Journal of Transportation Technologies, 2012, 2, 193-203
http://dx.doi.org/10.4236/jtts.2012.23021 Published Online July 2012 (http://www.SciRP.org/journal/jtts)
Latent Class Approach to Estimate the Willingness to Pay
for Transit User Information
Pietro Zito*, Giuseppe Salvo
Department of Energy—Transportation Group, University of Palermo, Palermo, Italy
Email: *pietro.zito@unipa.it
Received April 8, 2012; revised May 2, 2012; accepted May 28, 2012
ABSTRACT
The aim of analysis is to understand how unreliable information influences user behaviour and how much it discourages
public transport use. For this purpose, a Stated Preference Survey was carried out in order to know the preferences of
public transport users relating to information needs and uncertainty on the information provided by Advanced Traveller
Information System (ATIS). The perceived uncertainty is defined as information inaccuracy. In our study, we considered
the difference between forecasted or scheduled waiting time at the bus stop and/or metro station provided by ATIS, and
that experienced by user, to catch the bus and/or metro. A questionnaire was submitted to an appropriate sample of
Palermo’s population. A Latent Class Logit model was calibrated, taking into account attributes of cost, information
inaccuracy, travel time, waiting time, and cut-offs in order to reveal preference heterogeneity in the perceived informa-
tion. The calibrated model showed various sources of preference heterogeneity in the perceived information of public
transport users as highlighted by the analysis reported. Finally, the willingness to pay was estimated, confirming a great
sensitivity to the perceived information, provided by ATIS.
Keywords: Preference Heterogeneity; Latent Class Model; Perceived Information; Uncertainty; Willingness to Pay
1. Introduction
The Advanced Traveller Information Systems (ATIS)
includes a broad range of advanced computer and com-
munication technologies. These systems are designed to
provide transit riders pre-trip and real-time information,
so as to make better informed decisions regarding their
mode of travel, planned routes, and travel times. ATIS’s
include in-vehicle devices, terminal or wayside based
information centres, information by phone or mobile, and
internet.
There is a substantial literature concerning the user be-
haviour in relation to information provided by ATIS,
distinguishing the following [1]:
On one side, the viewpoint of marketing concerning
the potential of ATIS as a business case, either stand
alone or as part of an effort to gain or retain users for
urban transit [2-6];
On other side, the viewpoint of ATIS as a potential
tool for Travel Demand Management (TDM), [7-13],
who investigate the expectations of travel information
provision as a means to change traveler behavior as
the modal shift from private car to transit;
Finally, the viewpoint of individuals, when these face
with choice-situations under uncertainty, they can
make mistakes since travel choices often involve un-
certainty on travel time, route choice, scheduled wait-
ing time and so on [14-18].
The paper focuses on some issues relating to how tran-
sit users may be uncertain about how to perceive the in-
formation when they are unreliable and affected by error
or uncertainty.
Abdel-Aty et al. [2], studied the effects of ATIS on
route choice by stated preference analysis observing a
consequent reduction in travel time uncertainty. Also,
Abdel-Aty et al. [3], studied the commuter propensity to
use transit with a computer-aided telephone interview
conducted in Sacramento and San Jose, California. The
results indicated that approximately 38% of the respon-
dents who currently do not use transit might consider
public transport if the appropriate information is avail-
able. Moreover, using an ordered probit model produced
results that show the significant effect of several com-
mute and socioeconomic characteristics on the propen-
sity to use public transport.
Recently, Molin and Timmermans [5] evaluated the
willingness to pay for additional information through
web enabled public transport information systems. Dzie-
kan and Kottenhoff [19], showed the main effects of the
ATIS: reduced wait time, positive psychological factors,
such as reduced uncertainty, simplified use and a greater
*Corresponding author.
C
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P. ZITO, G. SALVO
194
feeling of security, increased willingness to pay, adjusted
travel behaviour, such as better use of wait time or more
efficient travelling, mode choice effects, higher customer
satisfaction and better image.
