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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>a configurable agent-based model of the decision to perform com muting behaviour</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Robert Greener</string-name>
          <email>Robert.Greener@lshtm.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Daniel Lewis</string-name>
          <email>Daniel.Lewis@lshtm.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jon Reades</string-name>
          <email>j.reades@ucl.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Simon Miles</string-name>
          <email>simon.miles@kcl.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Steven Cummins</string-name>
          <email>Steven.Cummins@lshtm.ac.uk</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
          <xref ref-type="aff" rid="aff4">4</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>ATT'22: Workshop Agents in Trafic and Transportation</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Bartlett Centre for Advanced Spatial Analysis, Bartlett School of Planning, University College London</institution>
          ,
          <addr-line>London</addr-line>
          ,
          <country country="UK">UK</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Centre for Urban Science &amp; Progress London, Department of Informatics, King's College London</institution>
          ,
          <addr-line>London</addr-line>
          ,
          <country country="UK">UK</country>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>Population Health Innovation Lab, Department of Public Health, Environments &amp; Society, London School of Hygiene &amp;</institution>
        </aff>
        <aff id="aff4">
          <label>4</label>
          <institution>Tropical Medicine</institution>
          ,
          <addr-line>15-17 Tavistock Place, London</addr-line>
          ,
          <country country="UK">UK</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>Interventions to increase active commuting have been recommended as a method to increase population physical activity, but evidence is mixed. Social norms related to travel behaviour may influence the uptake of active commuting interventions but are rarely considered in their design and evaluation. In this study we develop an agent-based model that incorporates social norms related to travel behaviour and demonstrate the utility of this through implementing car-free Wednesdays. A synthetic population of Waltham Forest, London, UK was generated using a microsimulation approach with data from the UK Census 2011 and UK HLS datasets. An agent-based model was created using this synthetic population which modelled how the actions of peers and neighbours, subculture, habit, weather, bicycle ownership, car ownership, environmental supportiveness, and congestion (all configurable parameters) afect the decision to travel between four modes: walking, cycling, driving, and public transport. The developed model (MOTIVATE) is a configurable agent-based model where social norms related to travel behaviour are used to provide a more realistic representation of the socio-ecological systems in which active commuting interventions may be deployed. The utility of this model is demonstrated using car-free days as a hypothetical intervention. In the control scenario, the odds of active travel were plausible at 0.091 (89% HPDI: [0.091, 0.091]). Compared to the control scenario, the odds of active travel were increased by 70.3% (89% HPDI: [70.3%, 70.3%]), in the intervention scenario, on non-car-free days; the efect is sustained to non-car-free days. While these results demonstrate the utility of our agent-based model, rather than aim to make accurate predictions, they do suggest that by there being a 'nudge' of car-free days, there may be a sustained change in active commuting behaviour. The model is a useful tool for investigating the efect of how social networks and social norms influence the efectiveness of various interventions. If configured using real-world built environment data, it may be useful for investigating how social norms interact with the built environment to cause the emergence of commuting conventions. agent-based modelling, active travel, physical activity, car-free days Funding: This research was funded by KCL-LSHTM seed funding. Robert Greener is supported by a Medical Research Council Studentship [grant number: MR/N0136638/1]. Steven Cummins is funded by Health Data Research UK (HDR-UK). HDR-UK is an initiative funded by the UK Research and Innovation, Department of Health and Social Care (England) and the devolved administrations, and leading medical research charities.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Recently, policies have been introduced which aim to encourage more physically active modes of
transport, particularly walking and cycling, to incorporate more physical activity into everyday
life [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Reduced car dependency is likely to mitigate other risk factors known to impact health,
including noise and air pollution, the risk of road trafic injury [
        <xref ref-type="bibr" rid="ref2 ref3 ref4">2, 3, 4</xref>
        ], all-cause mortality and
cancer incidence [
        <xref ref-type="bibr" rid="ref5 ref6 ref7">5, 6, 7</xref>
        ], and obesity [
        <xref ref-type="bibr" rid="ref8 ref9">8, 9</xref>
        ]. Governments are therefore investing to improve the
environment to remove active-travel barriers. However, intervention evaluations are dificult,
time-consuming, and expensive, and few have produced robust impact evidence [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>
        Interventions assume that environment changes will automatically result in individuals
adapting their behaviour [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. However, this ignores the role of norms of travel behaviour
in influencing the uptake of such interventions. A social norm is an understanding held by
members of a population as to what a ‘proper’ behaviour is under a given set of circumstances.
