Journal of Transportation Technologies, 2011, 1, 34-46
doi:10.4236/jtts.2011.13006 Published Online July 2011 (
Copyright © 2011 SciRes. JTTS
The Sensitivity of Model Results to Specification of
Network-Based Level of Service Attributes: An
Application of a Mixed Logit Model to Trave Mode Choice
Bharat P. Bhatta
Sogn og Fjordane University College, Sogndal, Norway
Received April 1, 2011; revised May 2, 2011; accepted May 12, 2011
The need for travel demand models is growing worldwide. Obtaining reasonably accurate level of service
(LOS) attributes of different travel modes such as travel time and cost representing the performance of
transportation system is not a trivial task, especially in growing cities of developing countries. This study
investigates the sensitivity of results of a travel mode choice model to different specifications of net-
work-based LOS attributes using a mixed logit model. The study also looks at the possibilities of correcting
some of the inaccuracies in network-based LOS attributes. Further, the study also explores the effects of dif-
ferent specifications of LOS data on implied values of time and aggregation forecasting. The findings indi-
cate that the implied values of time are very sensitive to specification of data and model implying that utmost
care must be taken if the purpose of the model is to estimate values of time. Models estimated on all specifi-
cations of LOS-data perform well in prediction, likely suggesting that the extra expense on developing a
more detailed and accurate network models so as to derive more precise LOS attributes is unnecessary for
impact analyses of some policies.
Keywords: Data Specification, Level of Service Attributes, Travel Mode Choice, Network Models, Mixed
Logit, Error Components Logit
1. Introduction
The need for travel demand models is growing due to
rising travel activities in response to increasing incomes
and urban population in large cities in many developing
countries in Asia and Africa. Detailed and accurate data
relating to land use, transportation systems and their per-
formance, and people’s travel behavior including their
socioeconomic characteristics are needed to estimate the
travel demand models. Such detailed data are not often
collected routinely in most developing countries. Even if
the data are available, they may not be accurate enough.
Data on travel behavior and socioeconomic characteris-
tics are obtained from travel surveys while the data re-
lating to transportation level of service (LOS) attributes
are mostly obtained from the zonal-based network mod-
els. Developing detailed and correct network models that
can produce reasonably accurate estimates of LOS at-
tributes is not trivial [1]. All cities may not have ade-
quate resources including human resources, money,
technology and so on to develop such a network. Some-
times the LOS attributes have to be derived in a short
time. Many rapidly growing cities in Asia and Africa
usually lack appropriate network models and hence LOS
attributes which indeed seriously constrain modeling
travel demand. However, the data limitations are not con-
fined to developing countries only. Even highly devel-
oped country like Norway may sometime lack accurate
data to model travel behavior. The modeler therefore has
to use available data and consequently modeling activi-
ties should account for such data limitations [2]. A LOS
variable used in a model may contain a mixture of sys-
tematic and random errors or errors may not have any
particular pattern in general. Some of the errors can be
known, for example, missing toll, which can be corrected
easily later, while others are unknown and cannot be
In light of the situations discussed above, this paper
explores the sensitivity of model results to different spe-
cifications of network-based LOS attributes using mixed
logit (ML) model with mode choice for work trips in
Oslo as an example. Specifically, we used two different
data sets of network-based LOS attributes. The first data
set of LOS attributes (“striplos”) was obtained from net-
work models developed in 2002 for the whole country.
The LOS attributes were derived from scratch for the
whole country with limited resources within a short time.
Travel times by car were taken from an uncongested road
network although most car drivers in the Oslo-region
experience congestion. Coding of road tolls on the toll
cordon in Oslo was missing. Public transit fares were
estimated as a function of distance despite the fact that
Oslo has a flat fare system and the remaining region has
a fare system based on the number of fare-zones trans-
versed. Some public transit routes were also missing.
Those LOS attributes were used to estimate national
transport models for the whole country [3] based on a
national travel survey conducted in 2001.
Striplos had some obvious deficiencies with respect to
cost of travel by public transport and car. These are rela-
tively easy to detect and make corrections for. Errors that
stem from the coding of road network and public trans-
port routes are more difficult to detect and make correc-
tions for. In preparing the data, we made the same cor-
rections that were made in estimating the national mod-
els. We used the same values for both directions if LOS
attributes were missing for one direction. We also che-
cked for unreasonable directional asymmetry of attrib-
utes for car driving.