Polak and Jones [20], under the DRIVE European Pro-
ject, studied the effects of pre-trip information on travel
behaviour using a stated preference approach in Bir-
mingham and Athens. The analysis revealed firstly that
there was requirement for multimodal pre-trip travel in-
formation although the sample studied was made up of
regular car users, and that the quantity and type of pre-
trip information requested by travellers depends on a
range of personal, journey related, contextual and na-
tional factors. Moreover, they emphasised the importance
to travellers of the timeliness and relevance of the pro-
vided information especially when relevant network in-
cidents happen.
Nijkamp et al. [21] conducted a survey before and af-
ter the application of ATIS in the city of Birmingham
and Southampton (QUARTET and STOPWATCH pro-
ject respectively). Due to the small sample examined in
the QUARTET project their result was considered unre-
liable, whereas in the city of Southampton the survey
revealed a rise in using public transport, especially, in
study and leisure trips, and mobility optimisation of peo-
ple in choosing the mode and route able to reduce travel
time. A methodology was developed by Mishalani et al.
[22], aiming to understand the effect of real-time infor-
mation on bus stops, under three different methods to
forecast bus stop arrival time: 1) static information, 2)
real-time information up-date using historical data, 3)
real-time information using data coming from an Auto-
matic Vehicle Location (AVL) system. Measures of the
difference between predicted and effective waiting time
when people approach a bus stop showed that the third
method revealed to be more reliable than the other two
methods.
Several authors analysed the commuters’ behaviour
under ATIS environment, in particular travel time and
route choice, such as [23]. Grotenhuis et al. [24] investi-
gated the desired quality of integrated multimodal travel
information in public transport. Polydoropoulou and
Ben-Akiva [6], Chorus et al. [16], Lappin [25] showed
that perception of information can be explained by be-
havioural factors. Furthermore, Chien et al. [26] and Tan
et al. [27] set up decision support systems: the former to
provide real-time pre-trip information on bus arrival
times; whereas the latter to find a reasonable path in
transit networks validated by a survey.
The impacts of benefits and technical performance of
communication technology application in the city of
Helsinki was studied by Lehtonen and Kulmala [28]. The
system provided several public transport telematics, such
as real-time passenger information, bus and tram priori-
ties at traffic signals and schedule monitoring. Before
and after field studies, an interview and survey, a simula-
tion and socioeconomic evaluation indicated a 40% re-
duction of delay at signals, improving on regularity and
reliability of public transport, and reductions of 1% - 5%
in fuel consumption and exhaust emissions. Moreover,
the information systems were regarded very positively,
and, in particular the information displays at stops were
considered necessary. Similarly, Luk and Yang [29]
showed the benefits of ATIS application in Singapore.
Travel information may play a central role in reducing
uncertainty influencing the transport demand [30] and/or
reducing the perceived waiting time [31].
Some studies have pointed out as individuals, when
face with choice-situations in a state of uncertainty, can
make mistakes since travel choices often involve uncer-
tainty on travel time, route choice, scheduled waiting
time and so on [14-18]. In particular, Chorus et al. [16]
discussed travellers’ need for personalised and more ad-
vanced types of travel information.
The paper focuses on some issues relating to how
transit users may be uncertain about how to perceive the
information when they are unreliable and affected by
error or uncertainty. The main innovative task of analysis
is to understand how unreliable information influences
user behaviour and how much it discourages public
transport use. For this purpose, a stated preference survey
was run by submitting a questionnaire to a sample of po-
pulation of Palermo, in order to know preferences of
public transport users, information user needs and how
unreliable information provided by ATIS influences user
behaviour.
We consider two competing alternatives, namely pri-
vate car and public transport; distinguishing between car-
drivers and transit-users and therefore are interested to
evaluate the reaction of both users categories to the in-
formation provided by ATIS for public transport.
The perceived uncertainty is defined as the informa-
tion inaccuracy. In our study, we considered the differ-
rence between forecasted or scheduled waiting time at
the bus stop and/or metro station provided by ATIS, and
that experienced by users, who want to catch the bus
and/or metro.
Furthermore, another original aspect regards the pre-
ference heterogeneity in the information perceived by
public transport users, identifying in the decision process
the unobserved heterogeneity sources. The presence of
preference heterogeneity in the interviewed population
sample allows one better to explain the underlying indi-
vidual choice mechanisms. For this task, a latent class
model was calibrated, taking into account attributes of
cost, information inaccuracy, travel time, waiting time,
and their cut-offs and comparing the results with those of
the traditional multinomial logit.