By norms, we refer to emergent social norms, i.e., behaviour which becomes prevalent through
interaction, rather than prescriptive norms (obligation, prohibition, and permission).
Mobilityrelated social norms may relate to the desirability owning or driving a car, or the appropriateness
of riding a bicycle. Social norms may difer according to population groups (age, gender, etc.)
and may be conditioned by environment or culture and are often socially and spatially patterned.
      </p>
      <p>
        A social norm encompasses two strongly related ideas: first, that individual behaviour – and
the willingness to change that behaviour – is strongly influenced by both previous performances
of that behaviour (‘habit’) and the social context within which the behaviour unfolds; and second,
that the observation of other people’s behaviour (peers, neighbours, the public, etc.) can either
shift or reinforce a behaviour. Therefore, the behaviour of individuals cannot be easily separated
from the broader social and community systems in which they are embedded. Environmental
interventions to promote active commuting are complex primarily due to the social and physical
systems within which these interventions occur, the contextually contingent nature of impacts,
and the agency of groups and individuals whose behaviours they aim to influence [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ]. This
suggests that to generate better representations of the systems into which active commuting
interventions are deployed, incorporation of social norms related to travel behaviour is required.
Using norms related to travel when evaluating active commuting interventions may help reduce
uncertainty over efectiveness and support practitioners in making more informed decisions.
      </p>
      <p>In this paper, we describe the development of an agent-based model that incorporates norms
related to travel behaviour and then, to demonstrate its utility, we simulate the impact of
introducing car-free days as a hypothetical use case. We present MOTIVATE (Modelling
Normative Change in Active Travel), an open-source, agent-based model, which has configurable
built environments and populations, that simulates the shift to active commuting as a result
of interventions. We briefly review the related work and its relation to ours in Section 1.1.
We describe in Section 2 how we generate a synthetic population using a microsimulation
approach, before describing the design and development of MOTIVATE. Then, we describe how
we implemented an intervention of car-free Wednesdays, followed by the statistical methods
used. We then provide the results of this intervention – car-free days increased the odds of an
active journey by 77.7% (HPDI: [77.7%, 77.7%]). Finally, we discuss our results in comparison to
existing transport models, while recognising the strengths and limitations.</p>
      <sec id="sec-1-1">
        <title>1.1. Related work</title>
        <p>
          Agent-based models (ABMs) are a tool that allow the simulation of the dynamic processes of
behaviour change at the population level (the model) by accounting for interactions between
heterogeneous individuals (the agents) and their environment [
          <xref ref-type="bibr" rid="ref13">13</xref>
          ]. While there exist ABMs
exploring transport systems at a low-level [
          <xref ref-type="bibr" rid="ref14">14</xref>
          ], there do not exist models that investigate
the impact of social norms on transport behaviour. The existing work is focussed mainly on
trafic flow and route decisions [ 15, 16, 17]; our work focusses on the decision for the method of
commuting and is not focussed on modelling the flow of people through an environment. We aim
to produce a configurable agent-based model of the decision process which takes a wide range
of inputs resulting in commuting behaviour. This difers from existing simulations which focus
on how agents flow through cities, with built environment and socio-demographic attributes
being a key determinant of commuting behaviour. By focussing on the decision, we can focus
our eforts on how a diverse range of inputs, such as the actions of peers and neighbours, habit,
subcultures, congestion, bicycle and car ownership, and dynamic characteristics such as the
weather afect the decision to undertake diferent transport methods. This allows us to explore
the parameters’ efect on interventions, without being concerned about trafic flow.
        </p>
        <p>Furthermore, there do not exist models of the decision to commute that incorporate social
norms. In our model, social norms exist as the joint efects of friends, neighbours, and a mobility
culture to which agents belong. Other work has modelled how the actions of friends influences
norms around smoking cessation using agent-based modelling [18]. Further normative
agentbased models have shown that cultural heterogeneity can cause heterogeneity in results [19].
