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Exploring passenger anxiety associated with train travel
Yung-Hsiang Cheng
ÓSpringer Science+Business Media, LLC. 2010
Abstract Although people are often encouraged to use public transportation, the riding
experience is not always comfortable. This study uses service items to measure passenger
anxieties by applying a conceptual model based on the railway passenger service chain
perspective. Passenger anxieties associated with train travel are measured using a modern
psychometric method, the Rasch model. This study surveys 412 train passengers. Ana-
lytical results indicate that the following service items cause passenger anxiety during
trains travel: crowding, delays, accessibility to a railway station, searching for the right
train on a platform, and transferring trains. Empirical results obtained using the Rasch
approach can be used to derive an effective strategy to reduce train passenger anxiety. This
empirical study also demonstrates that anxiety differs based on passenger sex, age, riding
frequency, and trip type. This information will also prove useful for transportation planners
and policy-makers when considering the special travel needs of certain groups to create a
user-friendly railway travel environment that promotes public use.
Keywords Train passenger Anxiety Measurement The Rasch model
Introduction
From the perspective of transportation policy-makers, public transportation systems are
considered useful solutions to meet the growing demand for mobility (Li 2003; Ibrahim
2003; Hine and Scott 2000). However, as the number of people using a public transpor-
tation system increases, the likelihood that anxiety and crowding will arise also increases
(Cox et al. 2006). Even the most robust individuals may experience challenges when
traveling. For example, security, comfort, and going to the toilet can produce significant
amounts of anxiety (McIntosh et al. 1998) and long delays (Kuhmann et al. 1987;
Kuhmann 1989; Martin and Corl 1986; Thum et al. 1995; Weiss et al. 1982). The challenge
Y.-H. Cheng (&)
Department of Transportation and Communication Management Science, National Cheng Kung
University, No. 1, University Road, Tainan City 701, Taiwan, ROC
e-mail: yhcheng@mail.ncku.edu.tw
123
Transportation
DOI 10.1007/s11116-010-9267-z
for urban planners and decision-makers is to identify strategies that deal with resistance to
traveling by public transportation (Murray et al. 1998). Therefore, the travel anxiety
experienced by train passengers warrants further investigation. This can be considered a
useful reference for improving the user-friendliness of railway systems.
Anxiety is an emotion and, thus, is a subjective, uniquely individual experience (Sadock
and Sadock 2003). The North American Nursing Diagnosis Association (NANDA) defined
anxiety as ‘‘a vague, uneasy feeling of discomfort or dread accompanied by an autonomic
response, with the source often non-specific or unknown to the individual; a feeling of
apprehension caused by anticipation of danger’’ (Schweitzer and Ladwig 2002, p. 144).
Anxiety can also be considered a response to what is yet unknown in one’s self or an
environment (James 1999). Anxiety in this study is defined as a vague, uneasy feeling of
discomfort caused by the uncertain services and environment variables while traveling by
train.
Anxiety can be a result of uncertainty associated with environmental and cognitive
variables (Phillips et al. 1972). Travel-associated anxieties are common (McIntosh et al.
1998), and transportation conditions are considered sources of psychological anxiety
(Novaco et al. 1979). Several studies have examined the traveler’s experience on various
transportation modes. Bor (2007) focused on air transportation and provided a general
overview of the psychological aspects of air travel and, specifically, how air travel affects
the behavior of airline passengers and crews. Stradling et al. (2007) who surveyed bus
users in Edinburgh, Scotland, to understand their experience of taking buses, identified the
following eight items that reduce intention to take a bus: feeling unsafe; preference for
walking or cycling; problems with service; unwanted arousal; preference for car use; cost;
disability, and discomfort; and self-image. Li (2003) examined perceived travel time and
evaluated the urban commuter experience using commute characteristics (commute
duration and transfer frequencies), episodes, the travel environment, and expectancy.
However, the anxiety associated with travel was not further investigated in the study by Li.
Episodes in this study are concerned with access, wait time, train ride, and train transfer,
which characterize the transportation process, particularly that of public transportation.
Few studies have investigated train passenger anxieties. Some relevant studies focused
on a specific episode such as accessibility to a railway station (Keijer and Rietveld 2000;
Givoni and Rietveld 2007). Cox et al. (2006) examined rail passenger crowding and stress
inside a train. Several items were identified that may moderate the impact of a high-density
environment on perceptions of crowding. Therefore, this study aims to fill the gap in
literature by addressing possible episodes associated with train travel, including access to
stations, searching for cars and platforms, waiting, riding, transferring, and service, to
assess passenger anxiety during train travel from a service chain perspective.
Substantial differences may exist between travel experiences based on personal char-
acteristics such as age, sex, and disability (Ga
¨rling 2005; Stradling et al. 2007). In terms of
sex-based differences, Lynch and Atkins (1988) investigated the effects of women’s fears
and apprehension about being attacked and harassed on use of transportation facilities.
Harris and Miller (2000) also revealed that females perceive risk of being attacked by a
stranger significantly more than males.
This study proposes a railway system service chain approach to diagnose all the service
items causing anxiety. Passenger anxiety during train travel can be considered a latent
construct describing an unobservable and immeasurable characteristic. This study con-
tributes to academia using the Rasch method to measure anxieties associated with service
items during train travel. The Rasch model can compare person parameters with item
parameters, which are then subjected to a logarithmic transformation along a logit scale to
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clearly identify which items cannot be easily overcome by certain train passengers. Thus,
an effective strategy to reduce passenger anxiety can be derived. This study also investi-
gates how the difference in some socio-economic characteristics of passengers affects the
anxiety associated with train travel. In practice, study results can serve as reference for
railway system operators seeking to improve their services and physical environments.
Service conditions of Taiwan Railway Administration (TRA)
The Taiwan Railway Administration (TRA) is a wholly government-owned public insti-
tution responsible for managing, maintaining, and operating passenger and freight service
on its 1,067-mm gauge rail lines. The TRA currently has approximately 13,000 employees
working at 218 stations over a total line distance of 1,097 km. The average daily transport
volume during 1993–2007 was about 480,000 passengers and 26,480,000 passenger-
kilometers. Average daily freight transported during the same period was 33,000 tons and
2,510,000 ton-kilometers.
