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Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
The need of latent variables for modelling decision-making in evacuation
simulations R. Lovreglio1, D. Borri1, E. Ronchi2, A. Fonzone3, L. dell’Olio4
1 Department of Civil, Environmental, Planning, Building and Chemistry, Politecnico di Bari, Via
Edoardo Orabona, 4, 70126 Bari, Italy; 2Department of Fire Safety Engineering, Lund University, P.O. Box 118 SE-221 00 Lund, Sweden; 3 Transport Research Institute, Edinburgh Napier University, 10 Colinton road, Edinburgh, EH10
5DT, United Kingdom; 4 Transport Systems Research Group, Universidad de Cantabria, Avda. de los Castros, s/n39005,
Santander, Spain;
Abstract Evacuation models generally tend to make over-simplifications in the representation of human
behaviour in fire due to the difficulties to capture its complexity. This work shows how ‘new’
discrete choice model approaches allow overcoming this issue. A description of the existing state-
of-the-art of discrete choice models is introduced to highlight the potential of those models. Three
case studies are introduced describing an application of the Random Utility Theory to simulate
evacuees’ decisions pertaining to the strategic, tactical and operational levels. This work highlights
the need for new datasets including indicators which allows estimating latent factors which may
affect evacuees’ decision.
Keywords: human behaviour in fire; decision-making; random utility theory; latent factors.
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
1. Introduction
The use of Performance Based Design (PBD) is gradually increasing in the field of fire safety
engineering since traditional prescriptive methods often provide an excessively rigid framework
which cannot address the emerging challenges of new buildings [1].
The main goal of the PBD is to estimate the safety of a building by comparing two times, namely
the Available Safe Egress Time (ASET) and the Required Safe Egress Time (RSET). The ASET is
the time starting with the beginning of an emergency (i.e. a fire ignition) and ending when the
conditions of the environment under consideration (i.e. buildings, transportation systems, etc.)
becoming untenable for human life. RSET is the time necessary by occupants to evacuate this
environment safely. The comparison of the ASET and the RSET, therefore, allows estimating the
safety condition in a given evacuation scenario.
RSET depends upon evacuees’ behaviour and a reliable measurements of this time cannot be
carried out without a deep understanding of the complexity of human behaviour [2]. Different
models and computational tools have been developed to estimate the RSET [1,3]. These models can
be divided into two classes, namely macroscopic and microscopic [4]. Macroscopic models
investigate the system as a whole by using fluid-inspired differential equations whereas microscopic
models focus on the behaviour and decisions of individual evacuees and their interactions with
other evacuees in the crowds [4]. Even though microscopic models are generally more
computationally expensive, they received a great deal of attention in the last decades since they
represent a closer representation of the issue under consideration (i.e. individual evacuees forming a
crowd) [1]. Microscopic models can be divided into cellular based (e.g. floor field cellular automata
model), physical force based models (e.g. social force model), rule based, etc. [4–6].
The current paradigm for existing microscopic evacuation models is the time-line model, which
divides the RSET into different times [7,8]. Each time depends on different decisions that need to
be taken by each evacuee as well as by each simulated evacuee (i.e. agent) in the simulated
environment [2]. These decisions can be divided into three hierarchical levels, namely strategic,
tactical, and operational[9].
All these decisions are affected by several factors which can concern the social and physical
environmental (e.g. the behaviour of other evacuees, the dynamic of the fire, etc.) and personal
characteristics (e.g. gender, age, past experiences, etc.). Some of these factors can be directly
observed whereas there are others, which are latent. The latent factors, however, can be statistically
estimated by using indicators (i.e. observable psychometric measurements). To date, different
statistical approaches are available to address this issue, namely factorial analysis [10], item
response theory [11], Random Utility Theory[12,13], etc. However, these latent factors are quite
often not taken into account in existing evacuation models since over-simplifications are preferred
because of the difficulties to capture human behaviour into computers as mathematical equations or
rules [14,15]. Another reason behind these over-simplifications is the lack of data on human
behaviour in fire [16]. Even though different databases have been built investigating both real
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
emergencies (e.g. HEED database for the 9/11 WTC evacuation study) and experimental
evacuations, further studies are still needed [17,18].
This work investigates latent factors in order to improve existing evacuation models. This is done
by discussing pros and cons of different modelling approaches for discrete choices (i.e. classic
logistic regression vs. mixed and hybrid logistic regressions) [19,20].
