Travel preferences of public transport users under uneven headways

Abstract

Public transport is affected by different types of randomness which impact the reliability they offer. The source of this randomness may come, for example, from casual uncertainty sources, such as accidents or protests, or from systematic uncertainty, related to service supply, such as dwelling time or travel time between consecutive stops. In addition to these sources of variability, an extra source of uncertainty experienced by users arises due to the public transport vehicle not being immediately available to avoid a wait of uncertain length. In a frequency-based system (without schedules), even under perfect regularity, users are not sure about the next vehicle's time of arrival. This article aims to find out the impact that reliability has on travellers' public transport alternative choice. To do so, an experiment of stated preferences is carried out, where the design characteristics are four operational attributes: speed, frequency, headway regularity, and average demand. Every scenario is randomly generated, based on the operational characteristics of the specific scenario. This means the alternatives presented resemble real-life operation and they are different between respondents. A Hybrid Discrete Choice Model was estimated, which addresses preference heterogeneity by considering two latent attitudes: punctual behaviour and crowding aversion. Overall, results indicate that headway irregularity has a significant effect on travellers' choices, both in terms of waiting time and passenger density. This confirms this attribute should not be ignored in any public transport model, especially when it comes to evaluate projects which improve the system's reliability but not necessary its average level of service.

Full text

Travel preferences of public transport users under uneven headways
Jaime Soza-Parra, Sebastián Raveau, Juan Carlos Muñoz
Department of Transport Engineering and Logistics
Pontificia Universidad Católica de Chile, Chile
ABSTRACT
Public transport is affected by different types of randomness which impact the reliability they offer. The
source of this randomness may come, for example, from casual uncertainty sources, such as accidents or
protests, or from systematic uncertainty, related to service supply, such as dwelling time or travel time
between consecutive stops. In addition to these sources of variability, an extra source of uncertainty
experienced by users arises due to the public transport vehicle not being immediately available to avoid
a wait of uncertain length. In a frequency-based system (without schedules), even under perfect
regularity, users are not sure about the next vehicle's time of arrival. This article aims to find out the
impact that reliability has on travellers’ public transport alternative choice. To do so, an experiment of
stated preferences is carried out, where the design characteristics are four operational attributes: speed,
frequency, headway regularity, and average demand. Every scenario is randomly generated, based on the
operational characteristics of the specific scenario. This means the alternatives presented resemble real-
life operation and they are different between respondents. A Hybrid Discrete Choice Model was
estimated, which addresses preference heterogeneity by considering two latent attitudes: punctual
behaviour and crowding aversion. Overall, results indicate that headway irregularity has a significant
effect on travellers’ choices, both in terms of waiting time and passenger density. This confirms this
attribute should not be ignored in any public transport model, especially when it comes to evaluate
projects which improve the system’s reliability but not necessary its average level of service.
Keywords: headway regularity, travellers’ behaviour, stated preferences survey
Declarations of interest: none

1. INTRODUCTION
Mode choice models, which are used to predict individuals’ behaviour regarding the use of different
modes of transport, typically consider average attributes such as in-vehicle time, waiting time, fare and/or
accessibility as explanatory variables (Ortúzar & Willumsen, 2011). However, it is been observed that
travellers also consider time attributes’ variability when deciding how to travel, instead of only
considering their average values (Carrion & Levinson, 2012; Kouwenhoven et al., 2014). This variability
also has an important effect on their stated satisfaction regarding a public transport service (J. Allen et
al., 2018; Soza-Parra et al., 2019). This level of service attributes’ variability is part of a wider concept
of high relevance to travellers: service reliability. In public transport, different stages of every trip are
susceptible to be variable. The vehicles are not immediately available so the user must access a station
where the service is provided and then wait for the vehicle to arrive. In both of these stages, disruptions
can affect user experience. Once inside the vehicle, different factors such as traffic congestion, driver
behaviour, unexpected disruptions, and different crowding experiences generate differences between
day-to-day experiences. In case of multiple-leg trips, when requiring one or more transfers, the sources
of uncertainty increase.
In the case of frequency-based public transport services (which is common when medium to high-
frequency is offered), the variability on key attributes as the expected waiting time and comfort is
strongly affected by the headway irregularity between consecutive vehicles. Still, most behavioural
models (usually based on random utilities) neglect its effect. Its impact is sometimes recognized as part
of the expected waiting time since the average waiting time experienced by a user exceeds half of the
average headway because of headway variability. Consider that even if headways were to be completely
regular, a user arriving randomly to the stop will face a random waiting time. Thus, in most cities waiting
time is uncertain and its average value provides limited information. When it is assumed that headway
variability only affects the average waiting time experienced by travellers, many other effects are
neglected. As Muñoz et al. (2020) argue, headway regularity also affects service reliability (by stabilizing
the level of service of consecutive vehicles), comfort (by reducing the average passenger density
experienced by all users), and travel times (by reducing the average waiting time experienced by all
users).
To study the attributes that influence travellers’ choice between different travel alternatives, two types
of data sources can be typically used: revealed preferences and stated preferences. The main difference
between them is that revealed preferences reflect actual choices already made by different individuals,
while stated preferences are obtained from respondents choices under hypothetical scenarios (Ortúzar &
Willumsen, 2011). Both sources of information have different advantages and disadvantages, but it is
agreed that revealed preferences are more trustworthy than stated preferences, as the former are based on
actual choices. However, the high collection and processing costs of this type of data summons stated
preferences as an attractive option. Also, identifying a revealed preference scenario in which users face
choices with the attributes of interest within the range and with the variability that allows some
conclusions to be made, is often unavailable. In the case of identifying the impact of service variability,
it might require raising a large amount of data to understand what variability each user faces in his/her