Applied agent-based modelling work has shown how norms, the (food) environment, and peer
influence interact to cause changes in fruit and vegetable consumption [ 20].</p>
        <p>The methods for incorporating norms is discussed in greater detail elsewhere [21]; however,
here we primarily focus on the emergence of norms through transmission [22, 23, 24]. We also
model how the norms influence behaviour through internally directed enforcement [25, 26, 27, 28],
where there is internal pressure to conform with the norm due to the inherent social desire to
conform with the prevailing norm. The sanction for not conforming is implicit, as there is a
benefit to fitting in that is lost if not conforming.</p>
        <p>While there exist many studies investigating norms in health outcomes there do not
exist ones that use norms to investigate active commuting behaviour. Our model addresses
this by exploring the decision to perform active commuting by including an agent’s norm in
their decision-making. These norms emerge through observing the behaviours of friends and
neighbours and through cultural influence, and they influence behaviour through the desire to
ift-in.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>2. Materials &amp; Methods</title>
      <p>To develop an ABM with relevance, we selected the London Borough of Waltham Forest (UK),
who have been a leader in interventions to increase active travel [29], as a reference, which could
be replaced by other users. Our approach involved three steps: (i) create a synthetic population,
mirroring Waltham Forest; (ii) create an ABM of active commuting; and (iii) demonstrate the
utility of the ABM through a hypothetical active travel intervention: car-free Wednesdays.
2.1. Synthetic population generation using microsimulation
To generate realistic agent behaviours, an Iterative Proportional Fitting (IPF) microsimulation
approach [30, 31] was used to assign attributes (e.g., sex, ethnicity, distance to workplace) as a
constraint on modal choice. IPF microsimulation is a well-established statistical method for
commuting behaviour [30] which will seek to generate synthetic population based upon a series
of constraints from observed data. Data from the UK Household Longitudinal Survey (UK
HLS) (2014–16) [32] on active commuting behaviour for London (n=6 310) was combined with
2011 Census population data for Waltham Forest [33] using IPF to produce a realistic agent
population whose socio-demographic attributes and behaviours were highly correlated (99.9%).</p>
      <p>Following integerisation and expansion using the Truncate, Replicate and Sample (TRS)
approach [31] we identified an absence of questions about bicycle access from the ‘ethnic boost’
component of the UK HLS dataset. To solve this, we modelled access to a bicycle using a logistic
regression model conditioned on sex, age group, ethnic group, employment status and car usage.
Inferring access in this way yielded a synthetic population in which 46.5% of people had access
to a bicycle, similar to the National Travel Survey estimate of 42% [34].</p>
      <p>Commute distances reported in the UK HLS
data were often rounded (e.g., 5, 10, 15, etc.) and
Table 1: Modal distribution of commutes. thus are subject to misclassification. To generate
Mode Local (%) City (%) Beyond (%) more accurate measures of commute distance
Car 43.5 25.9 54.0 we used data from a ‘safeguarded’ 2011 Census
Cycle 3.5 2.8 0.8 table [35]. For Waltham Forest, we observed that
PWuabllkic Transport 2311..55 710..12 450..20 the mean straight line walking distance for an
individual was 2.64 km; cycling distance was 7.72
km (with a bimodal distribution); car distance
was 9.36 km; and public transit distance was 10.72 km. These are the average distances that
individuals in Waltham Forest commute on a daily basis. The empirical distributions informed
the choice of either a log-normal or Gaussian Mixture Model to generate individual agent
commute distances. Commute distances could not be negative, or greater than 10 km (walking),
40 km (cycling), or 80 km (public transit or private car) as these are infeasible. Values outside
these bounds were ignored, with another value being drawn. Commutes were then classified as
local (0 to 4 943 m; mean=2 588 m), city (4 944 to 20 059 m; mean=10 536 m), or beyond (&gt;20 059
m; mean=31 096 m), yielding the modal distribution (Table 1).</p>
      <sec id="sec-2-1">
        <title>2.2. Model development</title>
        <p>The agent-based model was developed in Rust [36]. The source code for the model and for the
statistical analysis, as well as the raw results, are publicly available to download [37].</p>
        <p>In developing the model we deemed the following variables to be of importance: the weather,
as it would likely impact walking and cycling; environmental supportiveness, as neighbourhoods
better supporting active travel should have more active travel; congestion, as people living in
neighbourhoods which have congested roads may be more likely to walk or cycle; subculture,
there exist certain mobility subcultures afecting their propensity to adopt active travel modes