The second set of LOS attributes (“nylos”) on the
other hand was obtained from the well established net-
work model. The network model has been existed in the
Oslo-region since 1990 and has been continuously up-
dated and improved. Travel time by car for the morning
peak was also available. It was assumed that a return trip
in the afternoon peak would take approximately the same
time although it may not be necessarily true. Public
transport assignment was also based on another network
model that, it is believed, should give better estimates of
different travel time components of public transport. The
coding of the road network was also better and more
detailed. The nylos overcomes most of the deficiencies
that striplos had so it is in general a typical LOS data of
transportation system performance. Presumably, LOS
attributes of nylos should be more accurate than that of
striplos. However, nylos is by no means a perfect data set
either. The nylos was used to re-estimate the simultane-
ous mode/destination choice model for work trips in the
Oslo-region estimated for the national travel demand
model [4].
There could be many instances in many cities, espe-
cially in developing countries, where LOS attributes
have to be obtained with limited resources both with re-
spect to time, money and technology. The purpose of this
paper is therefore to investigate the implications of using
LOS attributes measured at different levels of accuracy
in model results, including forecasting. We also explore
whether it is possible to correct for the aforesaid limita-
tions relating to network-based LOS attributes.
As type and severity of errors in different variables
may vary from case to case, the results presented in this
paper can only be an example of the consequences of
estimating the same model on two different sets of LOS-
data, of which one presumably is of better quality than
the other. As long as we are unable to quantify the qual-
ity of a data set and relate this in a meaningful way to the
results of model estimation, it is impossible to draw gen-
eral conclusions.
The remainder of the paper is organized as follows.
Section 2 discusses the current state of knowledge rele-
vant to the study. Section 3 describes the data. Section 4
explains the theoretical background and modeling ap-
proach. Section 5 presents the results and discussion fol-
lowed by conclusions in Section 6.
2. Review of Literature
This section briefly reviews the literature related to data
accuracy and model results, and disaggregate travel
mode choice model estimation with different specifica-
tions of network-based LOS attributes.
2.1. Data Accuracy and Model Results
Alonso [5] investigates the implications of imperfect data
on modeling and prediction. His investigation is not re-
lated to transportation but his conclusions are generally
applicable to all fields including transportation using
statistical analysis and modeling. Based on simple nu-
merical exercises, he generalizes a few rules of thumb
for model building as follows: 1) avoid inter-correlated
variables, 2) add if possible, 3) multiply or divide if ad-
dition is not applicable, and 4) avoid taking differences
or raising variables to powers as far as possible. He con-
cludes in general that it is the correlation of input vari-
ables that causes large errors in outcome variables so he
suggests avoiding the correlated variables. Most of the
LOS attributes used in travel demand modeling are
highly correlated. Given Alonso’s prescription, we could
somewhat reduce the output errors if we could exclude
the correlated variables in the model. He also suggests
using simpler models if the input data are not that accu-
rate. Given Alonso’s thesis, formulation of a model may
also help minimize the output errors. Unfortunately, we
cannot exclude cost and time, which are highly corre-
lated variables, to estimate the travel demand models.
Copyright © 2011 SciRes. JTTS
Later Daly and Ortuzar [6] and Ortuzar and Willum-
sen [1] apply Alonso’s original ideas in transportation.
Daly and Ortuzar [6] theoretically and empirically ex-
plore data aggregation in travel demand modeling, dif-
ferent types of errors in modeling and forecasting, and
the trade-off between model complexity and data accu-
racy with focus on the forecasting of mode and destina-
tion choice. They recommend that 1) the model building
should take into account the efficient allocation of mod-
eling resources, 2) errors, especially those which violate
basic assumptions of the model, should be minimized,
and 3) since measurement error is an important compo-
nent of the overall error in modeling, it should be mini-
mized given the budget. They thus emphasize the most
efficient allocation of modeling resources.
2.2. Mode Choice Model with Different
Specifications of Network-Based LOS
Interest on mode choice model estimation with different
specifications of network-based LOS attributes is not new.
We briefly review the studies in this section.
