i)<d_{ref}(i,j)}$
---|---|---|---
Social circle size, $k$ | $0.05\pm 0.13$ | $10\pm 5$ |  $97$%
Activity space size, $C$ | $0.07\pm 0.12$ | $8\pm 3$ |  $97$%
New ties/week, $n_{tie}$ | $0.2\pm 0.3$ | $2\pm 1$ |  $91$%
New locations/week, $n_{loc}$ | $0.2\pm 0.6$ | $2\pm 1$ |  $90$%
Social circle entropy, $H_{SC}$ | $0.006\pm 0.014$ | $0.7\pm 0.3$ |  $97$%
Activity space entropy, $H_{AS}$ | $0.004\pm 0.008$ | $0.5\pm 0.2$ |  $97$%
Social circle stability, $J_{SC}$ | $0.002\pm 0.005$ | $0.15\pm 0.05$ |  $99$%
Activity space stability, $J_{AS}$ | $0.002\pm 0.004$ | $0.12\pm 0.05$ |  $99$%
Social circle rank turnover, $R_{SC}$ | $0.07\pm 0.15$ | $2\pm 1$ |  $98$%
Activity space rank turnover, $R_{AS}$ | $0.2\pm 0.6$ | $2\pm 1$ |  $97$%
Table S1: MDC dataset: Persistence of social and spatial behaviour.  For each of the social and spatial metrics, $\overline{d_{self}}$ is the average self-distance and $\overline{d_{ref}}$ is the reference distance between an individual and all others, averaged across individuals. The third column reports the fraction of cases where $\overline{d_{self}(i)<d_{ref}(i,j)}$, averaged across the population.  Figure S1: MDC dataset: correlation between the four dimensions of social and spatial behaviour. (A) Activity space vs social circle size. (B) Activity space vs social circle composition measured as their entropy. (C) Average number of new locations vs new ties per week. (D) Stability of the activity space vs the stability of the social circle measured as the Jaccard similarity between their composition in consecutive time-windows. (E) Rank turnover of the activity space vs the rank turnover of the social circle. Coloured filled areas correspond to cumulative probabilities estimated via Gaussian Kernel Density estimations. Grey lines correspond to linear fit with angular coefficient $b$ reported in the legend. The Pearson correlation coefficient, with corresponding p-value, is reported in the legend. Model M1: Activity space size, $C$ | coeff | p val | LMG
---|---|---|---
Social circle size, $k$ | $5\pm 1$ | $<10^{-11}$ | 0.98
gender | $0.1\pm 0.6$ | 0.8 | 0.01
age group | $0.6\pm 0.6$ | 0.3 | 0.01
time coverage | $-0.4\pm 0.6$ | 0.4 | 0.0
[$R^{2}=0.40$, $F=16.80$, $p_{F}=0.0$] |  |  |
Model M2: Activity space entropy, $H_{AS}$ |  |  |
Social circle entropy, $H_{SC}$ | $0.11\pm 0.04$ | 0.009 | 0.28
gender | $0.04\pm 0.04$ | 0.3 | 0.03
age group | $-0.08\pm 0.04$ | 0.06 | 0.21
time coverage | $-0.14\pm 0.04$ | 0.002 | 0.48
[$R^{2}=0.20$, $F=6.50$, $p_{F}=0.0$] |  |  |
Model M3: New locations/week, $n_{loc}$ |  |  |
New ties/week, $n_{tie}$ | $0.5\pm 0.1$ | 0.002 | 0.69
gender | $0.01\pm 0.15$ | 0.9 | 0.04
age group | $0.2\pm 0.1$ | 0.2 | 0.1
time coverage | $-0.3\pm 0.1$ | 0.06 | 0.17
[$R^{2}=0.13$, $F=3.78$, $p_{F}=0.0$] |  |  |
Model M4: Activity space stability, $J_{AS}$ |  |  |
Social circle stability, $J_{SC}$ | $0.02\pm 0.01$ | 0.1 | 0.82
gender | $-0.006\pm 0.012$ | 0.6 | 0.15
age group | $-0.003\pm 0.012$ | 0.8 | 0.03
time coverage | $({-10}\pm{1213})\cdot 10^{-5}$ | 1.0 | 0.0
[$R^{2}=0.04$, $F=0.80$, $p_{F}=0.5$] |  |  |
Model M5: Activity space rank turnover, $R_{AS}$ |  |  |
Social circle rank turnover, $R_{SC}$ | $1\pm 0$ | $<10^{-15}$ | 0.97
gender | $0.04\pm 0.15$ | 0.8 | 0.02
age group | $-0.2\pm 0.1$ | 0.1 | 0.01
time coverage | $-0.06\pm 0.15$ | 0.7 | 0.0
[$R^{2}=0.55$, $F=27.24$, $p_{F}=0.0$] |  |  |
Table S2: Linear regression models for the MDC dataset. For each model, we
report the $R^{2}$ goodness of fit, the $F-test$ statistics with the
corresponfing p-value $p_{F}$. We show the coefficients (coeff) calculated by
the regression model, the probability (p val) that the variable is not
relevant, and the relative importance (LMG) of each regressor computed using
the Lindeman, Merenda and Gold method. Gender is a binary variable taking
value 1 for females and 2 for males.