daily trip experiences (chosen or not). Besides, most massive revealed preferences data sources for public
transport, that is, smartcard and GPS information, lack socio-economical information about users.
As the purpose of this study is to expand our understanding about public transport travellers’ behaviour
under variable service scenarios, we conducted a stated preference experiment. Besides this type of
experiments allow a higher degree of control over the study variables and every respondent can answer
more than one time, improving the cost-efficiency of the survey. Finally, in terms of studying variable
attributes or scenarios, this type of experiments is as flexible as needed.
Over the last decades, different stated preferences experiments involving service variability have been
conducted, in which typically two or more travel alternatives are presented, with average travel times,
cost, and some representation of the variability that travel time entails. These representations deal with
service variability through presenting a list or a range of possible values for a given attribute, or graphical
representations of different attributes variability (Batarce et al., 2015; Bates et al., 2001; Copley et al.,
2002; Devarasetty et al., 2012; Hensher, 2001; Hjorth et al., 2015; Hollander, 2006b; Jackson & Jucker,
1982; Kouwenhoven et al., 2014; H. Li et al., 2017; Z. Li et al., 2010; Small et al., 1995, 1999; Tilahun
& Levinson, 2010). However, almost none of these studies intends to capture the broad impact of service
variability in the level of service, focusing instead on a single attribute variation. Furthermore, just a
small fraction of them have been applied in a public transport context.
Despite the correlation between headway irregularity and low comfort, to the best of our knowledge only
Batarce et al. (2015) incorporates crowding effects and waiting time variability specifically (instead of
analysing travel time variability as a whole) and the effects on choices in their study, finding no
significant impacts. This could have happened because of the large amount of information presented to
each respondent, which may ignore certain information that seems less relevant or important, biasing
their responses. Excess of information is a major problem when designing an experiment focused on
public transport since to fully characterise an alternative it would be necessary to specify in-vehicle times,
waiting times, cost, crowding and the variability of those attributes.
Another approach to address reliability is to study travellers’ learning. This method recognizes that the
variability of travel or waiting times is not understood in the same way as an average cost or time, since
it relates to the repetitive realisation of the same trip (Bogers et al., 2008). An example of this method is
presented in Avineri & Prashker (2005) for private car route choices. They study a network consisting
of two different alternatives with different average and variability of travel time, and in which the average
fastest route is the more unreliable. They conclude that travellers’ sensitivity to travel time differences
decreases when travel time variance increases, and that, in some cases, less attractive alternatives could
increase their attractiveness by increasing travel time variability. According to our knowledge, very few
studies have conducted such methodology, and none has been applied to a public transport context.
Consequently, it is important to define a variability representation which is well understood and does not
vanish its proper effect on respondent choices.
Despite its relevance, service reliability, both for in-vehicle time and waiting time, has been scarcely
incorporated into choice models in planning, especially in a context of high demand and high frequency

public transportation systems. Instead, its effect has been generally approached through psychological
studies that are more complex than the behavioural assumptions with which the individuals’ choices are
usually modelled. Examples of this are the Prospect Theory (Kahneman & Tversky, 1979) or Regret
aversion (Loomes & Sugden, 1982). This might explain why obtaining a reliability valuation for choice
models has been so elusive. Besides, there is a range of subjective factors which influence people
decisions. Because of their nature, they are not measurable directly.
The most relevant theorical framework analysing the value of headway variability correspond to the work
of Fosgerau, (2009) and Benezech & Coulombel (2013). In general terms, as public transport travellers
do not always know in advance the moment the vehicle will arrive, they need to adjust their departure
time accordingly. Thus, to the usually modelled travel time, it is necessary to incorporate an access time
and a variable waiting time. These studies, however, lack to properly incorporate the dynamics of vehicle
bunching, which modify the level of service, especially when it comes to passenger density. In a high
frequency and high demand context, when passenger densities over 5 passengers per square metre are
usual, it is worthy to extend our knowledge regarding traveller choices.
To include these elements in different choice scenarios, Hybrid Discrete Choice Models have been
proposed. One of their characteristics is the possibility to include perceptions or attitudes in the form of
latent variables (Ben-Akiva et al., 2002; Raveau et al., 2010). In our case, these variables should expand
the capabilities of our models to better understand the impact of public transport uncertainty on passenger
choices. Thus, in this work, this type of modelling consideration is incorporated. To do so, a set of
attitudinal questions need to be incorporated. To sum up, our methodology consists of a stated preference
experiment which considers attributes variability and subjective variables.
The purpose of this research is to contribute to the understanding of the impact of service reliability,
through the analysis of an uneven headway operation, on the choices of public transport travellers by
modelling a traditional random utility model. To do so, an experiment of stated preferences was
conducted in Santiago de Chile, with headway regularity as a key design factor. In this experiment, this
attribute is presented implicitly, through its impact in different day experiences. Thus, the contributions
of this article are the proposal of a method to design a stated preference survey which resembles actual
alternatives by presenting consecutive days’ variability and the link between different attributes, the
evaluation of the impact of latent attitudes in the perception of travel time and passenger density, and a
contribution to the relevance of headway regularity in travellers’ choices in a high frequency context.
The article is structured as follows: in Section 2, the survey design is described. The modelling approach
and results are discussed in Section 3. Finally, conclusions and further research are presented in Section
4.
2. SURVEY DESIGN
In this section, we discuss three different aspects of the survey design. Firstly, the manner how attributes’
variation is presented to respondents. Secondly, the methodology to generate the interaction between
different attributes. Finally, we introduce the final survey design considerations.