The present work starts with an overview of the time-line model and the decisions affecting
different phases. Then a brief discussion concerning the difference of the existing discrete choice
modelling approaches is provided. A set of case studies is introduced in order to discuss the impact
of latent factors on different evacuation choices (i.e. decision to evacuate, exit choice and local
movement). A discussion on the need of new modelling frameworks able to ‘harness’ the
complexity of human behaviour in fire emergencies is presented.
2. Decision-making during evacuations
The time line model addresses the calculation of RSET by dividing it in several different time
intervals. During each time interval, an evacuee has to deal with different decisions, which can
make him/her passing to another time interval of the time-line model. To date, different
subdivisions of RSET have been proposed. One of the most used in the literature is that proposed
by [7,21,22]. Equation 1 shows the time intervals according to this subdivision.
𝑅𝑆𝐸𝑇 = 𝐴𝑇 + 𝑃𝐸𝑇 +𝑀𝑇 Eq. 1
where:
AT: Alarm Time;
PET: Pre-evacuation Time;
MT: Movement Time.
AT is the interval, which starts with the ignition of the fire and ends once the first alarm/warning is
provided to the evacuees. This interval can be divided in turn into the time interval required to
detect the fire (e.g. automatic detection system) and the time interval required to start the alarm or
providing warnings to the evacuees. AT can be equal to zero for evacuees since they could detect
the fire without any other warnings.
PET is the time interval which starts with the alarm and ends once an evacuee starts moving toward
a safe place. This time interval is also known in the literature with different names (i.e. pre-
movement time, delay time, waiting time, initial response time, time to start, and delay time to start)
and it is the sum of two sub-time intervals, namely Recognition and Response times.
The Recognition Time (RecT) is the interval between the first cues (i.e. alarm, warnings, etc.) is
perceived by an evacuee and the time at which s/he realises that s/he has to respond to the new
situation evacuating. During this time, an evacuee continues with the pre-alarm activities (i.e. the
activities s/he was doing before the cues). Moreover, during this time interval, s/he may start
seeking further information to have a clear understanding regarding the perceived cues [23].
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
Therefore, one of the first decision that can be taken by an evacuee is if he should start
investigating. Then, s/he needs to interpret the situation and takethe decision on how to
behave/respond (i.e. evacuating) [23].
The Response Time (ResT) is the interval between the decision to evacuate and the time at which
an evacuees begins to evacuate (i.e. to move directly toward a safe place). Literature argues that
different actions can be performed during this time (i.e. looking for belongings, getting up, etc.) and
that evacuating is rarely the first action performed by occupants [23]. Therefore, during this time
interval an evacuee can perform a complex decision-making through which s/he can plan all the
protective actions to take before starting evacuating [24]. During this interval, an evacuee may also
start choosing among different paths and exits.
It is worth highlighting that in this work the passage from the RecT to the ResT is assumed to be
defined by the decision of evacuating [23]. However, according to other authors, this passage
occurs once an evacuee starts responding to the emergency also by seeking further information and
trying to understand what is going on [21,22].
Finally, MT (also known as travel time) is the time required by an evacuee to reach a safe place
once the ‘proper’ evacuation has begun. During this time interval, an evacuee has to choose the path
to follow and the exit to reach to evacuate from the building. Then, s/he interacts locally with
obstacles and other evacuees (i.e. local interactions).
Some of the mentioned decisions (such as path choice) could be dynamic over time. In these cases,
the final choice is the result of partial ongoing choices. For instance, the final path of an evacuee
can be the result of the preliminary choices of hyperpaths (i.e. a set of attractive paths) which s/he
makes during his/her movement toward a safe place. Figure 1 shows an evacuee which have to
choose among four different paths leading to four different exits. When s/he starts evacuating, s/he
could choose between hyperpaths A and B as first choice at time t1. Then, s/he has to choose the
final path only once the paths forming a hyperpath diverge as second choice at time t2 (t2> t1).
Therefore, the evacuee postpones the decision of the final path at time t2 since s/he will have more
accurate information about the evolution of the scenario (e.g. number of evacuees queuing, smoke,
etc.) at that time.
Table 1 summarizes the time intervals defining RSET and the decisions that need to be taken for
each of them. These decision are also divided into strategic (choice of activities), tactical
(route/destination/schedule choice) and operational (interaction with other pedestrians and
obstacles) [25].