Passengers frequently criticize the reliability of the TRA system. The current average
train punctuality rate is \80% (MOTC 2008), and delays \10 min are considered allow-
able. When a delay exceeds 60 min, the TRA refunds the ticket price to passengers.
Furthermore, train frequency cannot meet passenger demand during peak hours, leading to
car crowding. Reports from the railway police authority indicate that two cases of sexual
harassment occur per month on average in the TRA system. Such security issues in the
TRA system warrant close attention. Furthermore, the passenger information system is also
commonly criticized because of incomplete and absent information for train transfers
guiding, the nature and causes of operation disruptions, and intervention measures when
trains are delayed.
Conceptual model for exploring anxiety associated with train travel
Passenger anxiety may be caused by different episodes in the railway system service chain.
Possible episodes leading to passenger anxiety are thus derived from the following com-
ponents: access to the railway system, railway station, platform, coach, transfer, and
railway service provision (Fig. 1).
Although railway systems can provide reliable, fast, and frequent service, getting to the
railway station is typically considered an essential part of rail travel (Givoni and Rietveld
2007; Brons and Rietveld 2009) and the accessibility of a railway station can be an
determinant of the railway use (Rietveld 2000). Travel times to and from a railway station
weigh more heavily on train travel times than accessibility (Keijer and Rietveld 2000).
Many social psychologists have identified the environment as a significant predictor of
negative outcomes (Evans 1982; Evans and Cohen 1987; Stokols 1992); that is, environ-
mental variables can be associated with anxiety (Chaboyer et al. 2005; Cutler and Garner
1995; McKinney and Melby 2002). Environment variables include ambient elements,
design elements, and social elements (Baker 1986). For public transportation, these include
seat availability, ride smoothness, spaciousness (or loading), air-conditioning, lighting,
cleanliness, spatial layout, furniture, and facilities design (Li 2003). All these can be
possible sources anxiety to a passenger entering the railway system.
Once on the train, passenger density can influence the perception of whether the coach
environment will cause anxiety. Cox et al. (2006) indicated that crowding is essentially a
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psychological phenomenon and perception resulting from the interaction of cognitive,
social, and environmental variables. Crowding is considered a possible threat to the health
of rail passengers. Conversely, riding a train alone also presents anxiety for some pas-
sengers. Furthermore, train noise can lead to anxiety (Stradling et al. 2007; Ljungberg and
Neely 2007).
The design and operation of public transportation systems provide an essential context
for considering transportation crime and security (Smith and Clarke 2000). Therefore,
security concerns are also considered an important source of passenger anxiety during
railway travel. Lynch and Atkins (1988) demonstrated that the risks and fears of physical
attack, harassment, and other anti-social behaviors influence the travel habits of many
urbanites. Personal security considerations must be incorporated into decisions concerning
the design, planning, operation, and management of transportation systems (Atkins 1990).
Public transportation services are considered an important component of overall
transportation planning and management processes (Murray 2001). Passengers often
transfer trains to reach their final destination. This transfer process can also be a source of
anxiety for passengers due to frequent missing and incomplete information. Therefore,
measurement items are mainly based on passenger perspectives and on relevant studies that
investigated passenger anxieties during train travel (Table 1).
Origin Enter train station
Fare collection
equipment
Buy
ticket
Entry
gate
Find the platform
Wait for train
Aboard train
Departure train
Go to exit area
Exit gate
Exit train station Destination
Riding
Go to station
exit
Station
Platform
Accessibility
Crowding
Delay Passenger guiding
information
Transfer
Noise
Seats
Time of a day
Gap
Timetable
Physical
abuse
Strangers on
the train
Taking train alone
Fig. 1 The travel process of riding a train
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Table 1 Measurement items of passengers’ riding anxiety
Question
Do you agree that the following episodes make you anxious during your travel by train? (5-point scale—5 for ‘‘strongly disagree,’’ 4 for ‘‘disagree,’’ 3 for ‘‘neutral,’’ 2 for
‘‘agree,’’ and 1 for ‘‘strongly agree’’)
Item Measurements Literature
Travel episodes
Accessibility When considering the convenience of transport to the
railway station
Givoni and Rietveld (2007), Brons and Rietveld (2009),
Murry (2001)
Transfer When I need to transfer via another train before arriving
at my destination
Stradling et al. (2007), Hine and Scott (2000), Brons
and Rietveld (2009)
Alone When I take the train by myself Stradling et al. (2007)
Time of a day When I take a night train Lynch and Atkins (1988), Stradling et al. (2007)
Delay When the train is delayed Stradling et al. (2007)
Physical abuse When possible attack could occur at the station, on the
platform, or inside the coach
Cox et al. (2006)
Strangers on the train When strangers sit next to me on the train Stradling et al. (2007)
Environmental variables
Passenger guiding information When I cannot quickly find my coach on the platform Hine and Scott (2000)
Seats When there is not enough waiting seats on the train or
platform
Hine and Scott (2000)
Timetable information provision Poor provision of timetable information (outdated,
difficult to get)
Hine and Scott (2000)
Gap When gap between the train and platform is large Hine and Scott (2000)
Crowding When the train is crowded Cox et al. (2006)
Noise Noise in the train Stradling et al. (2007), Ljungberg and Neely (2007)
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Data and methods
This study adapts the Rasch model to measure latent constructs of anxiety caused by train
travel using data from a survey that was administered to passengers traveling on the TRA
system.
Survey
A survey using a questionnaire based on measurement items from a process perspective of
using railway system services and literature measuring traveler anxiety associated with
train travel was developed as part of this research (Fig. 1). The questionnaire provided
respondents a definition of anxiety associated with train travel. Included in the question-
naire were questions associated with the environment, such as seat availability, passenger
information, and gap between a train and its platform, and train delay reflecting a service
provision. Table 1lists the measurement items. Respondents responded to items on a five-
point Likert scale, ranging from 5 for ‘‘strongly disagree,’’ 4 for ‘‘disagree,’’ 3 for ‘‘neu-
tral,’’ to 2 for ‘‘agree,’’ and 1 for ‘‘strongly agree.’’ Respondents also provided basic
demographic information for sex, age, education level, profession, and number of train
rides per month.