##  2 Results obtained with other windows

Figs. S3, S5, S5, S6 and Tables S3, S4, S5, S6, S7, S8, S9, S10 report the
results obtained choosing a time-window with length $T=30$ weeks (see main
manuscript, section ‘Methods’).

Figure S2: T=30, Distribution of social (above line) and spatial (bottom line)
metrics for the CNS and MDC datasets. Figure S3: T=30, CNS dataset:
correlation between the four dimensions of social and spatial behaviour. (A)
Activity space vs social circle size. (B) Activity space vs social circle
composition measured as their entropy. (C) Average number of new locations vs
new ties per week. (D) Stability of the activity space vs the stability of the
social circle measured as the Jaccard similarity between their composition in
consecutive time-windows. (E) Rank turnover of the activity space vs the rank
turnover of the social circle. Coloured filled areas correspond to cumulative
probabilities estimated via Gaussian Kernel Density estimations. Grey lines
correspond to linear fit with angular coefficient $b$ reported in the legend.
The Pearson correlation coefficient, with corresponding p-value, is reported
in the legend.  Figure S4: T=30, Relative importance of regressors LMG of each
regressor computed using the Lindeman, Merenda and Gold method for models M1
(A), M2 (B), M3 (C), M4 (D) and M5 (E). Plain bars show results for the CNS
dataset, dashed bars for the MDC dataset. Variables that are not significant
in the regression model are marked with *.  Figure S5: T=30, Relative
importance of personality traits for socio-spatial behaviour LMG of each
regressor computed using the Lindeman, Merenda and Gold method for the
multiple regression model of the principal components (table S7). Figure S6:
T=30, Relative importance of personalitry traits for spatial behaviour LMG of
each regressor computed using the Lindeman, Merenda and Gold method for the
multiple regression model of the principal components (table S10).

| $\overline{d_{self}}$ | $\overline{d_{ref}}$ | $\overline{d_{self}(i)<d_{ref}(i,j)}$
---|---|---|---
Social circle size, $k$ | $0.04\pm 0.13$ | $15\pm 6$ |  $100$%
Activity space size, $C$ | $0.04\pm 0.07$ | $8\pm 3$ |  $99$%
New ties/week, $n_{tie}$ | $0.06\pm 0.12$ | $0.9\pm 0.5$ |  $96$%
New locations/week, $n_{loc}$ | $0.1\pm 0.2$ | $1\pm 1$ |  $95$%
Social circle entropy, $H_{SC}$ | $0.002\pm 0.005$ | $0.7\pm 0.3$ |  $99$%
Activity space entropy, $H_{AS}$ | $0.002\pm 0.006$ | $0.4\pm 0.1$ |  $99$%
Social circle stability, $J_{SC}$ | $({6}\pm{15})\cdot 10^{-4}$ | $0.14\pm 0.05$ |  $100$%
Activity space stability, $J_{AS}$ | $({6}\pm{11})\cdot 10^{-4}$ | $0.10\pm 0.04$ |  $100$%
Social circle rank turnover, $R_{SC}$ | $0.04\pm 0.11$ | $2\pm 1$ |  $99$%
Activity space rank turnover, $R_{AS}$ | $0.04\pm 0.20$ | $2\pm 1$ |  $99$%