It is worth highlighting that the time line model provides a simplification that allows for
quantitative estimations of RSET. On the other hand, the main limitation of this model is that it is
not reversible. For instance, there could be evacuees that after taking the decision to evacuate could
think over it taking a second decision not to evacuate any longer.
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
Figure 1 – Example of hyperpaths for a building.
Table 1 – Time line model and decisions
Time Line Model
Required Safe Egress Time (RSET)
Alarm Time (AT)
Evacuation Time (ET)
Pre-Evacuation Time (PET) Movement Time
(MT) Recognition Time
(RecT)
Response Time
(ResT)
Decisions
- to start investigatinga
to start evacuatinga
Plan pre-movement activitiesa
Path and exit choiceb
Path and exit choiceb
Local interactionc
astrategic level; btactical level; coperational level.
In the following section, a brief introduction of the evolution of the discrete choice models is
provided to discuss assumptions and limitations of this modelling approach.
3. Classical vs. hybrid modelling approaches
Most of the choices described in the previous section are discrete (i.e. start investigating/evacuating,
path and exit choice) whereas others (i.e. local interaction) are continuous but can be reduced to
discrete ones [26]. One of the widely used framework for modelling discrete riskless (i.e. single
certain outcome for each prospect [27]) choices is Random Utility Theory [28]. Even though, the
main postulate of this theory states that a q decision-maker behaves rationally choosing the option
among the available alternatives which maximizes his/her utility (Uq), it can be defined as
descriptive theory (i.e. a theory about how decisions are actually made) [29]. Therefore, the concept
of rationality must not be misconceived with that postulated by the normative theory (i.e. full
rationality) [29]. This assumption is in line with the findings of cognitive scientists such as H.
Simons, who states that decision-makers have limited cognitive power (i.e. bounded rationality) and
knowledge of the world [30,31]. Therefore, a rational decision-maker ‘goes about making his or her
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
decisions in a way that is procedurally reasonable in light of the available knowledge and means of
computation’ by maximizing his/her utility [30]. According to this theory, the utility assigned by a q
decision-maker to the i alternative is defined as:
𝑈𝑖𝑞 = 𝑉𝑖𝑞(𝑿𝒊𝒒|𝜷𝒊𝒒) + 𝜀𝑖𝑞 Eq.2
𝑉𝑖𝑞 is systematic part which is a function of the observed factors (𝑿𝒊𝒒) and a vector of parameters to
estimate (𝜷𝒊𝒒) whereas 𝜀𝑖𝑞 is the random part including both the idiosyncrasies of each individual
and any measurement or observational errors made by the modeller [12,28,32].𝜀𝑖𝑞can assume
different distributions which lead to the definition of different random utility models (i.e. probit
model by assuming a normal distribution, logit model by assuming a Gumbel distribution, etc.). The
standard random utility models allows estimating a single latent factor (i.e. the decision-makers’
utility) by maximizing the likelihood of the preference indicators which could be from stated
preferences, revealed preferences or a combination of them (see Figure 1) [2,33,34]. The main
limitations of this formulation is that it is not flexible enough to deal with the presence of correlated
alternatives (e.g. independence of irrelevant alternatives of the logit models). Moreover, this
standard model allows estimating the heterogeneity among decision-makers only by using
observable personal factors defining them (i.e. gender, age, etc.).
Figure 1 - Generalized random utility model by [20]. The grey boxes in the figure define the
standard random utility model.
To date, several implementations have been done to overcome these limitations by introducing
further flexible disturbances. The mixed (or random parameters) logit is one of the attempts to solve
the issue concerning the correlated alternatives by introducing flexible disturbances [12,20]. This is
formally addressed by assuming that at least one component of 𝜷𝒊𝒒 is randomly defined. This
means that the modelling framework allows simulating the heterogeneity of the taste of the
decision-makers which cannot be described using observable factors [12].Another attempt to
capture unobserved heterogeneity is that provided by the latent class models. The general idea
behind this approach is to segment decision-makers’ population into different classes exhibiting
different choice behaviours by using a class membership model [20]. Even though these
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
formulations (i.e. mixed logit and latent class models) allow simulating another level of latency (i.e.
taste heterogeneity), they do not allow investigating the influence of latent constructs (i.e. attitude,
ambition, or personality) on the decision [19,35].