A random sampling strategy was used to collect data. Questionnaires were distributed to
every fifth passenger at the entrance to the Tainan and Kaohsiung stations during the study
period. In total, 800 questionnaires were distributed during March and April 2009 to com-
muters and long-distance passengers of these, 418 questionnaires were returned, of which 412
were valid. Six questionnaires were excluded due to missing items and response errors.
The Rasch model
Rasch (1960) developed the dichotomous Rasch measurement model to assess a subject’s
ability and item difficulty through a formulation of the relationship between ability and
difficulty, and the probability of success (Bezruczko and Linacre 2005). The Rasch model
is an example of objective measurement theory whereby ability and difficulty are measured
in logits (log-odds units).
Item responses on a Likert-type scale are ordinal data; however, these numbers only
indicate an ordered relationship and cannot be considered measures (Merbitz et al. 1989;
Wright and Linacre 1989). The scores allocated to each category are not true numbers
based on ordinal scales and, therefore, arithmetical operations and parametrical statistics
based on ordinal scales are invalid (Decruynaere et al. 2007).
Townsend and Ashby (1984) indicated that parametric statistics, such as the ttest or
one-way analysis of variance (ANOVA) Fstatistics are inappropriate for ordinal data.
Vittersø et al. (2005) indicated that survey-based comparisons with ordinal raw score data
may be misleading. Thus, in using the Rasch model, responses based on ordinal items are
transformed into an interval scale based on logits to which proper parametric statistics can
be applied (Anshel et al. 2009; Chang and Wu 2008).
After transforming ordinal raw data into an interval scale via the Rasch model, item
difficulty and passenger anxiety are calibrated on the same scale for subsequent inter-
pretation. The Rasch model can analyze changes in passenger responses after a service
item is improved. Via an item–person map, the Rasch model can examine how many
passengers can reduce their anxieties when various service items have been improved. The
Rasch model can derive an effective strategy to alleviate passenger anxieties from the
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perspective of railway system service providers. Since this study will compare anxiety
levels of different passenger groups, the interval scale can contribute to deriving an
accurate frame for comparison.
Figure 2shows the measurement concept of this study applied to the Rasch model. In
this study, each passenger nhas a unique ability, h
n
, that represents the capability of
passenger nto overcome the anxiety associated with an item. Each item ihas a difficulty
value ‘‘b
i
’’ that represents the difficulty passengers have in overcoming anxiety. In the
Rasch model, the passenger ability, h
n
, and item difficulty, b
i
, are calibrated on the same
scale. In Fig. 2, the right side ranks the items from high to low based on their difficulty
level, and the left side ranks passengers by their ability to overcome anxiety from high to
low. Therefore, crowding causes anxiety for all passengers. By comparing items and
passengers, one can easily identify the relationship between items and passengers. For
example, passenger B feels anxious about crowding and transferring trains because his or
her ability level is lower than the difficulty level of these two items, indicating that this
passenger cannot overcome the anxieties caused by these two items. Comparatively,
passenger B does not feel anxious about items on ‘train noise,’’ ‘‘the gap between a train
and its platform’’ and ‘‘attacks.’’
In this study, when a passenger indicates that an item will not cause him/her anxiety, the
service item is scored 1; otherwise, a score of 0 is assigned. The probability that a pas-
senger nwill indicate that he/she feels anxious about item iwith ease is as follows, where
h
n
represents a passenger’s ability to overcome anxiety and b
i
represents item difficulty:
P1hn;bi
j
ðÞ¼
ehnbi
1þehnbi:ð1Þ
0
+1.0
+2.0
-1.0
-2.0
Passenger
A
Passenger
B
Crowding
High ability of passenger
to overcome anxiety
Low ability of passenger
to overcome anxiety
Low difficulty item
High difficulty item
Passenger
C
Transfer
Noise
of train
Gap
Attacks
Fig. 2 Conceptual model for measuring passengers’ anxieties by the Rasch approach
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The probability that a passenger nwill report that he/she cannot overcome item iwith
ease is
P0hn;bi
j
ðÞ¼1P1hn;bi
j
ðÞ¼
1
1þehnbi:ð2Þ
The odds that a passenger nwill report that he/she can overcome item iwith ease is
P1hn;bi
j
ðÞ
P0hn;bi
j
ðÞ
¼ehnbi;ð3Þ
and the log of the odds ratio, or logit, is
ln P1hn;bi
jðÞ
P0hn;bi
jðÞ
¼hnbi:ð4Þ
A person’s ability (h
n
) and item difficulty (b
i
) are subsequently converted into odd ratios
or logits to identify the fit of data to the model. The person and item parameters in the case
of dichotomous responses can be estimated from response odds ratios in the dataset using
Eq. 4. Based on the dichotomous responses, the Rasch model was modified such that it was
applicable to polytomous rating-scale instruments, such as the five-point Likert scale
(Andrich 1978; Masters 1982). The modified Rasch model assigns b
ix
as the value of the
item parameter, indicating that train travel anxiety in this study for rating category xto
item i. Therefore, this study models the log odds of probability that a person will respond in
category xfor item i, compared with category x-1, as a linear function of the person
parameter, indicating the person’s perception of riding anxiety h
n
and the relative
parameter of category x, namely, b
ix
, for item i:
ln Pnix
Pniðx1Þ
¼hnbix:ð5Þ
According to the Andrich modification of the Rasch model for a polytomous response,
two formulations—the rating-scales model and partial-credit model—are widely applied in
assessing the values of items and person parameters.
The rating-scales model is utilized for instruments in which the definition of the rating
scale is the same for all items, whereas the partial-credit model is employed when the
definition of the rating scale differs among items. Notably, the partial-credit model is
similar to the rating-scales model, except that each item ihas its own threshold parameters,
F
ix
, for each category x(Wright 1977). This is achieved by a re-parameterization of Eq. 5:
bix ¼biþFix;ð6Þ
and the partial-credit model becomes
ln Pnix
Pniðx1Þ
¼hnbiFix:ð7Þ
In assessing the travel anxiety of railway passengers, one need not assume that the
rating scales of items are the same. Therefore, this study adopts the partial-credit model for
analysis.