Copyright © 2012 SciRes. JTTs
P. ZITO, G. SALVO 195
The existence of cut-offs and their utilization in deci-
sion problems is widely recognized. The decision maker
has limited ability to collect and process information.
Therefore he/she chooses in two stages. In the former,
the decision maker chooses the best one among available
alternatives, taking into account a non-compensative de-
cision process, in which any attribute is compared with
the relative threshold (cut-off). In the latter, the decision
maker weights remaining alternatives by a compensative
decision process considering their different attributes
[32].
The paper is structured as follows: Section 2 shows the
survey and user information needs; Section 3 describes
the theoretical aspects of the latent class logit model;
Section 4 points out the model specification; in Section 5
the outcomes are shown and critically discussed; in Sec-
tion 6 the willingness to pay is estimated and finally con-
clusion and future steps are given.
2. The Survey and Information User Needs
The survey was carried out in March 2009 in Palermo.
The latter is the main Sicilian city, with surface area of
158 square km and a population of about 700.000 in-
habitants, with a large historical area (about 2.7 square
km). This area is the centre of the main directional and
administrative functions of the island. Public transport by
bus covers almost all areas of the city, but only a few
lines run on a reserved lane (Figure 1). Thus perfor-
mances are influenced by congestion of private mobility
causing inefficiency in the level of service (travel and
waiting time and scheduling). Furthermore, the city has
few parking areas and has no interchange with other
transport modes (“Park & Ride”).
In the metropolitan area, the mass rapid transit system,
when completed, will be performed by a fundamental rail
transport network composed by light rail, through rail-
way and underground; and a feeder tram system with
three tram lines. The realization of an integrated mass
rapid transit system with interchange nodes and stations
will make it possible to improve trips inside the metro-
politan area, by using interchange parking areas and park
& ride policy (such as Roccella parking area).
At time of analysis, no real time information was pro-
vided by Road Local Public Transport Company (AM-
AT), whereas it was provided for railway system and
underground. The survey was conducted using a mail-
back self-completion questionnaire.
The first step in the design of the questionnaire was to
identify the most significant attributes for our analysis,
taking into account the cost, the information inaccuracy,
the travel time, the waiting time at the bus stop and the
terminal (Table 1).
In particular, the travel time from different origins and
Table 1. The choice scenario with levels of the attributes.
Attribute Private car Transit
Daily cost 6 € 2.60 - 3.20 €
Waiting time for transit/parking
research time for private car 10 min 5 - 15 min
Information inaccuracy - 4 - 10 min
Travel time 20 - 30 min 25 min
destinations were estimated elaborating a D.U.E. (Deter-
ministic User Equilibrium) process of assignment of the
private car O/D matrix (related to the rush hour and the
average working day) to the urban network (Comune di
Palermo, 1997). Daily cost was estimated considering
maintenance costs, motor vehicle tax, civil liability and
the number of kilometres travelled per year, which we
supposed to be equal to 15,000 km and a medium size
car; whereas for daily costs of public transport, the ticket
cost was increased of the information cost (10 - 30 cents
of euro) estimated by a pilot survey. Waiting time and
information inaccuracy were estimated by a pilot survey
in order to determine the waiting time experienced and
the information inaccuracy.
The full factorial design provides kn = 24 = 16 different
scenarios (where n is the number of attributes and k is the
number of levels). Thus, assuming the irrelevance of in-
teractions between attributes, in accordance with the
technique of Kocur et al. [33], we identified 8 different
scenarios (fractional factorial design).
In the questionnaire, firstly, we asked respondents to
give a value about their maximum threshold of the con-
sidered attribute (cut-offs), in order to achieve an im-
proved public transport service through the ATIS. Cut-
off information was gathered for following attributes:
information cost (upper bound), the information inaccu-
racy (upper bound), the waiting time (upper bound).
Further, we also asked to the decision makers to se-
lect between private car and transit in eight scenarios.
Also, other information was collected: frequency of use
of bus and private vehicle, evaluation of the importance
of some factors in choice of whether or not travel using
private and public transport, some transport habits (fre-
quency, purpose and maximum distance travelled with
transport modes), information user needs and quality
travel information, and some socioeconomic informa-
tion, such as household income, age, gender etc. (Ortúzar,
[34]).