The hybrid choice models are a ‘novel’ approach to address this issue. Their aim is to introduce
latent factors in the systematic part of the utility function. This framework is based on the
hypothesis that although the latent factors themselves cannot be observed, their effects on
measurable variables (i.e. indicators) are observable providing indirect information on the latent
factor by using structural equations and latent variable measurement equations describing the
relationship shown in Figure 1 [20].
Some applications of these models (i.e. logit and mixed logit) have been already used to solve some
evacuation issues. The next section provides a brief description of these applications and how these
can be improved by using the ‘new’ modelling approaches (i.e. latent class models and hybrid
choice models).
4. Case studies
Applications of standard random utility models (i.e. logit) for evacuation models have been already
used in some pioneering works to model exit choice [36] and local interactions [6,37]. The
following case study will introduce some new applications whose aim is to improve the predictive
capabilities of evacuation models. It is worth highlighting that these case studies are still in a
working phase, and further information can be found on the associated references [26,38,39].
4.1 Case Study 1: Decision to investigate and evacuate
This research investigates the possibility to model some decisions pertaining to the strategic level
(i.e. the decision to investigate and to evacuate) by using random parameter models. In this
research, both decisions are considered binary. Therefore, an evacuee is supposed to choose
between starting investigating or keeping doing his/her pre-alarm activity as a first decision and
choosing to evacuate or not as s second decision.
The proposed modelling approach is applied using data collected during unannounced evacuation
experiments in a cinema theatre in Sweden performed by Bayer and Rejnö (Figure 2) [40]. Video-
recordings were subsequently analysed by Nilsson and Johansson creating a dataset (Figure 2-a)
[23]. This dataset included choices from 571 different participants but no information about the
evacuees’ background.
In this case study, both decisions are assumed to be influenced only by social and physical
environmental factors since personal characteristics of the participants are not available. However,
the heterogeneity of the behaviour is captured by using the random parameter approach (i.e. mixed
logit). The analysis shows that the main factors influencing the decisions were the time elapsed
since the start of the alarm, the type of the alarm, the occupant’s position, and social influence.
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
(a)
(b)
Figure 2- (a) a frame of the video analysed by [23]; (b) schematic representation of the cinema
theatre.
4.2 Case Study 2: Exit Choice
This research investigates exit choice (i.e. tactical level) by using the stated preferences of 1500
participants to an online survey. The survey includes 12 different hypothetical scenarios (see Figure
3) which were administered through short videos (i.e. non-immersive virtual reality [41]). The aim
of these scenarios is to investigate the influences of social environmental factors (i.e. number of
people close to the exits, flow of the people through the exits, and number of people close to the
decision-maker direct to one of the two exits) and physical environmental one (i.e. presence of
smoke and evacuation lighting and distance of the exits). The hypothetical scenarios were defined
by using an efficient design [42]. The aim is to minimize the elements of the asymptotic variance
covariance matrix, resulting in more reliable parameter estimates for a design with a fixed number
of choice observations.
Figure 3 - Frame from one of the videos showing the hypothetical scenarios.
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
A preliminary study has been carried out to investigate the impact of environmental factors on this
decision. The results show that all environmental factors introduced in the survey statistically affect
the decision. Moreover, this study proves that there are heterogeneity in the perception of the
factors since all the parameters estimated are randomly distributed.
The survey also allows easily collecting respondents’ personal data as well as some indicators
defining the herding latency. However, these data have not included yet in the model.
4.3 Case Study 3: Local Movement
This work investigates improvements on the widely used floor field cellular automaton models
[6,31]. The kernel of these models is a multinomial logit model making evacuees choose to move
toward the neighbour cells by using a static and dynamic floor field (Figure 4). This work tries to
improve the existing kernel by introducing higher level of latency by introducing latent parameters.
The proposed approach is tested by using data from immersive virtual reality tunnel evacuation
experiment including 96 participants [43]. A trajectory data-set in the proximity of an emergency
exit is used to test a random parameter model (Figure 5). The findings of this application show that
the parameter making evacuees interacting with the static floor field is not randomly distributed.
This absence of heterogeneity can be due to limited number of participants involved in the
navigation or it could be associated with the use of virtual reality data.
Figure 4 - Allowed choices for a Moore neighborhood assumption and their probabilities.
Figure 5 – Trajectories of male (blue trajectories) female (red trajectories) participants approaching an
emergency exit in a virtual reality experiment.