The reliability estimations of the Rasch model are for both persons and items (Wright
and Master 1982). Person reliability indicates the replicability of a person ordering that can
be expected when this sample is given another set of items measuring the same construct.
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Item reliability indicates the replicability of item placements when the same items are
given to another sample with comparable abilities.
The infit and outfit values are the two parameters in the Rasch model for testing
goodness-of-fit index (GFI) (Prieto et al. 2003); that is, the infit and outfit values provide
information about how well items contribute to measured anxiety. The outfit mean square
statistic (MNSQ) is based on the conventional sum of square standardized residuals. When
Xis an observation, Eis the expected value based on Rasch’s parameter estimates and
there exists a r
2
represents the modeled variance of expectation. The squared standardized
residuals can then be expressed as
z2¼ðXEÞ2
r2
and outfit MNSQ is Pðz2Þ
n, where nis the total number of observations. In terms of the infit
MNSQ, each squared residual is weighed using its variance (r
2
). The infit MNSQ can be
calculated as
Pðz2r2Þ
Pðr2Þ¼PðXEÞ2
Pr2:
There is another form of fit value: Zstd. Zstd represents the probability of the MNSQ
value occurring by chance when the data fit the Rasch model. Zstd is a standardized fit
statistic and usually conforms to a zor tdistribution (Bond and Fox 2001). Infit Zstd and
outfit Zstd are statistics which are standardized and have approximate mean 0 and standard
deviation 1. Values of infit and outfit Zstd should be ranged between ±2.
Empirical result analysis
The responses of 412 train passengers were analyzed with WINSTEPS (Linacre 2006), an
interactive computer program that estimates h
n
for respondent nand b
i
for item iin logit
units. Notably, WINSTEPS can deal with polytomous responses by applying the Masters–
Andrich modification (Masters 1982) of the Rasch model.
Estimation methods for the Rasch measures
The estimated parameters and model fit statistics were calibrated via a Joint Maximum
Likelihood Estimation (JMLE) procedure (Wright 1996). The Rasch measures (person
ability and item difficulty) must be inferred from data. Following Fisher (1992), the
likelihood of the dataset, L, is the product of data point probabilities
L¼Y
n;i
Pnix :
The Rasch estimates are non-linear transformations of data. Typically, estimation with non-
linear functions requires an iterative approach until final estimates are acquired. The JMLEs
satisfy the optimal least squares criterion RnPL
i¼1jnEni
2¼0;where Rn¼PnXni:
The marginal score (R
n
) is the sum of all observations modeled to be generated by n
passengers, each data point (X
ni
) has a value of 1 when passenger novercomes item iand 0
otherwise. The expected value of the data points is E
ni
. Using Newton–Raphson iterations,
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enhanced estimates are generated that minimize discrepancies between marginal scores
and expected values of data points. Convergence criteria are used to determine when
iterations should cease.
Respondent profile
Of the 412 anonymous respondents, 52.18% were male and 47.82% were female. Average
age of respondents was 25.20 years (SD =7.41). These respondents took on average 3.78
train rides monthly (SD =2.16). Most participants were young; this phenomenon corre-
sponds well with the ridership of the TRA system.
Tests for unidimensionality
The fundamental assumption of the Rasch model is undimensionality. This assumption
indicates that subject responses are based on one latent trait. However, the requirement of
unidimensionality is rarely fulfilled (Hambleton and Swaminathan 1991; Rubio et al.
2007). Thus, one always conducts exploratory factors analysis (EFA) or confirmatory
factor analysis (CFA) to assess whether scales used have ‘‘essential’’ or ‘‘sufficient’’
unidimesionality (Rubio et al. 2007; Scherbaum et al. 2006; Reeve et al. 2007).
In this study, EFA is applied as the first step, because items are not from an item pool in
literature. Analytical results demonstrate that the first factor explains roughly 34% of vari-
ance. Thus, the criterion of 20% is fulfilled (Reckase 1979). This study then applied CFA, and
unidimensionality was also considered appropriate since the Normed Fit Index
(NFI) =0.905, Comparative Fit Index (CFI) =0.927, and GFI =0.911 exceed 0.90, and
the Standardized Root-Mean-Square Residual (SRMR) =0.0607(\0.1) (Reeve et al. 2007).
Item parameter estimates and results of fit statistic analysis
Item reliability and person reliability are 0.99 and 0.80, respectively (Table 2). Both person
reliability and item reliability can be interpreted as the Cronbach’s alpha reliability
coefficient (Wright et al. 1996). The widely accepted social science cut-off for Cronbach’s
alpha is C0.70 for an item set (Streiner and Norman 2004). In this study, both infit Zstd and
outfit Zstd are ranged between ±2, indicating that observational responses fit the model
well (Wright and Linacre 1994).
Item separation and person separation are also utilized to describe instrument reliability
for the sample. The larger the item separation or person separation index value increases,
the more number of distinct levels that can be distinguished in the measure increases
(Duncan et al. 2003). The separation index of 1.50 represents an acceptable level, 2.00
represents a good level, and an index of 3.00 represents an excellent level of separation
(Duncan et al. 2003). Analytical results show that both the item separation index (2.15) and
person separation (8.23) exceed 2, indicating that items are sufficiently spread out to define
distinct levels of anxiety measured in logits. All item estimates have an infit MNSQ and
outfit MNSQ of 0.92–1.15 and Zstd fit statistics between ±2. Both the MNSQ and Zstd fit
statistics meet the requirement that MNSQ be in the range of 0.8–1.2 and Zstd is in the
range of ±2. Thus, all items can be utilized to measure the latent construct of anxiety
during train travel.
Table 2also presents estimates of item difficulty (b
i
) from Rasch’s analysis. The dif-
ficulties of item measures are expressed in log-odds units (logits). A logit is defined as the
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natural log of an odds ratio. An item with higher logit indicates that passengers have high
levels of anxiety associated with this item. ‘‘Crowding’’ has the greatest bi value (1.16),
indicating that ‘‘crowding’’ cause the most anxiety during train travel. The item ‘‘delay’’
has the second highest b
i
value (0.65), indicating that passengers are also anxious when a
train is delayed. After ‘‘delay,’’ ‘‘When considering the convenience of transport to a
railway station,’’ ‘‘searching for right train on a platform,’’ and ‘‘transfer’’ have positive b
i
values, suggesting that these items also generate anxiety for passengers.