2.1. Variability Representation
Stated preference surveys have been widely used to understand people choices and behaviour in the last
decades. However, it is still unclear how to represent attributes that are uncertain in nature in these
experiments. Different schemes have been tried: regular schedules, circular schedules, probability
distributions, vertical bars, among others (Bates et al., 2001; Copley et al., 2002; Hollander, 2006; Small
et al., 1999) (Figure 1).
To represent service variability, each alternative consists of the level of service to be experimented by a
traveller in a sample of five consecutive days, i.e. representing a typical week of service. Each day is
characterized by a waiting time, an in-vehicle time, and a crowding level inside the vehicle. Among the
different options presented in Figure 1, we decided to present time attributes as bars, where longer bars
mean longer times and the length difference is proportional to the time difference. This approach was
found to be the easiest for respondents when comparing different travel times (Hollander, 2006a) and
also the clearest (Tseng et al., 2009).
a
b
c
d
Figure 1.- Variability representations
a.- Regular schedules (Small et al., 1999). b.- Circular schedules (Bates et al., 2001).
c.- Probability distributions (Copley et al., 2002). d.- Vertical bars (Hollander, 2006a).
To reduce the cognitive load of the survey, we made two design considerations. Firstly, we decided to
restrict variability only to crowding and waiting time, leaving in-vehicle time constant. Secondly, each

crowding level is presented combined with in-vehicle time. We have called this combination “crowding
bars”, which means that a long and crowded experience is represented by a long bar filled with the
respective number of passengers (Figure 2 represents three different trips of the same duration but with
different levels of crowding). This is consistent with the literature, which states that the impact of
occupancy in a public transport trip is directly related to its length through crowding multipliers.
Figure 2.- Crowding bars for 1, 3, and 6 passengers/m2
In our study, we expect respondents to compare different public transport services operating in a high-
frequency context. In principle, each of these services would be subject to variable waiting and in-vehicle
time. As this means two time-attributes are to be compared, horizontal bars were selected instead of
vertical bars, and the two alternatives were presented one above the other. By doing this, respondents
can compare vertically the length of these horizontal bars between alternatives. One possible alternative
to be presented in the survey is shown in Figure 3.
Figure 3.- Alternative example

During the design of a stated preference survey, it is important to define in advanced the type of
relationship to be tested (Rose & Bliemer, 2008). This way, the choice scenarios will consider these
expected results in the way they are constructed and represented. We defined a preliminary utility
function to estimate after the survey is applied as follows:
( )
(WT)j ttime j wtime j disp j
V TT WT disp WT
  
=  +  + 
(1)
Where, for each alternative j, TTj represents its in-vehicle time, WTj is the average waiting time and
disp(WTj) stands for a waiting time dispersion indicator. The objective is to identify the impact of service
unreliability in travellers´ preferences. The source of this uncertainty would come from headway
variability which we will assume exogenous. Thus, based on a given probability distribution for the
headways, representative observations of crowding inside the vehicle and waiting time are obtained. By
repeating this process five times we obtain the weekly travel experience that will be included in the
survey. It is important to highlight that monetary cost was not considered to reduce the cognitive load of
the survey and to better represent the fares of the public transport system in the city of study, which are
mostly invariant across trip alternatives. Besides, the utility function presented in (1) represent a
preliminary intuition; further specifications are tested after the data is collected, such as preference
heterogeneity within the sample.
2.2. Simulated Design
One of the most important criticisms towards stated preference surveys is their lack of realism. This lack
of realism could induce people to act differently in these hypothetical scenarios than in real life. To avoid
this, we identified two potential sources of lack of realism: i) presenting alternatives that could rarely be
observed in a real trip, and ii) neglecting the inherent uncertainty of random attributes. In order to reduce
these potential problems, we take two considerations in the survey design. Firstly, to address the realism
issue, we ask respondents about their typical travel time in their usual mode. This allows us to present
trip alternatives with in-vehicle times pivoting around this reported value. Secondly, to address the
uncertainty issue, we designed hypothetical scenarios based on four operational inputs instead of directly
defining the level of service to be experienced by each user. The four inputs are: i) speed, ii) frequency,
iii) a headway probability distribution and iv) an average passenger arrival rate (i.e. service demand). In
each choice scenario, the values associated to these four attributes are used to determine five
representative and coherent instances. These five instances are used to represent the service experienced
by someone during a work week. This service is defined by a constant in-vehicle time for all five days
and variable waiting times and vehicle crowding across days (Figure 3).
This type of information, that is, descriptive and experienced (as a full week of services is described in
advance, analogue to a learning process based on previous experiences) has proven to be the one that
best represents users’ learning process (Ben-Elia & Avineri, 2015). This way, reliability is not presented