[38]; the actions of neighbours and peers, as there is likely to be a peer influence; commute length,
as at some distances, some modes are impractical; habit, as what you have done before influences
what you will do in the future; bicycle ownership; and car ownership. The weather pattern,
environmental supportiveness, capacity (which determines congestion), subculture, commute
length, bicycle and car ownership are all configurable parameters to the model. Figure 1 gives
the relationship between all the global-level, neighbourhood-level, and agent-level variables and
travel behaviour, using arrows to denote the direction of influence. This shows the higher-level
structure of the model, without focussing on implementation details (for this, see the class
diagram in Appendix A). These parameters will be referred to in Tables 2, 3, and 4.</p>
        <p>There are two global-level variables which
both relate to the weather. These are given
in Table 2. The first is the weather pattern.</p>
        <p>This was generated by taking a Markov chain
model with two states: Wet and Dry. This
was informed from historical daily weather
data [39] from 2017; days with over 4.4 mm
of rain were chosen as Wet days, other days
were Dry. The threshold of 4.4 mm is the
point at which daily hires from TfL’s Cycle
Hire scheme fell. The Markov chain was used
as it is more likely to be bad weather if the
previous day was bad weather. The second
is the weather modifier , this states that for a
given weather and mode how is the agent’s
Figure 1: vnRaeerilgiaahtbiboleonsusrhahnipodotdrb-aelvetewvleeble,enahnadvgialooguberan.lt--lleevveell,
rdnaeemsgWiaeretetiedvtreeoifinsitaenatdflukioe2enn0t,chnweaetiohgnmehnbwoobdauaelrdkchihwnoagoendaagstnh,edbdear.c,syItenchdleoiunrupegro.ipsnaaelectoral wards in Waltham Forest in London,
UK. Each of these neighbourhoods has a number of parameters, given in Table 3. The
supportiveness value describes how much a given neighbourhood supports a given transport mode and,
if parameterised in future works, could be taken as a proxy for features such as the number of
public transport stations, number of cycle lanes, width of pavements, quality of roads, etc. In our
implementation, this means that the greater this value, the better the neighbourhood supports a
given mode. This value is used, rather than individual components of the environment, to allow
other users of the model to include parts of the environment of interest by converting their
values to a value between 0 and 1. For each neighbourhood and transport mode, there is also
a capacity beyond which there is congestion, which serves a negative influence on an agent’s
decision-making. Congestion is proportional to the excess transport (i.e., that in excess of the
capacity). The more congestion there is for a mode, the less likely it is an agent will take it.</p>
        <p>We also define three subcultures to which agents can belong; these associate a desirability with
each mode which expresses how ‘desirable’ it is to an agent belonging to that subculture. This
also falls within the range 0 to 1. There was driven by a substantive body of work surrounding
the role of cultural norms in mobility choices and policy formulation [40, 41]. Informed by this
work, we developed three hypothetical subcultures. Consequently, the first subculture, A, in
which modes are ordered cycling, driving, walking, and public transport. This group values
active travel as part of a healthy lifestyle, but also sees it as a consumption choice in which
money is spent on both bicycles and cars as signifiers of success, with public transit being seen
as the least desirable in that sense. The second subculture, B, is a pro-driving subculture, in
which modes are ordered driving, public transport, walking, and cycling. People belonging to
this culture are averse to active commuting; this is reflected in the ordering. The final subculture,
C, is a pro-active-travel subculture, with the ordering: walking and cycling (equal), then public
transport, then driving. People belonging to this subculture value taking active journeys.</p>
        <p>We defined 111 166 agents in the model – the number of commuters in Waltham Forest, as
identified by the microsimulation approach. The microsimulation approach described previously
was used to generate the synthetic population used in the model. The agents were randomly
allocated to a neighbourhood with the probability determined by the microsimulation approach
based upon car ownership, bicycle ownership, and population of the neighbourhood, and were
randomly allocated to a subculture uniformly. Two social networks that agents belong to
were also generated randomly. The first network is a global social network across all agents,
representing social and work relationships. The second is a neighbourhood-wide ‘neighbour
network’, representing the observation of other local (i.e., within the same neighbourhood /
electoral ward) agent behaviours by each individual network. The global network is a
WattsStrogatz small-world network ( = 3;  = 0.6 ) [42] and the neighbour network is a scale-free
network generated using the Barabási-Albert model of preferential attachment ( 0 = 10) [43].
