The need of latent variables for modelling decision-making in evacuation simulations

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.


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


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].


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.


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


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


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.


(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.


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.


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).


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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The need of latent variables for modelling decision-making in evacuation simulations

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