as an attribute by itself but as a result of several repetitions of the same trip. As will be described later
the sampling process we follow yields five instances that are as representative as possible of the
probability distribution, and we present them to the respondent in a random order.
Within this framework, in-vehicle time is obtained directly from speed. However, the waiting time
experienced by a user during a week depends on bus headway distribution. And this distribution depends
on the frequency being offered and headway variability. The crowding inside the vehicle that a user
would experience should be directly dependent of the length of the headway that the vehicle is trailing
and the passenger arrival rate to the stops. These relations between operational and experienced attributes
are summarized in Figure 4.
Figure 4.- Operational and experienced attributes
In our experiment we assign different levels to each operational attribute. For the speed, we consider two
levels, representing travel times 15% shorter and 15% longer than the travel time reported by the user at
the beginning of the survey. This allows us to face each respondent with a scenario that mimics the level
of service they experience daily. For the frequency we also consider two levels, yielding an average
headway of 5 and 10 minutes. For the passenger arrival rate we consider two levels yielding crowding
levels of 1 and 3 passengers/m2 in the case of a bus trailing a headway that matches the average headway.
The crowding inside the bus will be higher or lower if the headway that the bus is trailing is longer or
shorter than the average one. The actual headway is obtained from the headway distribution as is
explained in the next paragraph.
For the headway distributions we consider three levels named no variance (identical headways), irregular
headways, and vehicle bunching. For the 5-minutes average headway, the irregular scenario consists of
equally likely headways of 2, 5, and 8 minutes while the bunching scenario consists of equally likely
headways of 5, 10 and 0 minutes (bunched vehicle). The headway distribution, fh(h), is used to determine
the following waiting time distribution for a user arriving to the stop at any moment with identical
probability:
Operational
attributes
•Speed
•Frequency
•Regularity
•Passenger arrival
rate
Experienced
attributes
•In-vehicle times
•Waiting times
•Crowding

( )
( )
( ) ( ) ( )
( )
*
**
*
0
11
hwh
ww
Fw Fw
f w F w dw
E h E h
−−
= → = 
(2)
An underlying assumption of uniform arrival of passengers to stops is made to generate this waiting time
distributions. This is reasonable in a high frequency-based context (Ingvardson et al., 2018). The
headway and waiting times’ distributions for the three scenarios with 5-minute average headway are
presented in Figure 5. For the 10-minute average headway case, the distributions are identical, but with
twice as large headways and waiting times in each case.
Regular headways scenario
Expected waiting time: 2.5 min
Irregular headways scenario
Expected waiting time: 3.1 min
Vehicle bunching scenario
Expected waiting time: 4.16 min
Figure 5.- Headway and waiting time distributions for no-variance, irregular headways and vehicle
bunching scenarios.

To present to the respondents of the survey a set of five representative instances of this distribution, we
calculate its 10%, 30%, 50%, 70%, and 90% percentiles, to cover the entire distribution. Such a set
provides an unbiased sample of the experience of a frequent traveller of this service; this pseudo-random
approach represents what the traveller should expect from a typical week of usage. The order in which
these five instances are presented to the respondent is randomized to better represent a typical week.
The only remaining attribute to generate is the crowding level that the user would experience. At a first
glance one might think that the crowding level should be proportional to the waiting time, but it is not as
simple. Although long waiting times always respond to a long headway and therefore to a high crowding
level, short waiting times can happen in long or short headways and therefore they are not indicative of
the crowding level to be experienced by the traveller. For example, under an irregular operation
consisting of headways of 2, 5, and 8 minutes, a 7-minutes waiting time can only be experienced by a
user arriving during an 8-minutes headway, while a 1-minute waiting time could be experienced by users
arriving in any of the three possible headways. Thus, given an equally-probably discrete headway
distribution (as in Figure 5) and a specific waiting time, the probability that said wait occurred within a
specific headway is the inverse of the number of headways larger than that wait, K*.
( )
 
1
| * *
*
* # | *
ii
jj
P h h w w h w
K
K h h w
= = =  
=
(3)
Then, based on this probability, we randomly associate a headway to each waiting time and the crowding
experienced by the user corresponds to the passenger arrival rate times the associated headway. In
addition, it might be considered that this simulated approach generates highly correlated attributes for
each alternative. However, in an irregular operation, short waits could either be associated with low or
high passenger density levels (which resembles arriving just at the end of a short or long interval). Thus,
the average correlation of the waiting times and passenger densities presented in each scenario alternative
is 0.11.
One of the strengths of the methodology presented is that the attributes’ values presented to each
respondent are calculated following a complex approach. The entire scenario construction process can
be summarized in Figure 6. Therefore, this study does not analyse the effect of variable scenarios on
travellers’ choices but the effect of level of service attributes’ variability on their experience and
behaviour.

Figure 6.- Scenario construction diagram
2.3. Survey Description
The whole survey is structured as follows: typical travel description, discrete choice experiment,
attitudinal questions, and socio-economical characterization. A pilot survey was conducted to 40
different working age respondents. Based on the results and comments obtained in this trial, some
questions were reformulated and made easier to understand. The description of the adjusted final survey
is as follows.
Firstly, respondents described their current travelling characteristics. For their most common trip, they
identified the transport mode used in its most part, and its purpose.
Public transport users were asked for the average in-vehicle time for that trip. For the remaining modes,
respondents indicated their average travel time as well but also, they were asked for their estimation of
the in-vehicle time for the same trip but using public transport. These reported times are used to pivot
the survey design, to provide realistic choice scenarios.
Secondly, respondents were presented eight discrete choice scenarios with two independent public
transport alternatives each. These alternatives were unlabelled and represented generic public transport
services (i.e. no mode is mentioned). Based on the results of the pilot survey, in every choice scenario
only two out of the four operational attributes (speed, demand frequency and regularity) were different.
This allowed us to present respondents with scenarios without a high cognitive load, on which the number
of elements changing between alternatives was manageable. The eight scenarios are presented in Table
1. They were randomized in the order they were presented in the survey, in order to avoid any cognitive
load bias.
Operational
attributes
Waiting time
generation for
five days
Associate
headways
to each day
Experience attributes
for a week
Percentiles
Probabilities
Randomization
Frequency
Regularity
Waiting time
Travel time
Passenger density