The small-world network was chosen as networks of friends were expected to exhibit
smallworld properties and the scale-free network was chosen as there are expected to be highly
influential neighbours. The use of these two networks, as opposed to one global network, is
because friends are expected to have greater influence, and because the properties of the two
networks are likely to difer. Each agent also has a habit value for each mode which represents
their recent actions. This is calculated as the exponential moving average of their choices. This
was chosen as more recent actions are expected to have greater influence. The parameters used
to configure the agents are described in Table 4.
the previous congestion they have experienced. The cost describes how commuting distance,
environmental supportiveness, and the weather prevents commuting from being undertaken.
norm(, , ) =
number of friends of  performing  at time  − 1
number of neighbours of  performing  at time  − 1
number of friends of 
number of neighbours of 
⋅ social_connectivity()+</p>
        <p>⋅ neighbourhood_connectivity()+
subculture_desirability(subculture(), ) ⋅ subculture_connectivity()
budget(, , ) =
congestion_mod(neighbourhood(), , ) ⋅
(norm(, , ) +
habit(, , ) ⋅ consistency() )
(1)
(2)</p>
        <p>Every day ( ), each agent ( ), for each mode ( ), calculates their norm (Equation 1). This is a
combination of the actions of their friends, neighbours, and the pressure from their subculture.
By combining friends, neighbours, and subculture, it describes what there is social pressure
for, and therefore describes “a standard or pattern of social behaviour that is accepted in or
expected of a group” [44]. Behaviours of agents also influence the norms of others, resulting in
feedback loops in the system. A budget for each mode is created (Equation 2); where if there
was nothing preventing the use of the mode, this would be the willingness to perform it. Added
to the norm is the habit, discussed previously, weighted by how consistent the agent is. This
value is then multiplied by the congestion modifier (Table 3). Finally, these budgets are ranked
for the four modes to create a preference. This is the ranked travel budget; where if there was
nothing preventing the use of the mode, this would be the order of preference.
cost(, , ) =
1 ⋅ (commute_distance_cost(commute_distance(), ) +
2</p>
        <p>(1 − neighbourhood_supportiveness(neighbourhood(, )))) ⋅
(weather_sensitivity(, ) + weather_modifier (, ) + resolve(, , ))
(3)</p>
        <p>The cost of taking each mode is then calculated (Equation 3). The commute cost due to the
distance and the cost due to the neighbourhood supportiveness are averaged. Each agent’s
weather sensitivity is multiplied by the weather modifier for the environment (Table 2) and by
the agent’s resolve. Resolve is a calculated value which reduces the cost of performing an active
mode if there was wet weather the previous day and an active mode was taken; it increases
the cost if there was wet weather and an active mode was not taken. There is no efect if the
weather was dry the previous day. Resolve was implemented as it was hypothesised that those
who use active modes on a poor weather day are more likely to on a following poor weather
day, and those who did not use active modes are less likely to on a following poor weather day.
This weighted weather modifier is multiplied by the average cost. This is ranked in reverse –
modes with a higher cost will have a lower rank – and called the reverse ranked travel cost.</p>
        <p>Agents will then add the ranked travel budget and reverse ranked travel cost together, and
will then choose to select the mode with the highest combined rank which is available to them.
In other words, they cannot drive if they do not own a car, and they cannot cycle if they do
not own a bicycle. This means that agents choose the commute mode with the greatest gap
between budget and cost. This is primarily an economic calculation where the cost describes
the (not fiscal) cost to an individual, taking into account the weather and the environment, and
the budget describes the willingness to perform an action, based upon perceived benefit.</p>
        <p>The approach was chosen as it corresponds well to work identifying the (not just fiscal) cost
and benefits (such as health benefits) of commuting as key drivers of commuting behaviour [ 45].
While alternative, more domain-agnostic, models of behaviour, such as BDI [46] could have
been used, this approach fits the existing public health literature around active travel better.