Reid and Small [7] investigate the effects of using
temporal disaggregation of trip data on traveler behavior
models. Their main finding are: 1) peak average vari-
ables tend to underestimate headways for public trans-
port users and in-vehicle times for car trips; 2) model
coefficients become biased and the magnitude of the bias
can be quite severe in relatively complex choice func-
Train [8] explores the sensitivity of parameter esti-
mates to data specification in a logit model for travel
mode choice. He analyzes the effects of correcting some
of the inaccuracies in the network LOS attributes on the
estimated parameters. He compares the parameter esti-
mates of models estimated on the standard network data
and on temporally and spatially adjusted data so as to
correct the problems in the standard network data. He
seemingly concludes the following: 1) Temporal adjust-
ment of the standard network data is perhaps advisable
for analyzing policies affecting transfer wait times, 2)
Spatial adjustment seems advisable for policies affecting
distances to bus stops; and 3) It seems no adjustment is
needed for analyzing policies that affect neither walk
times nor transfer wait times. However, he evaluates the
sensitivity of the parameter estimates just by “eye-ball-
ing” without taking into consideration of the variances of
the estimates, their relative magnitudes, and the impacts
on aggregate forecasting. Further, he is not sure whether
the adjustments in the standard network data yield better
estimates of the values of walk and transfer wait times. It
seems that his findings are not clearly irrefutable.
Similarly, Ortuzar and Ivelic [9] investigate the effect
of using more precise measures of the variable ‘waiting
time’ in public transport modes. They conclude that
clearly better models are resulted in by more detailed
values, entailed replacing crude measures based on the
average frequency at different distances to the central
business district by more accurate values obtained with
the aid of state-of-the-art public transport assignment
models (cited in [6]).
Further, Ortuzar and Ivelic [10] examine both in the-
ory and in practice the problem of using less than fully
disaggregate date in estimating logit model of travel
mode choice for a trip to work. They replaced peak av-
erage values of travel times by more precise values for
each traveler depending on the exact time of the trips.
They estimated the models with and without temporally
disaggregate data on travel times. Contrary to their own
findings [9], they could not conclude that the models
estimated on temporally disaggregate data resulted in
significantly better models and stable parameter esti-
mates. They suggest assigning priority to cost over accu-
racy of model results in such cases.
Recently, Steimetz and Brownstone [11] use multiple
imputation approach to overcome the problem of noisy
data to estimate mode choice model in estimating com-
muters’ value of time. Similarly, to solve the problem of
sparse data, Monzon and Rodriguez-Dapena [12] use
double weighted estimator for long distance transport
mode choice models to estimate the choice of mode of
transport for long-distance trips. They successfully vali-
dated the method in the case study of the Madrid-Bar-
celona interurban corridor in Spain. They claim that their
results allow achieving a cheaper survey procedure for
interurban transportation planning activities.
Daly and Ortuzar [6] mention in their paper that the
coefficients of the detailed models are significantly better
than those of the models estimated on spatially aggre-
gated data of LOS attributes. From the review of the em-
pirical studies of disaggregate mode choice model esti-
mation using LOS attributes measured at different levels
of accuracy, they apparently conclude that the accuracy
of LOS attributes to estimate the mode choice models
depend on the relative importance of the various consid-
erations and the context. Finally, they recommend that 1)
The modeling process should take into consideration of
the most efficient allocation of modeling resources, and 2)
Although errors arising in modeling cannot be com-
pletely eliminated, errors, particularly that violate the
basic assumptions of the model, should be minimized.
2.3. Summary and Discussion
Measurement error is one of the major problems in sta-
Copyright © 2011 SciRes. JTTS
tistical analysis and modeling. It is generally accepted
that errors in input data create errors in models, and often
those errors can become far more serious in the model
than appears in the data. It is also mostly accepted that
developing an accurate and detailed network model to
derive accurate enough LOS attributes is not that trivial
[1]. Daly and Ortuzar [6] therefore emphasize that errors
especially those which violate basic assumptions of a
model should be minimized.
Studies on the problem of disaggregate travel mode
choice model estimation using LOS attributes measured
at different levels of accuracy are conducted in different
situations for specific problems with different assump-
tions. Additionally, those studies focus on different vari-
ables and do not have consistent findings. Consequently,
it is difficult to draw general conclusions. The study in
this paper examines the effects of using network LOS
attributes measured at different levels of accuracy on
relative magnitudes of the coefficients, specifically a
value of time implied by travel demand models, and ag-
gregate forecasting. The modelers will frequently en-
counter the situation dealt in this paper.