Table 1.- Survey scenarios
Scenario
Number
Trade-off
Attributes
Alternative
Speed
Frequency
Passenger
arrival rate
Regularity
1
Speed &
Frequency
Alt A
High
Low
Low
Bunched
Alt B
Low
High
Low
Bunched
2
Speed &
Demand
Alt A
High
High
High
Irregular
Alt B
Low
High
Low
Irregular
3
Frequency &
Demand
Alt A
Low
Low
Low
Regular
Alt B
Low
High
High
Regular
4
Speed &
Regularity
Alt A
Low
Low
Low
Regular
Alt B
High
Low
Low
Irregular
5
Speed &
Regularity
Alt A
Low
High
Low
Regular
Alt B
High
High
Low
Bunched
6
Frequency &
Regularity
Alt A
High
Low
High
Irregular
Alt B
High
High
High
Bunched
7
Frequency &
Regularity
Alt A
Low
Low
High
Irregular
Alt B
Low
High
High
Bunched
8
Demand &
Regularity
Alt A
High
Low
High
Regular
Alt B
High
Low
Low
Bunched
Thirdly, after the discrete choice experiment, respondents had to evaluate their level of agreement with
12 attitudinal statements on a scale from 1 to 7 (which is the educational grading scale used in Chile).
These statements are related to three different latent variables which may have an impact on travel
choices under uncertainty. These latent variables are crowding aversion, public transport easiness, and
punctual behaviour. They were selected because they relate with meaningful public transport evaluation
attributes, such as crowding multipliers (Tirachini et al., 2013; Wardman & Whelan, 2011), services
familiarity and expectations(LaRiviere et al., 2014; Martens & Fox, 2007), and travel time reliability
models (Bates et al., 2001; Fosgerau & Karlström, 2010). Based on the pilot survey, we were confident
that the statements were clearly understood and valid. Table 2 presents these statements, as well as the
designed attitudinal latent variable. These variables were then identified by a MIMIC model. This
methodology confirms that the proposed attitudinal statements were appropriate and can identify the
proposed latent variables. More details are presented in the next section. Fourthly, the survey ends with
a set of socio-economical questions. These questions asked about gender, age, education level, main
occupation, household size, monthly personal income, and the average number of weekly days they travel
by public transport. For the case of monthly personal income, respondents had to specify its value on a
printed table with 16 levels: starting at “under $100.000 CLP” (~$130 USD) to “over 1.500.000 CLP”
(~$2.000 USD). For the subsequent analysis, these attributes were considered as continuous variables.

Table 2.- Attitudinal statements
N°
Statement
Crowding
aversion
Public
Transport
Easiness
Punctual
Behaviour
1
It is hard for me to be punctual
✓
2
Public transport is a solution for environmental
issues
✓
3
It is easy to know how much time my most
common trip will take
✓
✓
4
I try to board the first bus or train, no matter how
crowded it is
✓
✓
5
Being late causes me an unpleasant feeling
✓
6
I can easily plan a public transport trip
✓
7
I leave home in advance to ensure I will arrive
on time and as comfortable as possible
✓
✓
8
I choose more comfortable travel options even if
they take more time
✓
✓
9
Waiting gives me an anxiety level that affects me
✓
10
Wherever I am, I know how to return home by
public transport
✓
11
Being late to my common destination can bring
me problems
✓
12
When leaving home, I know how crowded the
bus or train will come
✓
✓
The survey was applied during the first week of October 2019 in 10 different Public Notary Offices in
Santiago de Chile. The locations of these offices are displayed in Figure 7. These places were selected
as they gather people with heterogeneous characteristics from different areas of the city and long waits
to be attended are common, so these people usually have enough time to respond. In each location, a
surveyor asked each person waiting in the office if they were willing to respond the survey. These
surveyors were previously trained to conduct the survey on a web basis using identical tablets. Thus, the
simulated scenarios are generated on-line and each answer is recorded when submitted. A total of 1,314
respondents completed the survey, which corresponds to 10,512 choice scenarios.

Figure 7.- Public Notary Offices’ location
Regarding the sample, 65% of the respondents are public transport users and 31% are car users (private
car and taxi). Among car users, 71% declared that they know how long it would take to commute by
public transport. This strengthens the decision to use that value for pivoting travel time in the survey
questions. Table 3 presents some aggregated statistics regarding age, preferred transport mode, and
income of the members of the sample. Table 3 also includes the same statistics yielded by the latest origin
destination survey in Santiago, and the relative difference between the two groups.
Table 3.- Sample summary
% in sample
% in OD survey
Absolute difference
Age
[19 - 30] years
43.23%
26.59%
16.64%
[31 - 50] years
41.48%
36.99%
4.48%
[51 - 65] years
14.00%
23.08%
-9.07%
Over 66 years
1.29%
13.34%
-12.05%
Mode
Private car + Taxi
31.35%
43.67%
-12.32%
Public Transport
64.76%
49.97%
14.79%
Bicycle
3.88%
6.36%
-2.48%
Income
Low
25.27%
35.20%
-9.93%
Middle
55.56%
55.10%
0.46%
High
19.18%
9.70%
9.48%