We presented this method to domain stakeholders, including professionals working in local
government, who agreed that it seemed a reasonable reflection of the decision process.</p>
        <p>The parameters are configurable – a future model could use this as a base. However, depending
on the criticality of results, calibration and validation against real-world data would be required.</p>
        <p>Intervention scenario: We evaluate the implementation of a hypothetical intervention
‘car-free Wednesdays’ which prohibits the use of cars on that day. This was compared to a
control scenario of no intervention. In the car-free days (CFD) scenario, for the first year (day &lt;
365), there were no car-free days. From the first year onwards (day ≥ 365), there was a car-free
day every Wednesday (day mod 7 = 2). The model was then run for four further years.</p>
      </sec>
      <sec id="sec-2-2">
        <title>2.3. Statistical analysis</title>
        <p>For each intervention tested, a one-year burn-in period after the intervention is excluded. This
was chosen to ensure that the efect of the intervention had become stable. For each day the
model outputs the count of active journeys over all, as well as separated by subculture and
neighbourhood. These can be converted to a proportion by dividing the value by the total count
or the count by subculture and neighbourhood, as appropriate. This is outputted as a CSV file.
A Bayesian binomial regression model (Model 4) was fitted predicting the number of active
journeys made as a proportion of total journeys between 1 and 4 years post-intervention.</p>
        <p>is the number of active journeys (i.e., those made by
walking or cycling) in the  th scenario (1=control; 2=CFD) for the  th
  ∼ Binomial(  ,   ) population, which varies only by the 200 randomly generated
logit(  ) =   social network structures.   is the total number of journeys
  ∼ Student-T(3, 0, 1) (population multiplied by number of days). A Student-T(3, 0, 1)
(4) prior was used for the intercept (  ). This weakly informative
prior has heavy tails to allow for extreme values. The odds
ratio (OR) of CFD vs. control is exp( 2 −  1).</p>
        <p>This estimates the number of active journeys as a function of the total number of agents in
the population and scenario (control vs. CFD) (  ) and the probability of any given journey
being active (  ). The logit of the probability (ln (  / (1 −   ))) is defined as   which changes
only based upon the scenario. This statistical model assumes that the probability of an active
journey depends on whether the simulation is in the control or car-free days scenario. The prior
distribution Student-T(3, 0, 1) constrains the potential values of   to what could be reasonably
expected. This is a Bayesian binomial regression model [47], which, in layman’s terms, predicts
a combination of binary outcomes, active travel (1) or not (0), based upon an independent
variable (the scenario). A property of this is that the exponentiated   coeficient is the odds of
an active journey – i.e., for an inactive journey there are exp(  ) active journeys.</p>
        <p>Model 5 extends Model 4, where  is 1 if the count of
active journeys is not from Wednesdays, 2 if it is. The
  ∼ Binomial(  ,   ) value of Wednesday? is 1 if the observation is from a
logit(  ) =   +   ⋅ Wednesday? Wednesday (i.e.,  = 2 ), 0 otherwise. This separates the
  ,   ∼ Student-T(3, 0, 1) results for the car-free days from non-car free days.
Ev(5) erything else remains the same. The OR of Wednesdays
vs. non-Wednesdays in the control is exp( 1); in the CFD
scenario it is exp( 2). The OR for Wednesdays in the CFD
vs. control is exp (( 2 +  2) − ( 1 +  1)); for non-Wednesdays it is exp ( 2 −  1).</p>
        <p>Model 5 extends Model 4 by separating the efect of Wednesdays vs. non-Wednesdays. In
this model,   is the (logit) probability of an active journey in scenario  on a non-Wednesday
and   is the increase in the (logit) probability of an active journey in scenario  because it is a
Wednesday. A property of this model is that by exponentiating parameters, as described in the
preceding paragraph, odds ratios (OR) can be obtained. These describe the percentage change in
the odds as a result of (for example) it being a Wednesday vs. a non-Wednesday in the car-free
days scenario (exp( 1)). These models impose no structure upon the data, only assuming that
the probability is as a result of the scenario, and (for Model 5) whether the day is a Wednesday.</p>
        <p>Models were fit using Julia [ 48] and Turing [49] (using DynamicNUTS [50, 51]). Four chains
were used with 1 000 warm-up and 1 000 sampling iterations per chain. Trace plots assessed
convergence. Prior predictive checks [47, 52] assessed the suitability of the prior distributions.