We generally expect that requirement of accuracy of
LOS attributes may depend on the purpose of developing
a model to some extent [6,13]. A systematic error in one
or more variables may not necessarily result in severe
consequences if model applications also use the input
data having the same systematic error. The parameter
estimates will in most cases be robust to the error. But
systematic error may lead to severe consequences if the
purpose is to estimate the implied value of travel time
savings for different modes. Random measurement errors
always bias parameters in an unpredictable way [14].
3. Data
We use data from the Norwegian national travel survey
undertaken in 2001 in this study supplemented by a
similar travel survey undertaken in the Oslo-region in the
same period and the LOS attributes of transportation
system obtained from network models. The survey ran-
domly selected 20,751 people. The respondents were
asked about the socioeconomic characteristics of the
household, his/her travel activities including daily travels,
long travels, employment, work travel, spouse/cohabitant,
household, household access to transport resources, and
detailed information about the interviewees. A detailed
description of the design and conduct of the survey,
characteristics of the sample, and questionnaire adminis-
tered can be found in Denstadli, et al. [15]. The travel
survey therefore provides the information on actual
choice and socioeconomic characteristics of travelers
including their households. This study uses a sub-sample
for commuting trips to work, hereafter referred to as
work trips, in Oslo of the national travel survey. The
work trip is defined as a two way movement from home
to work and back. Some trips had secondary destinations
such as taking/collecting kids to/from kindergarten, shop-
ping at grocery, etc on the way to/from work. There are
2,946 such trips in the sub-sample. As a part of data
validation, several screening and consistency checks
were performed. Some observations were deleted during
the data validation process so the final data set had only
2, 876 work tours.
The possible alternatives for the population for work
trips in the study area consisted of five modes, viz.,
walking (WK), cycling (CK), car driving (CD), car pas-
senger (CP) and public transport (PT) with actual modal
shares of 8%, 6%, 52%, 5% and 29% respectively. These
five modes serve as the universal choice set. Each indi-
vidual traveler may have different choice sets given their
own circumstances and constraints. The criteria used for
alternative availability when estimating the models on
the different specifications of the LOS attributes were of
course the same. As mentioned earlier, the two data sets
of the network-based LOS attributes, namely, striplos
and nylos, were used to study the models in this study.
Interzonal trips are sometimes excluded from model
estimation since they do not appear on a network in the
centroid-to-centroid travel. The exclusion of these trips
results in biased sample thereby causing biased parame-
ter estimates of model and biased aggregate forecasting
[16]. In this analysis, instead of outright deleting the in-
trazonal trips, they were included in the estimation. It
was assumed that the length of the trip was equal to the
length of the centroid connector and low speed for intra-
zonal trips by cars since the trips are short and usually
stay on local roads. However, public transport was set
unavailable for the intrazonal trips.
4. Theoretical Framework and Model
In this section, we present theoretical framework under-
lying choice modeling and model formulation.
4.1. Theoretical Framework
Choice models based on random utility maximization
(RUM) hypothesis are the most widely used tools to
examine individual travel behavior [1,17-20]. In a RUM
framework of choice modeling, a decision maker facing
a mutually exclusive and collective exhaustive set of
finite number of alternatives obtains utility from each
alternative and chooses the one with the highest utility.
But the analyst is not able to observe the utility of alter-
Copyright © 2011 SciRes. JTTS
natives, therefore, decomposes the utility into two parts
for analytical purposes: 1) an observable part and 2) an
unobservable part. The utility of the alternative i
for the decision maker n, Uin, can therefore be written as:
Uin = Vin + εin (1)
where Vin and εin represent the observed and unobserved
parts of the utility of the alternative i for the decision
maker n respectively from the point of view of the ana-
lyst. Vin is the systematic or representative utility. The
systematic utility is deterministic in the sense that it is
broadly a function of a vector of attributes of the alterna-
tive, Zin, and a vector of characteristics of the decision
maker, Sn, so:
Vin = V (Zin, Sn) (2)
RUM models of travel demand is a highly researched
field where advanced models such as generalized ex-
treme value models allowing for advanced nesting struc-
tures (cross-nesting and multi-levels and recursive) and
models with mixed distributions (e.g. mixed logit) [20-22]
are developed. In recent years, advanced discrete choice
models, such as models with advanced nesting structures
and models based on mixed distributions, are increas-
ingly used to allow for flexible substitution patterns,
correlation across alternatives and/or random taste het-
erogeneity [22]. The mixed logit (ML) model is the most
advanced model among choice models. Initially, Boyd
and Mellman [23], and Cardell and Dunbar [24] used the
ML model in modeling automobile demand. Their mod-
els were not truly disaggregate because their dependent
variable was market shares rather than individual cus-
tomers’ choice and the explanatory variables did not vary
over the decision makers. The extremely high cost of
estimation (and hence implementing the results) pre-
vented the use of ML model for many years after the
initial development. The disaggregate ML model has
been in the extensive use since the advent of high speed
computers, mass storage devices, and simulation. The
flexibility of the model and decreased cost of computa-
tion have led to the widespread use of ML models in
diverse fields, including political science [25], resource
economics [26], transportation [27], peace and conflict
[28], and business [29], to name only a few.