Even though the sample does not perfectly replicate the aggregated population statistics, these differences
are far from being critical. The most significant under representation is people older than 65 years, which
should be expected since they visit public notary offices much less than the other age groups. In order to
avoid any possible any parameter estimation bias, the model should address preferences’ heterogeneity.
This modelling approach and the results obtained are presented in the following section.
3. MODEL DESCRIPTION AND RESULTS
As mentioned previously, a Hybrid Discrete Choice Model (HDCM) was formulated for this study. In
general terms, latent variables are included to capture heterogeneity in preferences for different attributes
in the discrete choice model. To do so, a Multiple-Indicator Multiple-Cause (MIMIC) model was
estimated, where the proposed latent variables are explained by different socio-economical
characteristics. Both models were estimated simultaneously, as the latent variable, and therefore its error
term, is part of both the measurement equations for the indicator and the utility function of the discrete
choice model (Ashok et al., 2002; Bierlaire, 2018; Bollen, 1989).
The three preliminary latent variables presented in Table 2 were studied and analysed through a MIMIC
model. However, only two of them, crowding aversion and punctual behaviour, were found to have a
significant impact in the discrete choice model. Our hypothesis is that the remaining latent variable,
public transport easiness, has an impact on the evaluation of the public transport system and could
influence mode choice (e.g. choice between private and public transport), but does not impact the choice
of services within public transport. For crowding aversion, the explanatory variables in the MIMIC model
were public transport frequency of use, age, income, gender and being a dependent employee. For
punctual behaviour, only age and being a dependent employee. For both latent variables, it was assumed
they were linear functions of the socio-economical attributes (Ortúzar & Willumsen, 2011; Raveau et al.,
2012). The measurement equation for statements 4 and 8 is
Statement Statement Statement CrowdingLV
i i i
V

= + 
(4)
and
Statement Statement Statement PunctualLV
i i i
V

= + 
(5)
for statements 1, 5, and 7. Thus, the answers to this attitudinal questions were modelled by estimating an
Ordinal Logit Model (Small, 1987).
For the discrete choice model, the systematic utility considered the interaction between in-vehicle time
with the punctual behaviour latent variable; the expected waiting time for each alternative; the coefficient
of variation of waiting times; the average passenger density and its interaction with the crowding aversion
latent variable; and the possibility of travelling seated (based on the number of days where available seats
are presented in the crowding bars). The coefficient of variation of waiting times was selected to explain

waiting time variability because it is dimensionless and presented a better fit when compared with other
specifications (such as standard deviation, variance, and reliability buffer time). A Binomial Logit Model
was considered, and its best specification (found through theoretical and statistical analysis, as statistical
significance, and likelihood ratio test) is as follows:
( )
, (WT)
PunctualLV TT WT (WT)
CrowdingLV Dens Seat
i
i j TT j i WT CV i
i
Dens Crowding j Seat i
V CV
  
  
=   +  +  +
+   + 
(6)
Where:
i
TT
Average in-vehicle time for alternative i
PunctualLVj
Punctual behaviour latent variable for person j
WTi
Expected waiting time for alternative i
CV(WT)i
Coefficient of variation of waiting times for alternative i
CrowdingLVj
Crowding aversion latent variable for person j
Densi
Average passenger density alternative i
Seati
Number of days with available seats for alternative i
The resulting Hybrid Discrete Choice Model framework is presented in Figure 8.
Figure 8.- Hybrid Discrete Choice Model framework

This HDCM was estimated simultaneously with 1,000 Halton draws to simulate the latent variables in
Biogeme (Bierlaire, 2018). The results for the MIMIC model and discrete choice model are presented in
Table 4 and 5, respectively. The final log likelihood is -16,528.16, which corresponds to a corrected ρ2
of 0.263.
For the MIMIC model, the results are divided by each of the two latent variables estimated: crowding
aversion and punctual behaviour. For each of them, first the measurement equations’ parameters are
presented (parameters to explain the attitudinal statements), followed by the structural equations’
parameters (parameters to generate the latent variable based on the socio-economical characteristics).
Table 4.- MIMIC model estimated parameters
Attribute
Parameter
Estimated
t-test
Crowding aversion
Statement 4
Constant
Statement 4

0.291
2.26
LV Effect
Statement 4

-0.882
-4.35
Statement 8
Constant
Statement 8

0.263
1.63
LV Effect
Statement 8

1
fixed
Public Transport Frequency of use
-0.084
-4.37
Age
0.012
3.18
Income
0.153
1.96
Gender
0.317
4.04
Dependent Employee
-0.198
-2.56
Structural Equation Standard Deviation
0.003
0.10
Punctual Behaviour
Statement 1
Constant
Statement 1

0.407
2.26
LV Effect
Statement 1

-1
Fixed
Statement 5
Constant
Statement 5

1.38
5.12
LV Effect
Statement 5

0.973
4.90
Statement 7
Constant
Statement 7

0.627
2.75
LV Effect
Statement 7

1.25
6.04
Age
0.037
8.04
Dependent Employee
0.124
2.05
Structural Equation Standard Deviation
0.018
0.57
In terms of crowding aversion,
Statement 8

was fixed (for identifiability purposes) and
Statement 4

estimated
parameter has the opposite (negative) sign. This means that both statements represent the same latent
variable but in contrasting directions. By reading statements 4 and 8 (Table 2) we observe that people

unwilling to travel uncomfortably present a higher crowding aversion. Then, by analysing the signs of
structural equation parameters, we conclude older people, higher income people and women tend to have
a higher crowding aversion while dependent employees and people that travel by public transport more
frequently tend to have a lower crowding aversion.
Similarly, analysing the punctual behaviour latent variable, this time
Statement 1

was fixed with a negative
value and both
Statement 5

and
Statement 7

estimated parameters have the contrary sign (i.e., positive). By
reading statements 1, 5, and 7, we see that people who finds easy to arrive on time, take measures to do
and have unpleasant feelings have a higher punctual behaviour. In terms of the socioeconomical attributes
in the structural equation, we see that both older people and dependent employees tend to have a higher
punctual behaviour.
In terms of the discrete choice model results, every parameter presented in Table 5 has a significant
impact when explaining public transport service choices. All parameters also have the expected sign. In
terms of in-vehicle time, results show that travellers with a higher punctual behaviour value are more
sensitive this attribute. Besides, when testing different model specifications, the constant effect of in-
vehicle travel time turned not significant when the interaction to the latent variable (Punctuality) was
added.
In terms of comfort, average passenger density as well as the number of days with seats available have a
significant impact. As expected, those travellers with a higher crowding aversion are more sensitive to
the average passenger density. As mentioned, a higher crowding aversion value is present in women,
older people and higher income people. The opposite happens with dependent employees and frequent
public transport users, whose perception of average passenger density is lower.
Table 5.- Discrete choice model estimated parameters
Attribute
Parameter
Estimated
t-test
In-Vehicle time
TT