Figure 3shows passenger anxiety and item difficulty on the same logit scale. The
horizontal bars on the left indicates the distribution of passengers according to their anxiety
Table 2 Estimates of item measures and fit statistics from the Rasch analysis
Item Estimate
(bi) (logits)
Error Weighted fit
(infit)
a
Unweighted
fit (outfit)
b
MNSQ
c
Zstd
d
MNSQ Zstd
d
6 When the train is crowded 1.16 0.6 1.07 1.0 1.06 0.9
11 When the train is delayed 0.65 0.7 1.15 2.0 1.14 1.8
3 When considering the convenience of transport to
the railway station
0.34 0.6 1.02 0.3 1.04 0.6
7 When I cannot quickly find my coach on the
platform
0.30 0.6 0.93 -1.0 0.94 -0.9
1 When I need to transfer via another train before
arriving at my destination
0.23 0.6 1.02 0.4 1.01 0.2
9 Noise in the train -0.02 0.6 0.96 -0.6 0.95 -0.7
2 When there is not enough waiting seats on the
train or platform
-0.05 0.6 1.03 0.5 1.02 0.4
13 When I take a night train -0.19 0.6 0.92 -1.2 0.92 -1.2
4 When the gap between the train and platform is
large
-0.26 0.6 0.94 -0.8 0.94 -0.9
8 Poor provision of timetable information
(outdated, difficult to get)
-0.36 0.6 0.97 -0.5 0.96 -0.6
5 When possible attack could occur at the station,
on the platform, or inside the coach
-0.44 0.6 1.07 1.1 1.11 1.6
12 When strangers sit next to me in the train -0.51 0.6 0.93 -1.1 0.93 -1.0
10 When I take the train by myself -0.86 0.6 1.00 0.0 1.00 0.1
Item reliability 0.99
Item separation index 2.15
Item infit MNSQ 1.0
Item infit Zstd 0.0
Person reliability 0.80
Person separation index 8.23
Person infit MNSQ 1.0
Person infit Zstd -0.2
a
Weighted (infit) statistics for any item derive most information from the responses of passengers close to
this item
b
Unweighted (outfit) statistics monitor responses of passengers toward the extremes of the scale more
closely
c
MNSQ represents mean square fit statistics of the item parameters
d
Standarised fit statistics have a tdistribution, where the values outside the range ±2 are problematic
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levels. Items on the right are ranked by difficulty level. The higher an item is located up the
vertical axis, the more it causes riding anxiety. As passenger and item parameters are
relative, the average values of item difficulty are anchored as zero and thereby provide a
basis for comparisons. This item–person map can be used to determine how many pas-
sengers felt anxious with certain service items. In Fig. 3almost all passengers are located
under the service item ‘‘crowding,’’ indicating that many passengers feel anxious when a
coach is crowded. Conversely, ‘‘taking the train alone’’ rarely causes anxiety.
The benefit of the Rasch model lies in its ability to compare service items and passenger
anxiety along the same logit scale. Thus, this study further estimates the number of pas-
sengers who will not experience difficulties for a service item after this service has been
improved. Table 3compares the changes in number of passengers who experience anxiety
when faced with to ‘‘crowding’’ and ‘‘delays’’ under a certain magnitude of improvement
for both items. The first row shows the number of passengers who feel anxious about
‘‘crowding’’ and ‘‘delays’’ separately. Prior to improvements, 402 passengers feel anxious
about ‘‘crowding’’ and 366 passengers express anxiety about ‘‘delays.’’ After improving
‘‘crowding’’ and ‘‘delays’’ by 0.5 logit, 366 and 303 passengers expressed anxiety related
to ‘‘crowding’’ and ‘‘delays,’’ respectively. Thus, 36 passengers who no longer feel anxious
about ‘‘crowding’’ represent 8.74% of all passengers. However, 63 passengers who no
longer feel anxious by ‘‘delays’’ account for 15.29% of all passengers. When service items
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
3
1
13
14
30
34
45
34
41
30
23
6
20
10
4
2
0
1
0
2
0
0
28
17
40
1
01020304050
-6
-5
-4
-3
-2
-1
0
1
2
3
06. crowding (1.16)
11. delay (0.65)
03. accessibility (0.34) 07. passenger guiding information (0.30) 01. transfer (0.23)
M 09. noise (-0.02) 02. seats (-0.05) 13. time of a day (-0.19)
08. timetable information provision (-0.36) 04. gap (-0.26)
05.
p
h
y
sical abuse (-0. 44) 12. s tran
g
ers on t he train (-0. 51)
10. alone (-0. 86)
S
S
T
T
M
S
S
T
T
less frequent
logit
rare more
Number of
Passen
g
ers
Fig. 3 Item–person map of riding anxiety for trains
Transportation
123
‘‘crowding’’ and ‘‘delays’’ are improved by 1 logit, an increase of 99 and 150 passengers no
longer express anxious about ‘‘crowding’’ and ‘‘delays,’’ representing about 24.03% and
36.41% of all passengers, respectively. Consequently, more passengers can overcome
‘‘delays’’ than ‘‘crowding.’’ Despite the fact that crowding generates the highest levels of
anxiety for passengers, prioritizing improvements in train delays can reduce passenger
anxiety significantly.
From the item–person map, the Rasch model can examine how many passengers can
have their anxieties alleviated when various service items are improved by the same
magnitude (logit). Figure 4shows relationships between improvement magnitudes and
percentages of passengers feeling less anxious. Regardless of the magnitude of service item
(logit) improvement, most passengers consistently had less anxiety toward delays than
crowding.