The ML is an intuitive, powerful and practical model
that prevents the three limitations of the multinomial
logit model by allowing for random taste variation, unre-
stricted substitution patterns, and correlation in unob-
served factors over time and space. McFadden and Train
[30] prove that the ML model is a highly flexible model
that can represent any RUM model. In order to realisti-
cally represent the individual choice behavior, the ML
model has become one of the most widely used models
in the field of demand modeling over the years. Since
ML is the most advanced and flexible model among dis-
crete choice models, we used the ML model of travel
mode choice in this paper.
4.2. Formulating a Mixed Logit Model
An ML model includes a flexible random term ηin repre-
senting additional unobservable factors, independent of
εin, in its utility function [19,21,22,30]. The ML model is
thus given by:
Uin = Vin+ ηin + εin (3)
As evident by the notation, the random terms ηin vary
across both alternatives and decision makers. The re-
searcher can assume any convenient and/or appropriate
distribution for ηin. Consequently, the ML model is very
flexible and free from restrictive assumption such as in-
dependent of irrelevant attributes. Unfortunately, the ML
choice probabilities have no longer closed form due to
the presence of ηin in utility function of the model. As a
result, we have to estimate the model with the help of
some numerical solutions such as numerical integration,
numerical approximation or simulation [19]. The choice
probability of alternative i for decision maker n with the
ML model is the integral of logit choice probability over
the assumed distribution of random terms as given by:
(|) ()d
inn nn
where Ln(i|ηn) is the logit choice probability ofalterna-
tive i for decision maker n conditional on ηn:
(| )
nn JV
The ML models are normally derived either to allow
flexible substitution patterns across alternatives or to
accommodate random taste heterogeneity across decision
makers [19,30]. The former approach gives rise to the
error components logit (ECL) model and the latter to the
random coefficients logit (RCL1) model. One can also
develop more advanced model to allow for random taste
heterogeneity, inter-alternative correlation, and hetero-
scedasticity by combining the ECL-RCL approaches [22].
The ECL model allows some elements of η to be shared
across some alternatives which in turn introduces corre-
lation between the random terms of these alternatives.
The ECL model thus closely resembles the models using
a nesting structure such as nested logit that accommo-
dates correlation across some of the alternative while it
simultaneously accommodates random taste heterogene-
ity and heteroscedasticity, which the nested logit model
1“Random coefficients logit” and “random parameters logit” are used
interchangeably in literature.
Copyright © 2011 SciRes. JTTS
does not [21].
The utility function of the ECL model is specified in
such a way that error components (EC) create correla-
tions among utilities of different alternatives [19]:
Uin = Vin+ γn’zin + εin (6)
where γn is a vector of random terms with zero mean and
a covariance matrix Σ and zin is a vector of observed
variables relating to alternative i. Put succinctly, zin is a
vector of binary variables that indicate the EC entering
the utility function of alternative i. The ECL model re-
duces to the logit model if zin is 0 for all the alternatives
meaning that the unobserved parts of the utility are un-
correlated across alternatives. Naturally, the choice pro-
bability with the ECL model does not have a closed form
and thus requires the numerical processes to solve the inte-
grals. The ECL model enables to estimate the error com-
ponents that measure the relative sensitivity of changes in
choice of different alternatives and to accommodate het-
eroscedasticity in the unobserved influences on the
choice. The choice probability of alternative i for deci-
sion maker n with the ECL formulation of the ML is then
obtained by integration over the distribution of γn [22]:
inn in
jnn jn
inn n
where ф (γn|0, Σ) is the joint normal density function of
the elements in γn.