-0.012
-4.82
Average waiting time
WT

-0.134
-9.19
CV of waiting time
(W )CV T

-2.741
-5.90
Average passenger density
Dens

-0.443
-11.30
Crowding aversion LV
Crowding

-0.118
-2.31
# Days with seats available
Seat

0.029
1.90
In terms of waiting time, there is a significant effect on the choice preferences of both its average and its
coefficient of variation. More importantly, we need to recall that the scenarios’ attributes presented were
constructed, as presented in Figure 4. Headway regularity has a direct effect over waiting times and
passenger density’s expected value and variability. As all of those experienced attributes have a

significant impact on respondents’ choices, we conclude that headway variability is a key attribute in
public transport alternative choice, even though its effects are perceived indirectly.
As the modelling framework consider random latent variables that interact with some of the alternatives’
attributes, this results on both in-vehicle time and passenger density parameter distributions.
The distribution of the parameter of the in-vehicle time is presented in Figure 9. As the punctual
behaviour latent variable has a positive value for every observation, we observe negative values for every
person of the sample, as expected. Besides, we observe a significant difference between dependent and
non-dependent employees. The average parameter for the former is -0.0184 while for the latter is -0.0166,
which indicates a 10.8% difference on average. This difference is significantly higher for people under
30 years old, reaching 18.4%. In terms of differences among age segments, respondents over 60 years
old present the highest parameter, -0.0306, followed by those between 30 and 50 years old with a value
-0.0199 and finally by those under 30 years old with a value of -0.0125. This means that those over 60
years old value travel time ~54% larger than those in the middle segment and ~145% larger than the
younger ones.
Figure 9.- In-vehicle time parameter distribution
As there was no cost attribute in the experiment, we compare the marginal rate of substitution (MRS)
between the alternatives’ attributes with respect to in-vehicle time.
If we consider each respondent specific parameters, we obtain a marginal rate of substitution of 7.59 for
expected waiting time and 1.63 min for the number of days with seats available. This means that

respondents, in average, value waiting time ~7.6 times more than in-vehicle travel time and are willing
to increase in ~1.6 minutes of in-vehicle travel time each day, ~8 minutes in total to have an extra day
with seats available during a week. The high value for the MRS of waiting time is explained by the survey
design, as the length of waiting time bars are in a different scale than those of in-vehicle travel time.
Otherwise, it would not have been possible for the respondents to compare those attributes, as waiting
times are significantly shorter than in-vehicle travel times. We elaborate on this issue in the Conclusions
and Further Research Section.
In terms of passenger density, we observe a significant impact of the crowding aversion latent variable.
This variable is significantly explained by gender (being women), public transport frequency of usage,
income, age, and being a dependent employee. The distribution of this parameter (as the sum of the
constant effect and the interaction with the latent variable), differentiated by gender, is presented in
Figure 10.
Figure 10.- In-vehicle passenger density parameter by gender
We observe a negative parameter for every observation in the sample and a significant difference by
gender, which is in line with our current knowledge (Allen et al., 2017; Soza-Parra et al., 2019). Though
the average parameter has only a 7.6% difference, with -0.495 for women and
-0.460 for non-women, we observe that 29.6% of non-women have a passenger density parameter shorter
than the smallest value of this parameter for women. In other words, around 3 out of 10 non-women
perceive passenger density less than every woman.
When incorporating the public transport frequency use into the analysis, these differences deepen. This
can be seen in Figure 11, where the distribution of the parameter for passenger density are presented for
public transport non-users, infrequent users (between 1 and 3 days a week) and frequent users (4 or more
days of usage) differentiating by gender.

Figure 11.- In-vehicle passenger density parameter by public transport frequency of use and gender
For both women and non-women a significant difference exists between the attribute distributions for
the three different levels of public transport use. For both cases, we observe a relative difference of ~14%
between the average parameter of non-users and frequent users. In terms of gender, women frequent
users have a similar passenger density distribution than non-women infrequent users. In fact, there is no
significant difference between these average parameters, equal to -0.472.
A similar analysis is conducted for three different age groups: under 30 years old, between 30 and 60
years old, and over 60 years old. This can be seen in Figure 12.
Figure 12.- In-vehicle passenger density parameter for different age groups

There are significant differences between these groups, and the relative differences are similar for both
women and non-women. In fact, in terms of average values for each age group, there is a ~9% difference
between the older and middle group and a ~7% difference between the middle and younger group for
both women and non-women. When comparing the same age group, there is a relative difference that
goes from ~7% for those younger than 30 years old, to ~9% for those over 60 years old.
All these analyses indicate that there are significant differences between women and non-women.
However, when we measure the marginal rate of substitution between this attribute and in-vehicle travel
time, as in Figure 13, we observe no gender difference. This means that regardless the gender, people are
willing to exchange the same number of minutes in order to decrease their passenger density, but in terms
of final utility, women will be worse.
Figure 13.- Marginal Rate of Substitution between Passenger Density and In-vehicle Travel time
gender
4. CONCLUSIONS AND FURTHER RESEARCH
This study has shown it is possible to model the effects of public transport reliability on travellers’
behaviour through a simulated stated preference survey that not just illustrates the different levels of
service to be observed in different days, but also coherently incorporates its impact in other relevant
service attributes. The results presented in this article are in line with our current knowledge and confirm
the importance of this attribute on travel decisions. Modelling and quantifying the impacts of public
transport reliability allows us to improve the understanding we have of the way in which travellers choose
their mode and route.