Table S3: T=30, CNS dataset: Persistence of social and spatial behaviour.For each of the social and spatial metrics, $\overline{d_{self}}$ is the average self-distance and $\overline{d_{ref}}$ is the reference distance between an individual and all others, averaged across individuals. The third column reports the fraction of cases where $\overline{d_{self}(i)<d_{ref}(i,j)}$, averaged across the population. Model M1: Activity space size, $C$ | coeff | p val | LMG
---|---|---|---
Social circle size, $k$ | $4\pm 0$ | $<10^{-46}$ | 0.95
gender | $-0.3\pm 0.2$ | 0.2 | 0.04
time coverage | $0.5\pm 0.2$ | 0.05 | 0.01
[$R^{2}=0.32$, $F=91.23$, $p_{F}=0.0$] |  |  |
Model M2: Activity space entropy, $H_{AS}$ |  |  |
Social circle entropy, $H_{SC}$ | $0.07\pm 0.02$ | $<10^{-4}$ | 0.34
gender | $-0.05\pm 0.02$ | $<10^{-3}$ | 0.16
time coverage | $-0.09\pm 0.02$ | $<10^{-8}$ | 0.51
[$R^{2}=0.12$, $F=26.82$, $p_{F}=0.0$] |  |  |
Model M3: New locations/week, $n_{loc}$ |  |  |
New ties/week, $n_{tie}$ | $0.58\pm 0.05$ | $<10^{-30}$ | 0.94
gender | $-0.09\pm 0.05$ | 0.04 | 0.04
time coverage | $0.03\pm 0.05$ | 0.5 | 0.01
[$R^{2}=0.22$, $F=55.56$, $p_{F}=0.0$] |  |  |
Model M4: Activity space stability, $J_{AS}$ |  |  |
Social circle stability, $J_{SC}$ | $0.027\pm 0.004$ | $<10^{-9}$ | 0.57
gender | $0.009\pm 0.004$ | 0.02 | 0.06
time coverage | $0.020\pm 0.004$ | $<10^{-5}$ | 0.37
[$R^{2}=0.18$, $F=30.32$, $p_{F}=0.0$] |  |  |
Model M5: Activity space rank turnover, $R_{AS}$ |  |  |
Social circle rank turnover, $R_{SC}$ | $0.81\pm 0.08$ | $<10^{-19}$ | 0.99
gender | $0.09\pm 0.08$ | 0.3 | 0.01
time coverage | $-0.001\pm 0.084$ | 1.0 | 0.0
[$R^{2}=0.18$, $F=31.70$, $p_{F}=0.0$] |  |  |
Table S4: T=30, Linear regression models for the CNS dataset. For each model, we report the $R^{2}$ goodness of fit, the $F-test$ statistics with the corresponfing p-value $p_{F}$. We show the coefficients (coeff) calculated by the regression model, the probability (p val) that the variable is not relevant, and the relative importance (LMG) of each regressor computed using the Lindeman, Merenda and Gold method. Gender is a binary variable taking value 1 for females and 2 for males. For this dataset, age is not relevant as all participants have similar age.  | PC 0 | PC 1 | PC 2 | PC 3 | PC 4 | PC 5 | PC 6 | PC 7 | PC 8 | PC 9
---|---|---|---|---|---|---|---|---|---|---
CNS | 0.40 | 0.18 | 0.10 | 0.07 | 0.07 | 0.06 | 0.04 | 0.03 | 0.03 | 0.02
MDC | 0.39 | 0.19 | 0.12 | 0.10 | 0.06 | 0.05 | 0.05 | 0.03 | 0.02 | 0.01
Table S5: T=30, Variance explained by principal components. The fraction of variance explained by each principal component for the CNS and MDC dataset.  | CNS | MDC
---|---|---
| PC 0 | PC 1 | PC 0 | PC 1
Social circle size, $k$ | 0.41 | 0.18 | -0.36 | 0.04
Activity space size, $C$ | 0.42 | -0.23 | -0.40 | -0.05
New ties/week, $n_{tie}$ | 0.33 | 0.27 | -0.24 | -0.35
New locations/week, $n_{loc}$ | 0.39 | -0.11 | -0.37 | -0.22
Social circle entropy, $H_{SC}$ | 0.29 | 0.33 | -0.36 | -0.23
Activity space entropy, $H_{AS}$ | 0.38 | -0.10 | -0.35 | 0.13
Social circle stability, $J_{SC}$ | -0.12 | -0.50 | -0.11 | 0.56
Activity space stability, $J_{AS}$ | -0.06 | -0.50 | -0.03 | 0.62