Passenger parameter estimates and fit statistics
Table 4shows the summarized passenger parameters. Passenger ability in the raw score is the
sum of scores for all 13 items. In this study, if a passenger agrees that an item causes anxiety,
then this passenger gets a low raw score. Here, h
n
is a passenger’s ability in logits; that is, the
interval scale unit after transformation. Passenger ability (h
n
) is a passenger’s ability to
Table 3 Relationship of service improvement magnitudes related to the numbers of anxious passengers
Improvement of 0.5 logit Improvement of 1 logit
Crowding Delay Crowding Delay
Without improvement 402 366 402 366
After improvement 366 303 303 216
Difference (passenger) 36 63 99 150
Percentage (%) 8.74 15.29 24.03 36.41
crowding
delay
36.41
24.03
14.32
8.74
4.61
5.58
15.29
26.21
0
5
10
15
20
25
30
35
40
0.25 0.5 0.75 1
logi
t
%
Im
p
rovement ma
g
nitude
Percentages of passengers
felling less anxious
Fig. 4 Relationships of improvement magnitudes associated with percentages of passengers’ feeling less
anxious
Transportation
123
overcome the anxiety associated with an item. As this ability increases, the likelihood of
overcoming anxiety caused by a service item increases. Conversely, when passenger ability is
poor, the likelihood of overcoming the anxiety is low. Passenger 274 is most likely unable to
overcome anxiety associated with the majority of service items as h
n
is relatively low (-5.75).
Conversely, passenger 286 is most likely to overcome anxiety associated with an as h
n
is high
(2.50).
Figure 5shows passenger infit and outfit values; the vertical axis represents infit Zstd,
the horizontal axis represents outfit Zstd, and each point represents a passenger. Since the
infit and outfit Zstd should be ranged between ±2, passengers with the infit Zstd and outfit
Zstd conforming the requirement are located inside the rectangle. Most person’s infit and
outfit values are ranged between ±2 (Fig. 5). The responses of passengers with infit Zstd
and oufit Zstd outside ±2 are considered outliers. For instance, infit Zstd and outfit Zstd
values outside of the upper right side of the square indicate that passengers are capable of
Table 4 Summarized estimates of passenger parameters and fit statistics from the Rasch analysis
Person number Raw score h
n
SE Infit Zstd Outfit Zstd
286 30 2.50 0.35 0.28 0.21
273 38 2.11 0.33 -0.42 -0.37
229 33 1.79 0.34 -2.31 -2.22
123 36 1.65 0.33 1.22 1.02
233 29 1.51 0.35 -0.12 -0.37
393 31 -2.57 0.35 -0.14 -0.12
358 47 -2.79 0.33 0.23 -0.13
59 32 -3.05 0.34 -2.02 -2.03
91 33 -3.81 0.34 -1.96 -1.84
274 39 -5.75 0.33 3.07 3.01
Mean 35.3 -0.4 0.4 -0.2 -0.2
SD 7.6 1.0 0.1 1.6 1.6
Fig. 5 Scatter plot of infit and outfit statistics for person estimates
Transportation
123
responding to difficult items, but respond incorrectly to easier items. Infit Zstd and outfit
Zstd on the lower left side of the square indicate that passengers are incapable of judging
the relative level of categories well; that is, the responses of these respondents do not vary
with item difficulty.
The ability parameter (h
n
) is utilized to compare differences between different groups.
Bond and Fox (2001) suggested that abnormal responses be modified or deleted. The study
has eliminated passengers with infit Zstd and outfit Zstd outside the range of ±2. The
remaining 307 passengers are analyzed according to sex, age, average monthly riding
frequency, and trip type to identify differences in anxiety levels for passenger groups with
different characteristic during train travel.
Table 5presents anxiety levels for different passenger characteristics. The ability mean
in the fourth column is the average h
n
of passengers in a group. A ttest is then applied to
examine the difference between two groups. In terms of age, anxiety experienced was
significantly different between the two groups (p\0.1). Passengers aged \40 years have
an ability level (-0.544) that is much lower than that of those aged C41 years (-0.093).
Passengers under 40 years are unlikely to overcome anxiety. Conversely, passengers aged
C41 have a higher ability to overcome anxiety caused by these service items. Furthermore,
significant group difference exists for sex, average monthly transportation frequency, and
trip type. For sex-based difference, females have more anxiety than males (M
Female
=
-0.657 vs. M
Male
=-0.369, p\0.05). In terms of average monthly riding frequency,
passengers who take a train once (or less) per month have more anxiety than those who
travel more than two times per month (M
B1
=-0.661 vs. M
C2
=-0.360, p\0.05).
Furthermore, long-distance travelers have more anxiety than commuters (M
Commuter
=
-0.108 vs. M
Long-distance
=-0.575, p\0.05).
Differential item functioning (DIF) analysis
Evaluating the degree to which measure meaningfulness is generalized across subgroups
within a population is important. Studies that focus on this aspect of validity at the item
level within an instrument are referred to as differential item functioning (DIF) studies
(Myers et al. 2006). Notably, DIF is a condition when an item functions differently for
respondents from different groups. Table 6presents the DIF results for male and female
passengers. The column of the DIF measure represents item difficulty logits for each item
for females and males separately. The DIF contrast column represents the difference
Table 5 Anxiety for various passengers’ characteristics
Passengers’ characteristic Group Sample Mean of ability pValue
Age B40 295 -0.544 0.052*
C41 12 -0.093
Sex Female 160 -0.657 0.020**
Male 147 -0.369
Riding frequency per month B1 162 -0.661 0.016**
C2 145 -0.360
Trip type Commuter passenger 37 -0.108 0.021**
Long-distance passenger 270 -0.575
*p\0.1, ** p\0.05
Transportation
123
between DIF measures. The ttest was applied for differences between measures of these
two groups. The pvalues reveals that anxiety associated with ‘‘poor timetable information’’
and ‘‘taking a night train’’ differed significantly between sexes. ‘‘Poor timetable infor-
mation,’’ however, causes more difficulties for male passengers with a measurement value
of -0.10 than female passengers with that of -0.50. ‘‘Taking a night train’’ had a logit
estimate of 0.27 for females, indicating that ‘‘taking night trains’’ may cause more anxiety
for females than males (-0.51).