In recent years, there has been a considerable interest
in using ECL models in order to accommodate inter-
alternative correlation and heteroscedasticity despite high
cost of estimation (and hence application) and identifica-
tion issues [31]. [21,32] are the two recent and the most
notable applications of the ECL model structures to in-
vestigate the factors influencing the time of day and
mode choice. The ECL model is also applied to analyze
the corporate bankruptcy and insolvency risk in Australia
4.3. Formulating the ECL Model of Mode
The ECL model was used to estimate the error compo-
nents that measure the relative sensitivity of changes in
mode choice and to accommodate heteroscedasticity in
the unobserved influences on the mode choice. We ex-
plored various possible specifications of the ECL models.
Mainly, we focused on two specifications: 1) common
unobserved factors between walking (WK) and cycling
(CK) (non-motorized modes), and 2) common unob-
served factors between car driving (CD) and car passen-
ger (CP) (car modes), or common unobserved factors
among CD, CP and public transport (PT) (motorized
modes). As WK and CK are both non-motorized modes,
the hypothesis is that they share unobserved factors that
introduce correlation between the utilities of those alter-
natives. Similarly, since CD, CP and PT are motorized
modes, they presumably share unobserved factors that
introduce correlation among the utilities of those alterna-
tives. Among those specifications, we chose the one
sharing the error components between alternatives be-
longing to motorized and non-motorized modes.
Based on the discussions above, we formulated the
ECL model by adding the error components to the utility
function as follows (by suppressing n):
Ui = Vi+ σnmt. ζnmt. NMT(i) + σmt. ζmt. MT(i)+ εi (8)
where ζnmt and ζmt are random variables drawn inde-
pendently from the standard normal distribution, and σnmt
and σmt are the standard deviations of the error compo-
nents. σnmt and σmt are actually the elements of the vari-
ance-covariance matrix capturing the correlation between
WK and CK, and CD, CP and PT respectively. In this
specification, NMT (i) is a dummy variable with 1 for
the alternatives belonging to non-motorized modes and 0
otherwise. This dummy variable thus determines whether
the error component relating to the non-motorized modes
is included in the utility function of alternative i. Simi-
larly, MT (i) is also a dummy variable with 1 for the al-
ternatives belonging to the motorized modes and 0 oth-
erwise and thus determines whether the error component
relating to the motorized modes enter the utility function
of alternative i. The utility of an alternative i contains at
most one of those two error components.
Estimation of this ECL model yields estimates of the
parameters of the standard deviations of the error com-
ponents (setting their mean to zero) in addition to the
coefficients of the variables included in systematic utility
functions. The variance of the error components related
to nonmotorized modes is estimated by normalizing the
variance of the error components of motorized modes to
one because we can only identify the sum of the vari-
ances in this particular formulation. The relative magni-
tude of the variances of the error components associated
with the non-motorized and motorized modes provide a
measure of the relative sensitivity of these two modes to
changes in the major attributes of travel modes such as
travel time and cost components.
Three types of variables such as characteristics of the
journey, characteristics of a traveler and his/her house-
holds, and performance of the transportation system as
measured by the LOS attributes of different modes are
included in systematic utility functions of travel modes
[1,13]. Table 1 illustrates names and definitions of the
variables including alternative specific constants (ASC)
where the first two letters refer to the mode (i.e. utility
function) where the variable enters. The models were
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Copyright © 2011 SciRes. JTTS
Table 1. Variable (including ASCs) definitions.
Variable Definition
CK_00 ASC for CK alternative
CD_00 ASC for CD alternative
CP_00 ASC for CP alternative
PT_00 ASC for PT alternative
WK_dist Walking distance to get to work
CK_dist Cycling distance to get to work
CD_time Generic travel time by different travel modes
GA_cost Generic travel cost by different travel modes
PT_wktm Access/egress time to get to PT
PT_invht Invehicle time with PT (in minutes)
PT_wait Waiting time for PT
PT_xfers Number of transfers to get to the work place with PT
CP_female 1 if the traveler is female, 0 otherwise
CD_parkgod 1 if guaranteed free parking at work , 0 otherwise
CD_parkfair 1 if fair parking possibility at work, 0 otherwise
CK_winter 1 if the trip was made during winter, 0 otherwise
CD_soj 1 if the trip involves a secondary destination, 0 other-
CD-dbfem 1 if good car access in the household, 0 otherwise
CP_time Car time by CP
PT_female 1 if the traveler is female, 0 otherwise
CD_tmrush Car time for the trip made during peak to Oslo
coded and estimated in BIOGEME [33] using 1,000
random draws. A set of “reasonable models” were for-
mulated (and reformulated) and estimated (and re-esti-
mated) based on a priori-consideration. The systematic
process of model building led to the final specification
(Table 3) based on goodness-of-fit measures, statistical
tests and informal tests.