We submitted 250 questionnaires (whose 110 correctly
compiled) to a sample of citizens chosen among potential
transit users (as students, employees, etc.). Furthermore,
the width of interviewed sample is about 0.3%, consider-
ing a universe of about 40,000 transit users per day (re-
lated to an average share of 15% in transit modal choice
in Palermo, ISTAT, 2006). Table 2 provides response
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Copyright © 2012 SciRes. JTTs
196
Figure 1. Road and rail public transport resp ectively .
Table 2. Response group characteristics (n = 110).
Attribute Proporti on % Cumulative % Attribute Proportion % Cumulative %
Age Frequency
18 - 24 10.10% 10.10% Daily 72.73% 72.73%
25 - 34 31.31% 41.41% 3/4 times for week 16.16% 88.89%
35 - 44 25.25% 66.67% 1/2 times for week 5.05% 93.94%
45 - 64 29.29% 95.96% 2/3 times for month 3.03% 96.97%
>65 4.04% 100.00% Once for month 3.03% 100.00%
Gender Type of looke d for information
Male 58.59% 58.59% Weather 13.57% 13.57%
Female 41.41% 100% Traffic cond. 11.56% 25.13%
Household income Route 22.61% 47.74%
<25,000 € 28.28% 28.28% Lim. traffic zone 11.06% 58.79%
25,000 - 50,000 € 39.39% 67.68% Availability of parking areas 11.06% 69.85%
50,000 - 75,000 € 20.20% 87.88% Altern. modes to private car 13.57% 83.42%
>75,000 € 12.12% 100.00% Dep./arr. time for transit 11.56% 94.97%
Owned car number Nothing 5.03% 100.00%
0 1.01% 1.01% Source of information
1 18.18% 19.19% Web site 32.00% 32.00%
2 41.41% 60.61% Map 16.00% 48.00%
3 30.30% 90.91% GPS 14.00% 62.00%
4 6.06% 96.97% TV/RD 5.33% 67.33%
5 3.03% 100.00% Call center 2.00% 69.33%
Household number Mobile phone 4.00% 73.33%
1 2.02% 2.02% E-kiosk 1.33% 74.67%
2 10.10% 12.12% News paper 14.67% 89.33%
3 25.25% 37.37% Nothing 10.67% 100.00%
4 46.46% 83.84% Purpose of trip
5 13.13% 96.97% Job/study 71.72% 71.72%
6 3.03% 100.00% Shopping/free time 28.28% 100%
P. ZITO, G. SALVO 197
group characteristics. For sake of notice, route (22.6%),
weather and alternative modes to private car (13.6%),
traffic condition and departure/arrival time for transit
(11.6%) are the information type most sought; whereas
web site (32%), map (16%) and GPS (14%) are the main
information sources. The Figure 2 shows reasons that
discourage the use of transit. It should be noted that 30%
of respondents consider service quality low, 24% the de-
parture and arrival time inadequate and 16% the depar-
ture and arrival time unreliable.
3. Latent Class Model
The main aim of this study is, on the one hand, to under-
stand how unreliable information influences user be-
haviour, and thus, how much it discourages public trans-
port use; on the other hand, it is to assay preference he-
terogeneity across respondents due to both observed and
unobserved effects. Only a part of the variability in the
intensity of the assay can be associated with measurable
socio-economic characteristics, and hence there remains
a component of heterogeneity associated with these un-
observable characteristics. This component can be re-
vealed and identified by models with variable parameters,
continuous distributions (mixed logit), or discrete distri-
butions (latent class). For a more detailed description on
advantages and disadvantages of both models see Green
and Hensher, [35]. These models have a high capability
to reproduce the individual choice behaviour and allow
one better to explain the underlying individual choice
mechanisms. For these tasks, we calibrated a latent class
model and compared it with a traditional multinomial
logit model.
Therefore, the heterogeneity across individuals is mo-
delled with a discrete distribution, assuming that indivi-
duals are implicitly sorted in a set of classes, C, with
class specific parameters and for each individual, a set of
probabilities defined over the classes.
The choice probability of the individual i, among j al-
ternatives, at choice situation t, given that he/she is in the
class c, is given by following equation:
Figure 2. Reasons that disincentive the use of transit.