Table 7presents the DIF analysis between long-distance travelers and commuters. Item
4, ‘‘gap between trains and platforms,’’ caused significantly different levels of anxiety for
commuters and long-distance travelers (p\0.05); that is, the higher item difficulty logit
for commuters (0.09) indicates that the ‘‘gap between trains and platforms’’ can result in
more anxiety for commuters.
By relating each passenger’s ability to overcome anxiety to various train riding fre-
quencies, some useful information can be generated easily (Fig. 6). The monthly train
travel frequencies of each passenger and their ability to overcome anxiety (logits) are
plotted on the horizontal and veridical axes, respectively. On the horizontal axis, pas-
sengers are divided into subgroups based on their monthly train travel frequencies, namely,
1, 2–7, 8–11 and 12–16, and[17. The maximum, mean, and minimum of the anxiety score
for each subgroup are also depicted in Fig. 6. An interesting relationship exists between
passenger monthly train travel frequency and the ability to overcome anxiety. Passengers
who ride the train infrequently have problems to overcome the train riding anxiety, pos-
sibly due to their unfamiliarity with TRA services. As monthly train travel frequency
Table 6 Differences among various gender groups in terms of each item for measuring riding anxiety
Items DIF measure DIF contrast
(F–M)
p
Female Male
Item 1. When I need to transfer via another train
before arriving at my destination
0.15 0.30 -0.15 0.2807
Item 3. When considering the convenience
of transport to the railway station
0.80 0.82 -0.02 0.9009
Item 6. When the train is crowded 0.25 0.20 0.05 0.7254
Item 9. Noise in the train 0.20 0.07 0.13 0.3956
Item 10. When I take the train by myself -0.99 -0.77 -0.22 0.1229
Item 12. When strangers sit next to me in the train -0.41 -0.38 -0.03 0.8531
Item 8. Poor provision of timetable information
(outdated, difficult to get)
-0.50 -0.10 -0.40 0.0043**
Item 11. When the train is delayed 0.54 0.51 0.03 0.8360
Item 4. When the gap between the train
and platform is large
-0.36 -0.34 -0.02 0.9080
Item 2. When there is not enough waiting seats
on the train or platform
0.00 0.12 -0.12 0.4042
Item 7. When I cannot quickly find my coach
on the platform
0.51 0.47 0.04 0.7843
Item 5. When possible attack could occur at the station,
on the platform, or inside the coach
-0.46 -0.37 -0.09 0.5018
Item 13. When I take a night train 0.27 -0.51 0.77 0.0000**
** p\0.05
Transportation
123
increases, the number of passengers who overcome anxiety increases, likely due to an
increased ability of passengers to learn. Passengers can learn how to overcome anxiety.
Additionally, frequent train travel can decrease one’s anxiety. However, overly frequent
train travel can cause various difficulties that have not been resolved by the TRA. Such
difficulties can therefore increase anxiety.
Conclusions and discussion
Travel behavior could be better understood when insights are accumulated into a psy-
chological mechanism. The application of the Rasch measurement, therefore, further
analyzes the effects of psychological resistance, such as anxiety, to use the public trans-
portation; these effects have seldom been identified in literature. This study provides a
preliminary demonstration of how the Rasch model can be used to measure passenger
anxieties associated with train travel. The application of the Rasch method is recognized in
management fields (Yang 2009; Oreja-Rodriguez and Yanes-Este’vez 2007); in our case,
the measurement of anxiety in train rides. The Rasch model can compare person param-
eters with item parameters on a same logit scale to clearly identify which items causing
anxiety cannot be easily overcome by certain train passengers. Empirical results from the
Table 7 Differences among various trip types of groups in terms of each item for measuring riding anxiety
Items DIF measure DIF
contrast
(A–B)
p
AB
Item 1. When I need to transfer via another train
before arriving at my destination
0.26 0.07 0.19 0.2591
Item 3. When considering the convenience
of transport to the railway station
0.33 0.39 -0.06 0.7482
Item 6. When the train is crowded 1.17 1.14 0.03 0.8446
Item 9. Noise in the train 0.00 -0.10 0.10 0.6111
Item 10. When I take the train by myself -0.85 -1.00 0.15 0.4197
Item 12. When strangers sit next to me in the train -0.41 -0.38 -0.03 0.8531
Item 8. Poor provision of timetable information
(outdated, difficult to get)
-0.50 -0.60 0.10 0.6064
Item 11. When the train is delayed 0.66 0.59 0.07 0.7105
Item 4. When the gap between the train
and platform is large
-0.31 0.09 -0.40 0.0365**
Item 2. When there is not enough waiting seats
on train or platform
-0.03 -0.19 0.16 0.3829
Item 7. When I cannot quickly find my
coach on the platform
0.30 0.28 0.02 0.8858
Item 5. When possible attack could occur
at the station, on the platform,
or inside the coach
-0.44 -0.38 -0.06 0.7211
Item 13. When I take a night train -0.21 -0.04 -0.17 0.3345
** p\0.05
Group A Long-distance passenger
Group B Commuter
Transportation
123
present study indicate that passengers have anxiety associated with ‘‘crowding,’’ ‘‘delays,’’
‘‘accessibility to railway stations,’’ ‘‘searching for the right train on a platform,’’ and
‘‘transfer processes,’’ as ordered by level of anxiety from most to least. Second, the Rasch
model provided empirical evidence of substantial group differences in anxiety by sex, age,
riding frequency, and trip type and allowed for further examination of the reasons of these
group differences. Third, the Rasch model analysis found that amelioration of train delays
is an effective strategy from the perspective of the service provider, even though the
highest level of passenger anxiety was associated with ‘‘crowding.’’
Survey responses in this study indicate that many services addressed in the question-
naire are in obvious need of improvement. Study results show that the gap between
customer satisfaction and railway service quality remains large for the TRA. Since the
TRA is a monopoly without competitions from other railway companies, responses to
passenger needs for service quality improvements may be slow. The incorporation of a
customer relationship management and its successful execution should be carefully
implemented in daily routine operations and company regulations to improve service
quality.