Social circle rank turnover, $R_{SC}$ | -0.17 | 0.26 | 0.28 | -0.19
Activity space rank turnover, $R_{AS}$ | -0.35 | 0.37 | 0.42 | -0.18
Table S6: T=30, Principal Components. The weight of each metric in the first two principal components, for both datasets.  |  PC 0 $R^{2}=0.17$, $F=17.08$, $p_{F}=0.0$ |  PC 1 $R^{2}=0.02$, $F=2.05$, $p_{F}=0.1$
---|---|---
| coeff | p val | LMG | coeff | p val | LMG
extraversion | $0.9\pm 0.1$ | $<10^{-15}$ | 0.89 | $0.06\pm 0.07$ | 0.4 | 0.04
openness | $-0.18\pm 0.09$ | 0.06 | 0.02 | $0.13\pm 0.07$ | 0.05 | 0.4
neuroticism | $0.1\pm 0.1$ | 0.1 | 0.03 | $0.15\pm 0.07$ | 0.04 | 0.43
agreeableness | $0.05\pm 0.10$ | 0.6 | 0.02 | $-0.04\pm 0.07$ | 0.5 | 0.09
conscientiousness | $0.04\pm 0.10$ | 0.7 | 0.04 | $-0.03\pm 0.07$ | 0.7 | 0.04
Table S7: T=30, Extraversion, openness, and neuroticism explain socio-spatial behaviour. The result of a multiple linear regression explaining principal components of socio-spatial data (Table S6). The value of each coefficient (coeff) is reported together with the probability (p val) that the coefficient is not relevant for the model. The relative importance of each coefficient (LMG) is computed using the LMG method.  | PC 0 | PC 1 | PC 2 | PC 3 | PC 4
---|---|---|---|---|---
CNS | 0.57 | 0.21 | 0.10 | 0.08 | 0.04
MDC | 0.55 | 0.24 | 0.12 | 0.06 | 0.03
Table S8: T=30, Variance explained by principal components (only spatial data). The fraction of variance explained by each principal component for the CNS and MDC dataset.  | CNS | MDC
---|---|---
| PC 0 | PC 1 | PC 0 | PC 1
Activity space size, $C$ | -0.55 | 0.01 | -0.55 | -0.10
New locations/week, $n_{loc}$ | -0.48 | -0.16 | -0.48 | -0.35
Activity space entropy, $H_{AS}$ | -0.48 | -0.14 | -0.44 | 0.20
Activity space stability, $J_{AS}$ | -0.06 | 0.96 | -0.02 | 0.88
Activity space rank turnover, $R_{AS}$ | 0.48 | -0.16 | 0.51 | -0.22
Table S9: T=30, Principal Components (only spatial data). The weight of each metric in the first two principal components, for both datasets.  |  PC 0 $R^{2}=0.11$, $F=11.55$, $p_{F}=0.0$ |  PC 1 $R^{2}=0.02$, $F=2.02$, $p_{F}=0.1$
---|---|---
| coeff | p val | LMG | coeff | p val | LMG
extraversion | $-0.56\pm 0.09$ | $<10^{-9}$ | 0.8 | $-0.12\pm 0.05$ | 0.03 | 0.38
openness | $0.20\pm 0.08$ | 0.01 | 0.07 | $-0.04\pm 0.05$ | 0.5 | 0.08
neuroticism | $0.03\pm 0.08$ | 0.7 | 0.07 | $-0.14\pm 0.05$ | 0.01 | 0.48
agreeableness | $-0.05\pm 0.08$ | 0.5 | 0.03 | $-0.002\pm 0.052$ | 1.0 | 0.01
conscientiousness | $-0.005\pm 0.081$ | 1.0 | 0.03 | $-0.03\pm 0.05$ | 0.6 | 0.04
Table S10: T=30, Extraversion, openness, and neuroticism explain spatial
behaviour. The result of a multiple linear regression explaining principal
components of spatial data (Table S6). The value of each coefficient (coeff)
is reported together with the probability (p val) that the coefficient is not
relevant for the model. The relative importance of each coefficient (LMG) is
computed using the LMG method.