Posterior predictive checks [47, 52] assessed the fit. The distribution was summarised using
the posterior mean and the 89% highest posterior density interval (HPDI) [47, 52]. 89% gives
greater numerical stability [53, 52], and is an interval for which the parameter is expected to lie.</p>
      </sec>
    </sec>
    <sec id="sec-3">
      <title>3. Results</title>
      <p>Since we observe the entire population in each scenario ( = 111 166 per simulation – the
commuting population in Waltham Forest) and obtain daily results ( = 783 – every weekday
for 3 years [from start of Y3 to end of Y5]) the generated credible intervals are narrow. For the
ifrst model (Model 4), in the control the odds of an active journey (walking or cycling) ( 1) were
0.091 (89% HPDI: [0.091, 0.091]); i.e., for every inactive journey, in the control there were 0.091
active journeys. CFD increased active journeys by 77.7% (OR 1.777; 89% HPDI: [1.777, 1.777])
compared to the control scenario; i.e., there was a 77.7% relative increase to the odds of 0.091.</p>
      <p>For Model 5, in the control scenario, the odds of an active journey on a non-Wednesday
( 1) were 0.091 (89% HPDI: [0.091, 0.091]). In the CFD scenario, the odds of an active journey
on non-Wednesdays were 70.3% (OR: 1.703; 89% HPDI: [1.703, 1.703]) compared to the control.
In the control, the odds of an active journey were 0.1% (OR: 1.001; 89% HPDI: [1.001, 1.001])
greater on Wednesdays than non-Wednesdays. In the CFD scenario, the odds of an active
journey were 22.4% (OR: 1.224; 89% HPDI: [1.224, 1.224]) greater on a Wednesday compared
to a non-Wednesday. Finally, the odds of an active journey were 108.2% (OR: 2.082; 89% HPDI
[2.082, 2.082]) greater on Wednesdays in the CFD scenario compared to the control.</p>
      <p>Figure 2a shows the CFD scenario, with the moving average of active commutes separated
by run and scenario. A run in the same scenario difers only by the social networks, which are
generated randomly. Focussing on the long-run, we observe that car-free days causes a step
change active commutes. Also, it appears to introduce more instability, as shown in the figure.</p>
      <p>Figure 2b shows the CFD scenario’s efect across the 3 subcultures. Focussing on the long-run
trend, in the control scenario, as expected, the pro-driving subculture (B) has the least number of
active journeys. This is followed by the pro-cycling subculture (A) and then the pro-active-travel
subculture (C). The CFD intervention causes the pro-driving subculture (B) to perform more
active journeys than the pro-active-travel subculture (C) in the control scenario. The others are
greater in turn (C is greater than A which is greater than B). The gap between the subcultures
is also widened with the intervention having most efect in the pro-active-travel group.</p>
    </sec>
    <sec id="sec-4">
      <title>4. Discussion</title>
      <p>This paper presents MOTIVATE, an agent-based model which incorporates social norms related
to travel in simulations of active commuting interventions. We demonstrated the model through
(a) Separated by scenario and run
(b) Separated by scenario, run, and subculture
(A / B / C)
a scenario introducing car-free days vs. a control. Introducing car-free days increased the odds
of active travel by 77.7% (89% HPDI: [77.7%, 77.7%]) in the four years following intervention
implementation. This is a large relative increase; however, absolute efects are modest, as the
odds in the control were 0.091 (89% HPDI: [0.091, 0.091]) – a 77.7% increase on the initial rate of
8.3% (the percentage is odds / 1 + odds) is an increase of ≈ 6.4 percentage points.</p>
      <p>Car-free days force an individual to make a change to commuting behaviour once per week.