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
5. Discussion
The common feature used in all the case studies is the introduction of random parameters which
allow improving the standard model by simulating the heterogeneity of evacuees’ taste. Therefore,
these models allow simulating two sources of uncertainty, namely Behavioural Uncertainty Per Se
(i.e. BUPS) and Behavioural Uncertainty of Taste (i.e. BUT) [39]. The former is introduced by
Ronchi et al. [44] stating that evacuations are stochastic processes per se (i.e. the same evacuees
facing the same exactly situation in different times may behave differently) and it is simulated by
using the random part defined in Equation 2. The latter is the uncertainty deriving from the
difference of evacuees’ tastes which is simulated by the random parameters included into the
systematic part defined in Equation 2. In fact, these random parameter could capture both the
different taste among evacuees and the different evaluation of a same context of choice by the same
evacuee [9].
These three case studies raise some issues concerning data collection. In fact, different approaches
(i.e. stated preferences, revealed preferences and a combination of them) can be used to collect data
aimed to study human behaviour in fire [2,45]. In the proposed case studies, both revealed
preferences (case study 1 and 3) and stated preferences (case study 2) were used.
From the point view of the latency study, the data used in the dataset of case study 1 does not allow
a deeper investigation of the latent factors which can affect the choice to investigate and evacuate
since no personal data and indicators were collected. This limit can be overcome in future
experiments by using non-anonymous questionnaires including questions on both personal factors
(i.e. gender, age, etc.) and indicators of latent constructs (e.g. attitude to herd, risk aversion, etc.).
However, the issue concerning the matching of questionnaire with participants observed through a
video could rise.
Case study 2 allows an easy collection of this information given the use of stated preference
surveys. However, the ecological validity (i.e. if participants show similar behavioural, emotional,
cognitive, and psychophysiological reactions in immersive and non-immersive virtual reality and in
the real world) of the findings of stated preferences for human behaviour in fire is a research issue
that still needs to be deeply investigated.
Case study 3 provides a dataset which has higher ecological validity of case study 2 but lower than
case study 1 according to the scale proposed by Kinateder et al. [45]. Moreover, this dataset
includes also personal evacuees’ data but no indicators for latent constructs. The main limitation of
this dataset is that the number of partecipants was lower than that of case study 1 and 2. This could
be one reason that explains the impossibility to capture the BUT in the case study 3. Future studies
using immersive virtual rality technology may add the indicators required for hybrid choice models,
although the number of partecipants will remain the key variable to capture this latency.
A common issue to adress for experiments on human behaviour in fire is ethical acceptability. In
fact, ethical standards (such as the Declaration of Helsinki [46]) need to be taken into account. All
the possible approaches need to ensure that the experienced emotions (e.g. fear, axiety, etc.) cannot
lead to temporal extreme side effects (e.g., panic attack, seizures, strong nausea, etc.) as well as
longer lasting difficulties for participants (i.e. traumatizations). This issue can be more relevant for
unannounced experiments (such as case study 1) rathen than non-immersive and immersive virtual
reality ones (such as case study 2-3).
Proceedings of the IX International Workshop on Planning and Evaluation, Bari, 16-18 March 2015
The three case studies show that there is a lot of potentials for future studies on human behaviour in
fire to develop new models with better predictive capabilities. Moreover, this work highlights that
the existing databases could be re-analised by using the modelling framework briefly described as it
was done for the case study 1. However, the main limitation is that the proposed freamewok is data-
based and these data can be difficult to collect [16,47].A solution to this issue could be the creation
of an open data-set to test and compare different models [26].
A final interesting research question, which arises from this work, is whether the assumptions and
considerations described in this paper hold true for large scale evacuation (i.e. evacuation of cities
or bigger areas). Even though many conceptual similarities can be found comparing a building and
an urban area, large scale evacuation includes other decisions (e.g. evacuation mode choice, etc.
[48]) which are not take into account for building evacuations.
6. Conclusion
This work investigates the possibility offered by Random Utility Theory to overcome the over-
simplification which are often used to model human behaviour in fire [15]. This work shows that
random utility models as well as hybrid models allow the inclusion of different levels of latency by
adding new features to the standard utility models. Three case studies are proposed to analyse the
choices taken to evacuate a building. These case studies show the potential of the different
approaches used to collect the data from a point view of the latency study. This work highlights that
a new analysis can be done by using the existing datasets and that the creation of open datasets
could facilitate the use of the described modelling framework.
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