,
,
,
1
Probin situationclass
choicebyindividual
exp
exp
i
itj c
itj c
J
itj c
j
tc
ji
VP
V

(1)
where Vit,j/c is the systematic utility of the perceived uti-
lity Uit,j/c expressed as:
,
,,, ,
it jc
itj citj citjcitjc
UV
 xβ (2)
xit,j is a vector of K attributes of choice j in choice situa-
tion t faced by individual i.
it,j/c is a random component
Independently and Identically Distributed (IID) extreme
value across individual, alternatives and choice situations;
whereas c
β
is the vector of class specific parameters.
Class probabilities are specified in according to the
multinomial logit form:


1
Prob classfor individual
exp , 1,, , 0
exp
θz
θz
ci ic c
C
ci
c
ci
Pc C
 
(3)
where zi is a vector of observable characteristics (as such
as, socio economic and psychometric characteristics of
individual) and
c a vector of parameters (last of which is
fixed at zero). The probability that a individual i makes a
specific choice j is expressed by:



,,
1
,
1
,
11
exp
exp
exp ex p
i
C
it jic
itj c
c
it jc
Cci
CJ
c
ci it jc
cj
PPP

xβ
θz
θzx
β
(4)
An issue that the analyst has to face is the choice of
the number of classes, C. This parameter must be im-
posed exogenously; Train [36], suggests two criteria to
assist in determining the number of classes, C. The for-
mer is Akaike Information Criterion AIC and the second
is the Bayesian Information Criterion BIC. This latter is
defined by:


BIC2log maximized likelihood
log
no. ofparametersn


(5)
where n is the number of observations.
4. Specification of Model
The stated preference survey on an individuated sample
was carried out in order to collect data and hence, to cali-
brate the demand model. In our analysis, we took signi-
ficant attributes into account: information cost, informa-
tion inaccuracy, travel time, waiting time; socio econo-
mic characteristics: household income and daily travelled
Copyright © 2012 SciRes. JTTs
P. ZITO, G. SALVO
198
distance; and cut-offs relating to information cost (upper
bound), information inaccuracy (upper bound), and wait-
ing time (upper bound). The significant discrete ran-
domly distributed parameters over classes are those re-
lating to information inaccuracy, cut-off of the waiting
time, Alternative Specific Constant ASC and household
income whereas all others are non-random parameters.
Let Vcar/c be the private car utility function; Vtransit/c
the public transport utility function; Ci the daily cost in €
for i = car, transit; TTi the total daily travel time in mi-
nutes for i = car, transit; PR the parking research time in
minutes; WT the waiting time in minutes; IA the informa-
tion inaccuracy in minutes; hinc = decision-maker’s
household-income (classes 1 range less than 25,000 €; 2
range 25,000 - 50,000 €; 3 range 50,000 - 75,000 €; 4
range more than 75,000 €); ASCcar the private car specific
constant; TD the daily travelled distance in km (classes 1
range less than 5 km; 2 range 5 - 10 km; 3 range 10 - 15
km; 4 range more than 15 km); cutoffc, cutoffWT, cutoffIA
the cut-offs relating to cost (upper bound), information
inaccuracy (upper bound), waiting time (upper bound).
Cut-offs were coded by penalties dummy variables that
take the values 1 if the threshold is not violated and 0
otherwise, for each decision maker;
cut,c/c,
cut,WT/c,
cut.IA/c
the cut-off parameters;
c/c,
WT/c,
TT/c,
IA/c,
hinc/c, the
parameters of the cost, of the travel time, of the waiting
time of information inaccuracy and of the household
income.
The utility functions of the competing alternatives are
expressed as follows:
car cc ccarWTcTTccar
hinc ccar c
VCPRT
hinc ASC
 
 

T
(7)
/
,
,,
TT c
IA c
transitcc ctransitWTctransit
cut c cc
cut WTcWTcutIA cIA
VCWTTT
IA cutoff
cutoff cutoff






(8)
All coefficients of the utility functions were achieved
by a calibration process. The calibration of the latent
class logit model was performed by the simulated log
likelihood using the NLOGIT® 4.0 software. During the
calibration process, different number of classes were
tried and tested, but the best results were achieved using
three classes.