This constraint not only reduces the use of inactive modes on that particular day but may also
act as a ‘nudge’ to change overall commuting preferences by exposing individuals to active
commuting and shifting norms around active commuting on non-car-free days. This is shown
in our model, as on non-Wednesdays, in the car-free days intervention scenario, the odds of
active travel were 70.3% (OR: 1.703; 89% HPDI: [1.703, 1.703]) greater than the control scenario.</p>
      <p>A ‘nudge’ of car-free days, in our model, causes a lasting change in behaviour. Unless agents
need to divert from their habit, they will not. By forcing a change in habit, this results in a
change in norm. The short-term change in habit due to car-free Wednesdays results in the
influence given as peers and neighbours changing, resulting in a change in norm for those
observing the new non-car-free behaviour – the forced change in habit destabilises the norm.</p>
      <p>
        Our model difers from existing models of transport [
        <xref ref-type="bibr" rid="ref14">14, 15, 16, 17</xref>
        ]; it is not a trafic simulation
– we do not aim to model trafic flow through a city. The intended purpose is not to make accurate
predictions of how people commute to work. Rather, it is to explore how a range of inputs,
including multiple social networks capturing the efect of peers, as well as neighbours, habit, and
variable environment parameters, such as the weather, afect the decision to perform behaviour.
For example, in Figure 2b we show how the CFD intervention may afect members of diferent
psychological subcultures diferently. We also see that habit causes the CFD intervention to be
sustained on non-car-free days, where there were 70.3% (OR: 1.703; 89% HPDI: [1.703, 1.703])
more active journeys than the control scenario. This model can be used to explore the efect of
interventions on various aspects of the decision-making process, such as habit, social networks,
congestion, and the actions of peers and neighbours. This is a complement to models that more
accurately model the spread of individuals through urban environments. By combining the
evidence generated by real-world studies, trafic simulations, and simulations of the
decisionmaking process (such as ours), a greater understanding of transport behaviour may be attained.
      </p>
      <p>In common with all simulations, the results presented in this paper are not necessarily
an accurate prediction of real-world efects; the only way to obtain this is to perform the
intervention in the real-world. However, the utility of the model is in allowing the comparison of
the efectiveness of interventions under consistent conditions in order to aid decision-making. In
this study, car-free days are efective. Such information, accounting for model assumptions, may
help better select and prioritise active commuting interventions in the absence of strong evidence
on efectiveness. It may also help funders prioritise evaluations of promising interventions
identified by simulations [ 54]. This model may be helpful to understand currently radical policies
and how the underlying social structures impact the efectiveness of these interventions.</p>
      <sec id="sec-4-1">
        <title>4.1. Strengths and limitations</title>
        <p>The strengths in this approach have been the use of microsimulation to generate a realistic
synthetic population for use in the model. This has been grounded in data from oficial statistics.
The open-source nature of the model allows for adaptation and use of the model by others.</p>
        <p>Future work could address some weaknesses. The environmental data is not calibrated –
geographic data could do this. Personal journeys and the processes changing car and bicycle
ownership could be considered. Encouragement to purchase bicycles or give-up cars may
work, though we cannot currently assess this. The fiscal cost of travel is also disregarded; this
is a major factor. Future work could consider the efect of price given your social and built
environment. There is room to include variables as part of the travel budget or cost as needed.</p>
        <p>The HPDIs cannot be interpreted as intervals of what would happen in the reality. Normally,
statistical models directly model real-world data, as such the statistical model is one of the
realworld data-generating process, and assuming that the model is not mis-specified intervals can be
interpreted in the terms of the real world. This is not the case in this statistical model. Here, the
model it is directly modelling results from the agent-based model, and it can only be interpreted
in terms of the simulated model ‘world’ – the agent-based model is the data-generating process.
In order to interpret it in terms of the real world, we would need to strengthen the link between
the simulated model world and reality through further calibration and validation.</p>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Conclusion</title>
        <p>The MOTIVATE model and the findings presented are an initial step in helping to improve
understanding of active commuting interventions which seek to increase population physical
activity. The presented agent-based model incorporates social norms related to travel behaviour
in order to provide a more realistic representation of the socio-ecological systems in which
active commuting interventions are deployed. The utility of the model has been demonstrated
by simulating introducing car-free Wednesdays. Utilising in silico studies, such as MOTIVATE
and more traditional trafic simulations, could be a cost-efective way of aiding public health
decision-making and setting research priorities. This ABM is representative of new classes of
model that draw on both social and environmental efects that point towards insights across
applications not only in health, but in any area where place and network-based efects overlap.</p>
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      </sec>
    </sec>
    <sec id="sec-5">
      <title>A. Class diagram of MOTIVATE</title>
      <p>Arrows between classes are omitted for space. See method signatures for the relationships.
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  </body>
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