This study finds that the highest level of passenger anxiety is associated with
‘‘crowding.’’ This finding is consistent with that obtained by Cox et al. (2006), who
indicated crowding is a possible threat both to the rail industry and passengers. The coach
crowding suggests that passenger demand at a certain service level is not met. Increasing
train frequency to provide additional system capacity and reduce crowding during peak
demand periods would help. Obviously, the cost of adding trains should be covered by
revenue by increased demand. However, the rail operator should consider the trade-off
between sacrificing service quality for passengers in crowded trains and the increased cost
of adding trains.
Delays generate the second highest levels of anxiety, which corresponds to analytical
result obtained by other studies indicating that long delays increase frustration and anxiety
(Kuhmann et al. 1987; Kuhmann 1989; Martin and Corl 1986; Thum et al. 1995; Weiss
et al. 1982). The current train punctuality rate of the TRA is \80% (MOTC 2008).
Additionally, a delay of \10 min is considered allowable and only when delays exceed
-0.15
-0.02
-0.16
-0.66
-2.66
0.98
-1.51
1.68
-1.25
2.45
-5.92
2.03
-5.92
max 0.98
-0.45
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
12-7 8-11 12-16 17
0
mean
min
Avera
g
e ridin
g
fre
q
uenc
y
in one month
Passenger’s ability to overcome anxiety( n)
θ
Fig. 6 Relationship of riding frequency and passengers’ anxiety
Transportation
123
60 min are tickets refunded to passengers. The currently low requirement for train punc-
tuality of the TRA can easily cause dissatisfaction and anxiety. Therefore, the priority
should be to avoid any delays. Even when a delay occurs, the causes need to be identified
and analyzed. Providing prompt and appropriate information to passengers regarding the
length of a delay, reason for a delay, and possible service recovery for passengers should
alleviate passenger anxiety.
Accessibility to a railway station can cause anxiety for passengers; this finding is
consistent with a conclusion by Keijer and Rietveld (2000) who emphasized that local
accessibility to railway stations is an important determinant of railway use. Most TRA
stations are located in the central business district. However, a convenient public trans-
portation feeder system is not yet well established. Furthermore, parking space for cars and
scooters at railway stations is still lacking.
This empirical study also shows that transfer processes are an important service item
causing passenger anxiety; this finding is in agreement with those obtained by Li (2003)
and Hine and Scott (2000), indicating that passengers may be anxious when transferring
trains, particularly with incomplete information. Finally, searching for the right train on a
platform is also a possible source of passenger anxiety, meaning that information tech-
niques for guiding passengers have room for improvement. Installation of an advanced
passenger information system to guide passenger flow, including clear directional signs,
electronic signage, and broadcasts indicating which trains are on which platforms would be
very helpful.
In terms of group differences, empirical results demonstrate a distinct difference in the
level of anxiety between sexes. This is compatible with a finding obtained by Lynch and
Atkins (1988). This study shows a sex-based difference in responding to the items ‘‘When I
take a night train’’ and ‘‘Poor provision of timetable information (outdated, difficult to
get).’’ Female passengers experienced less anxiety than male passengers when faced with
poor timetable information and when train travel information was not promptly updated.
Female passengers experienced a greater level of anxiety than male passengers while
taking night trains. This analytical result is in agreement with that acquired by Lynch and
Atkins (1988), who determined that females experience a greater level of insecurity when
traveling in darkness. Empirical evidence from the Rasch model analysis outlines how
fears about safety limit the freedom of most females when traveling by train alone after
dark. Lee et al. (2009) provided some suggestions about how to improve safety and
security of TRA train travel. However, security issues for female passengers did not garner
the attention of TRA managers. Although control of security problems such as physical
abuse by other passengers is difficult, this problem has a great effect on passengers.
Therefore, we recommended measures such as providing a women’s coach, installing
additional surveillance equipment, and increasing police visibility be considered to alle-
viate passenger anxieties.
Except for sex-based differences, this study also provides evidence that commuters and
long-distance passengers have different levels of anxiety. The major difference between
these two groups is their response to the gap between a train and its platform. The reason
may be that the rolling stock purchasing policy of the TRA results in a wide variety of
rolling stock, leading to a matching problem between various trains and fixed height of
platforms. Therefore, we suggest that commuter trains only stop along platforms reserved
for commuter trains; this same principle should apply to long-distance trains.
When the same magnitude of difficulty for various service items are reduced, shorter
delays can reduce passenger anxieties more than can reducing train crowding based on the
Transportation
123
person–item map. The Rasch model analysis can thus determine that amelioration of train
delays is more effective that reducing crowding.
Limitations and future research
The Rasch model analysis can facilitate the identification of effective strategies that
alleviate passenger anxiety. The estimated costs of such strategies can be examined in a
future study. Furthermore, passenger anxiety during train travel may be related to the mood
of train passengers. Therefore, the relationship between anxiety and the mood of passen-
gers can be further explored in future research.
This study focused mainly on railway passengers in Taiwan. Future studies can expand
this focus by investigating rail passenger anxiety in other countries to compare cultural
differences in train travel.
In regards to the measurement approach, this study used a one-parameter Item Response
Theory (IRT) model, the Rasch model, based on a one-dimensional assumption to measure
passenger anxieties associated with train travel. The two-parameter IRT model or three-
parameter IRT model can be used for development or exploration of scale items or
dimensionality. However, the sample size required for reasonably precise estimates of a
two-parameter model is at least 1,000 (Lord 1980; Myers et al. 2006).
Acknowledgments The author of this paper sincerely acknowledges the valuable suggestions of three
anonymous reviewers, which have immensely helped to enhance the quality of the paper over its earlier
version. The author thanks the National Science Council (NSC) of Taiwan, ROC, for financially supporting
this research. Ms. Yu-Chun Tsai is appreciated for her assistance in data collection and processing.
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Author Biography
Dr. Yung-Hsiang Cheng holds a Ph. D. in Transportation from Ecole Nationale des Ponts et Chausse
´e
(France) and is an assistant professor of Department of Transportation and Communication Management
Science at National Cheng Kung University, Taiwan, ROC. His past experiences include transportation
engineer at Ministry of Transportation, Taiwan, and researches at the SNCF (French National Railway
Company). His research specialties include railway transportation, transportation management, and logistics
management.
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