5. Outcomes of Models
The results of the calibration process of the latent class
logit model are reported in Table 3, comparing them
with those of the traditional multinomial logit. The latent
Table 3. Comparison between latent class logit and multinomial logit model with cut-offs.
Latent Class Logit
Multinomial Logit Class 1 Class 2 Class 3
Attribute Parameter
Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio Coeff. t-ratio
C
c/c 1.656 5.726 2.365 7.034 2.365 7.034 2.365 7.034
WT
WT/c 0.073 4.283 0.106 5.311 0.106 5.311 0.106 5.311
TT
TT/c 0.036 2.141 0.053 2.690 0.053 2.690 0.053 2.690
IA
IA/c 0.237 8.045 0.144 3.591 1.417 7.816 0.808 4.549
cutoffc
cut,c/c 1.324 7.134 1.287 5.288 1.287 5.288 1.287 5.288
cutoffWT
cut,WT/c 1.058 5.653 0.485 1.848(*) 1.644 2.070 3.170 5.109
cutoffIA
cut.IA/c 0.638 3.146 2.295 6.287 2.295 6.287 2.295 6.287
hinc
hinc/c +0.186 +2.037 +0.067 +0.442(*) +1.925 +4.126 +1.098 +4.193
ASAcar ASCcar/c +2.142 +2.394 +5.853 +5.407 6.564 3.296 5.941 2.700
Estimated Latent Class Probabilities
ProbCls1 - - +0.649 +7.311
ProbCls2 - - +0.159 +3.268
ProbCls3 - - +0.192 +4.181
Model Simulation
Log-likelihood (0) LL (0) 548.972 548.972
Log-likelihood (B) LL (B) 415.629 365.282
Chi-square [d.o.f.]
2[] 266.666 [8] 367.381 [19]
Adj. pseudo R2 R2 0.242 0.334
Observations N 880 880
BIC - 1.082
Note: ASAcar is the Alternative Specific Attribute equal to one; (*): non-significant parameter.
Copyright © 2012 SciRes. JTTs
P. ZITO, G. SALVO 199
class logit model is statistically significant, and it has a
higher log-likelihood (365.3) than multinomial logit one
(415.6). Further, it has a greater capability to explain
the individual choice behaviour. The pseudo R2 (0.334)
is higher than multinomial logit (0.242), but the number
of parameters to be estimated is greater (20) rather than
nine parameters of multinomial logit, and hence it is
more complex.
All parameters estimated have the correct sign and are
significant, except two, the waiting time cut-off
cut,WT/1
and the household income
hinc/1, for the first class. It
should be noted that cost is the most important attribute,
whereas waiting time coefficient is about twice the travel
time coefficient, in accordance with the scientific litera-
ture. Further, the coefficient of the information inaccu-
racy is the second best attribute. This shows that the de-
cision maker gives a great importance to the reliability of
the information provided and the disutility related to un-
certainty of information is perceived very negatively.
This aspect is also justified by opinion of respondents
about the low quality of service, and often the low qua-
lity of the information provided. The survey shows that
respondents meet difficulties about finding information
and considering it reliable. All cut-offs are significant
and have the correct sign, since the cut-off has the effect
of enhancing the coefficient of the relative attribute. All
class probabilities are statistically significant, highlight-
ing the existence of heterogeneity in the estimates of pa-
rameters over the sampled population. The existence of
heterogeneity is caused by Information Inaccuracy, Wait-
ing Time cut-off, House-hold Income and Alternative
Specific Constant. Furthermore, it should be noted that
all other are non-random parameters.
Thus, the calibrated model suggests that heterogeneity
(differences in parameters of classes) may be, in part,
explained by differences in personal household income
level in the information perceived (on the reliability of
information) and in the perception of waiting time. Fur-
ther, high values of Alternative Specific Constants over
three classes suggested the analyst should take into ac-
count other attributes relevant for decision process. How-
ever, this aspect does not compromise the focus of analy-
sis which is to understand how unreliable information
influences the choice behavior and how it is a great
source of heterogeneity.
Figures 3 and 4 show the plots of choice probability in
term of additional information cost and information in-
accuracy.