The proposed methodology is novel as the hypothetical choice scenarios presented to the respondents
were simulated instead of previously designed. Typical efficiently designed scenarios generate specific
combinations of attributes to get optimal parameters’ variance (i.e., to estimate those parameters properly
with as few observations as possible). However, these scenarios might not reflect close-to-real scenarios,
which might bias the discrete choice experiment. Thus, our approach increases the realism in a stated
preference context by simulating each choice alternative. This simulation was based on personal travel
information and different operational attributes. Our proposal did not have a negative impact on
parameters’ standard deviation, as the results were supported by high significance values.
Results show that headway irregularity has a significant effect on travellers’ choices. On one side, in
terms of waiting time, headway irregularity increases both its average and its coefficient of variation, and
both effects were found significant. On the other side, in terms of passenger density, headway irregularity
has two opposite effects: it increases the average passenger density but also increases the chance of
travelling seated. Then, headway regularity affects the whole set of parameters in this choice model,
which confirms that service reliability has a significant effect on travellers’ choices, and it should not be
ignored in any public transport model.
Results also provide significant evidence of the presence of deep psychological characteristics which
influence the perception of different travel attributes. Our proposed approach expands typical systematic
taste variation modelling by incorporating random latent variables for each individual, also considering
socio-economical characteristics to address heterogeneity in preferences. Regarding punctual behaviour,
our approach considers differences in the sensitivity to average in-vehicle time. To the best of authors
knowledge, this is the first time this latent variable is considered in a public transport discrete choice
context and a mean-variance approach. This effort should be extended, in order to consider not only in-
vehicle time but its variability (something that was outside the scope of this study), as well as expected
and excess waiting times.
One possible limitation of this work is that the results are based on the specific context of Santiago de
Chile. However, the public transportation system’s characteristics offered in this city resembles those
which are proper of many different cities worldwide, especially in emerging countries. Cities in which
public transport plays a major role in people’s mobility and therefore most services, bus, or train, operate
under medium to high frequencies. In such context passengers often do not know in advance when the
next vehicle will arrive. Also, Santiago has a fare integrated public transport system in which many
passengers must incur in one or more non-coordinated transfers to reach their destination. Thus, although
these conclusions are highly valuable and valid for many different public transportation systems, they
might not be relevant to systems operating schedule-based low frequency services.
Another limitation comes from the survey design. The high value obtained for the expected waiting time
rate of substitution is quite likely due to the different scales used in the horizontal bars for waiting and
travel time in each question for each respondent. If the same horizontal length scale had been used for
both waiting and in-vehicle travel times, it would have been difficult for the respondents to value waiting
times, as in-vehicle times tend to be significantly longer. Thus, the relative length of waits makes waiting
time to be over-represented in the diagram. This means that the impact of waiting time (and even of the

variability of waiting time) might be overestimated. However, this issue does not modify our conclusions
regarding the relevance of waiting time variability in public transport passengers’ preferences.
Additionally, if we correct the MRS of waits by the average proportion between in-vehicle times and
waiting times horizontal bars’ lengths among the sample (which is 2.27), we get a value of 3.35, which
is closer to what the literature suggest. However, this analysis is far to be conclusive on this matter and
only represent an intuition on how to potentially solve this issue. Then, it might be worth studying if it is
possible to estimate revealed MRS coming from stated surveys considering scaling corrections.
Combined with previous work related with the causes of headway irregularity, projects that improve the
reliability of the system can be properly evaluated with the type of model presented in this study, fully
understanding the benefits that this brings and how users respond to these changes. For example, the
impact of bus corridors can now be better understood, as it is clearer than the effects are not only in the
form of in-vehicle time reduction, but also in headway regularity, and the reduction of waiting times and
crowding inside vehicles. All these attributes significantly influence travellers’ behaviour, and therefore
assignment models should consider them in order to quantify projects benefits.
All of the above mentioned should lead us to a better planning of the public transport systems of our
cities. It becomes clear than headway regularity should be considered as a key attribute in every public
transport operation. Throughout this article, we have provided evidence that headway variability does
not only affects travellers’ behaviour indirectly through expected waiting time and passenger density,
but it also influences their choices directly. Passengers do consider waiting time variability when
choosing their preferred travel alternative. Thus, public transport reliability, understood through the
perspective of headway regularity, is worth studying further.
Acknowledgements: This research was supported by the Centro de Desarrollo Urbano Sustentable,
CEDEUS (Conicyt/Fondap 15110020), the Bus Rapid Transit Centre of Excellence funded by the Volvo
Research and Educational Foundations (VREF), and the scholarship funded by CONICYT for Ph.D.
studies (CONICYT-PCHA/Doctorado Nacional/2016). In addition, we would like to thank our surveyors
and to Mrs. Myriam Amigo, Mrs. Linda Bosch, Mr. Fernando Celis, Mr. Juan Facuse, Mrs. Mónica
Figueroa, Mr. Sergio Jara, Mr. Luis Alberto Maldonado, Mrs. Patricia Manríquez, Mrs. Lorena
Quintanilla and Mrs. Dora Silva for their selfless assistance providing their public notary offices to
conduct our survey.

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