Some scenarios were constructed to show how choice
probabilities change increasing cost and improving of
information inaccuracy by a given percentage over the
base or reference scenario. The choice probabilities are
reported in Table 4. Scenario 1 is characterized by a 10%
increment in information cost and a 50% improvement in
information inaccuracy. Scenario 2 foresees a 20% in-
crement in information cost and a 50% improvement in
information inaccuracy. It should be noted how a 6.7%
increment in choice probabilities can be achieved in-
creasing of 10% the information cost and improving the
reliability of information provided.
The elasticity of attribute cost, information inaccuracy,
travel time and waiting time provides useful information
on the sensitivity of the calibrated model to the variation
in a given attribute. The direct elasticity shows the effect
due to a change in the value of the independent variable
against the value of the dependent one. Table 5 shows
the values related to the direct elasticity effect of the
analyzed attributes against the probability of choosing
between two alternatives (Private car, Transit), averaged
over the set of observations. These data show how an
increment in cost equal to 1% induces an average reduc-
tion in choice probability equal to about 3.7% for the
private car and 1.5% for transit. They also highlight high
cost-related demand elasticity; whereas for the attribute
relating to information inaccuracy, the reduction of
choice probability is about 0.52%, and the demand elas-
ticity found for the travel and waiting time is inelastic,
and indeed its value is lower than one.
Finally, we tested the calibrated models on an inde-
pendent data set (not used for the calibration process)
made up of 11 respondents, in order to validate calibrated
models. Some statistical indexes were used to test the
Figure 3. Probability choice in terms of information cost.
Figure 4. Probability choice in terms of information inac-
curacy.
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P. ZITO, G. SALVO
200
Table 4. Choice probability in different scenarios.
Scenario base (%) Scenario 1 (%) P (Sc.1 - Sc.b) (%) Scenario 2 (%) P (Sc.2 - Sc.b) (%)
Public transport 54.83 61.53 6.70 57.36 2.53
Private car 45.17 38.47 6.70 42.64 -2.53
Table 5. Direct elasticity split by choice alternative.
Alternatives Cost Travel Time Waiting Time Information Inaccuracy
Private Car 3.686 0.344 0.276 -
Transit 1.509 0.292 0.231 0.517
goodness of fit between stated and estimated choices,
nominally correlation coefficient (R), determination co-
efficient (R2) and Root Mean Square Error (RMSE). Ta-
ble 6 shows statistical indexes for the validation data set.
The calibrated models have a good capability to simulate
users’ choices; in particular models with cut-offs are able
to explain better the heterogeneity of users’ choices.
6. Willingness to Pay
The Willingness to Pay (WTP) for an attribute of alterna-
tive j is the ratio of the marginal utility of the attribute on
the marginal utility of its cost, which in the case of linear
form of utility is the ratio of the attribute coefficient on
the cost coefficient.
VTT
WTP VC
(9)
Table 7 shows the Willingness to Pay for each class. It
should be noted that WTPs related to travel time (TT)
and waiting time (WT) for the latent class model are
close to multinomial logit’s ones. The Willingness to Pay
for information inaccuracy (IA) attribute is variable over
classes and for class 1 is low (3.6 €/h), whereas for
classes 2 and 3 are about 36 €/h and 20 €/h, respectively.
This confirms the great importance given in information.
Therefore, the random parameter related to informa-
tion inaccuracy is distributed in according to a discrete
distribution. This implies a distribution of the WTP. An
approach to achieve the entire distribution of WTP is to
construct estimates of individual specific preferences
deriving the conditional distribution, by using Bayes rule
to find the conditional density for the random parameters
(Hensher et al. [37]).
/
/
/
1
ˆˆ
ˆ
ˆˆ
ic ic
ci C
ic ic
c
PP
PPP
(10)
/
1
ˆˆ
ˆ
C
ici
cP
βc
β
(11)
By followed approach we have estimated the condi-
tional distributions of WTP related to the information
inaccuracy, that is reported in Figure 5.
Table 6. Statistical indexes on validation data set.
R R2 RMSE
0.69 0.45 0.225
Table 7. WTPs for each class in €/h.
Latent Class [€/h]
WTP Multinomial Logit
[€/h] Class 1 Class 2Class 3
WT 2.645 2.689 2.689 2.689
TT 1.304 1.345 1.345 1.345
IA 8.587 3.653 35.949 20.499
WTP
_
I
A
0.0083
0.0166
0.0248
0.0331
0.0414
0.0000 010 20
30
40 50-10
Kernel densit
y
estimate for
Density
Figure 5. Conditional distributions of WTP against IA.
Table 8 shows the descriptive statistics of WTP re-
lated to the information inaccuracy. It should be noted as
the mean value and the standard deviations of WTP are
12.02 €/h and 11.39 €/h respectively. Further, ordering
WTP values, we have pointed out the trend of WTP as
shown in Figure 6. Thus, the respondents have high-
lighted a high willingness to pay to achieve accurate and
reliable information about their travel. We can affirm that
the WTP for information inaccuracy is much greater than
travel and waiting time WTPs. Further the perceived in-
formation is a source of heterogeneity as pointed out by
Copyright © 2012 SciRes. JTTs
P. ZITO, G. SALVO 201
Table 8. Descriptive statistics of WTPs.
WTP_IA [€/h]
Mean Value 12.02
Std. Dev. Value 11.39
Min Value 3.65
Max Value 35.82
Number of observation
Figure 6. Trend of WTP against IA.
outcomes of calibrated models.
7. Conclusions
The aim of analysis is to understand how unreliable in-
formation influences user behaviour and how much it
discourages public transport use. For this purpose, a
Stated Preference Survey was carried out in order to
know the preferences of public transport users relating to
information needs and uncertainty about the information
provided by Advanced Traveller Information System
(ATIS). The perceived uncertainty is defined as the in-
formation inaccuracy. In our study, we have considered
the difference between forecasted or scheduled waiting
time at the bus stop and/or metro station provided by the
ATIS, and that experienced by the user who wants to
catch the bus and/or metro.
An original aspect regards the preference heteroge-
neity in the travel choice behaviour due to information
perceived by public transport users, identifying in the
decision process the unobserved heterogeneity sources.
The presence of preference heterogeneity in the inter-
viewed population sample allows one better to explain
the underlying individual choice mechanisms. For this
task, a latent class logit model was calibrated, taking into
account attributes of cost, information inaccuracy, travel
time, waiting time, and their cut-offs and comparing its
results with those of the traditional multinomial logit.
The latent class logit model has greater capability to ex-
plain the individual choice behaviour, but the number of
parameters to be estimated is greater rather than parame-
ters of multinomial logit, and hence it is more complex.
All parameters are statistically significant except two,
parameters of waiting time cut-off and household income,
for the first class. All class probabilities are statistically
significant, highlighting the existence of heterogeneity in
estimates of parameters over the sampled population.
The presence of heterogeneity is caused by parameters
Information Inaccuracy, Waiting Time cut-off, House-
hold Income and Alternative Specific Constant whereas
all other are non-random parameters.
The cost is the most important attribute, whereas the
waiting time coefficient is about twice the travel time
coefficient, in accordance with the scientific literature.
The information inaccuracy is the second best attribute.
This shows that the decision maker gives great impor-
tance to the reliability of the information provided and
the disutility relating to uncertainty of information is
perceived very negatively. All cut-offs are significant
and have the correct sign, since the cut-off has the effect
of enhancing the coefficient of the relative attribute.
Two scenarios were constructed and compared with
the base scenario, showing changes in the choice pro-
babilities, increasing the information cost and the im-
proveing information inaccuracy. The marginal effects
on transport demand have highlighted high cost-related
demand elasticity; whereas for the attribute relating to
information inaccuracy, the reduction in choice probabi-
lity is about 0.5%. This means that even a few minutes
between the waiting time provided by information sys-
tem and that experienced by user who wants to catch the
bus and/or metro have a big weight in the user’s choice.
Thus the impact on the user’s choice could be limited
with adequate reliability of information, and in general of
transit service. After, calibrated model have been tested
on an independent data set to appraise prediction per-
formance showing fairly good estimates.
Finally, the WTP for each time attribute was estimated,
highlighting how population sample gives great impor-
tance in reliable information provided by ATIS. The
WTP for information inaccuracy is much greater than
travel and waiting time WTPs.
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