In addition to the ECL model of mode choice esti-
mated on nylos, four ECL models on different specifica-
tions of striplos with identical specification of systematic
utility function were estimated as follows:
· Model 1 (base case): The first model was estimated
on the LOS attributes at “face value” except the correc-
tion for missing direction and unreasonable asymmetry
in LOS attributes.
· Model 2: In the second model, public transport
fares in Oslo were corrected, but the fares in the rest of
the region and between Oslo and the rest of the region
were not adjusted.
· Model 3: In the third model, missing toll in Oslo
was corrected for in addition to the correction made in
the Model 2.
· Model 4: In the fourth model, an attempt was made
to account for congestion in Oslo in addition to the cor-
rection made in the Model 3 since striplos did not have
separate LOS values for peak and off-peak hours. Re-
spondents had reported when the trip was taken and this
enabled us to adjust for congestion by using a variable
where driving time interacts with a dummy for peak
travel, i.e., instead of higher driving times during peak
hours, the model had additional coefficient for driving
time. This variable was added to the utility of car driving
in the model
First the differences in LOS attributes between striplos
and nylos are discussed. Then estimation results of the
models based on statistical significance of coefficients,
goodness-of-fit measures such as final log-likelihood,
log-likelihood ratio index (2
) and adjusted log-like-
lihood ratio index (2
), expected signs of the coeffi-
ents and relative magnitudes of the coefficients within
each model are compared. The implied value of time
(VOT), the trade-off between travel time and travel cost,
Table 2. Differences in LOS attributes.
Attribute Mean diff. Var. Minm. Maxm. Mean diff. /Mean nylos R2 of linear regn2
CD_time –5.35 41.79 –51.24 20.36 –0.151 0.937
CD_cost –5.83 47.64 –44.30 16.17 –0.144 0.979
PT_wktm –2.83 629.18 –240.98 129.73 –0.080 0.205
PT_invht –2.85 224.36 –121.42 87.16 –0.064 0.835
PT_wait 6.65 256.21 –62.50 165.00 0.392 0.515
PT_xfers 0.44 1.02 –3.03 4.00 0.641 0.432
PT_fare 11.68 781.32 –55.20 163.20 0.301 0.605
WK_dost –1.40 6.95 –31.64 13.85 –0.051 0.991
PT_fare_c 8.81 706.42 –55.20 163.20 0.227 0.611
CD_cost_c –1.84 12.86 –44.30 17.59 –0.046 0.993
2Striplos = a + b Nylos + u, where a, b, u, striplos, and nylos are intercept, coefficient, error term, the values of the respective attributes of striplos and
nylos respectively. This may not be theoretically meaningful relation. But the purpose was to have some indication of the extent of importance of
systematic and random components between the respective LOS attributes.
Copyright © 2011 SciRes. JTTS
was chosen as a measure of relative magnitude of coeffi-
ents within a model. Additionally, market shares of dif-
rent travel modes and aggregate direct and cross elastic-
ies under different policy scenarios are compared.
5. Results and Discussion
This section presents and discusses the results regarding
differences in LOS attributes, estimation results of mod-
s, aggregate elasticity and aggregate forecasting.
5.1. Differences in LOS Attributes
First, the actual differences and degree of correlation
between the corresponding LOS attributes of the two
data sets were examined. Table 2 summarizes statistics
on difference between striplos and nylos. As expected for
the base case, nylos gave, on average, higher values for
car time and car cost. After correction for road tolls, the
mean and standard deviation of the difference became
much smaller for car cost (CD_cost_c). The remaining
difference can mainly be attributed to differences in
driving distance caused by differences in coding of the
road network. But correction for public transport fare
(PT_fare_c) did not help much to reduce the difference.
The mean differences were smaller both in absolute
and relative terms with access/egress time (PT_wktm)
and invehicle time of public transport (PT_invht), but the
variance was much greater, especially for PT_wktm. The
striplos had, on average, higher values and the differ-
ences were relatively big for waiting time (PT_wait) and
number of transfers (PT_xfers) of public transport. This
probably reflects a mixture of coding and different as-
signment algorithms. The distance based function used to
estimate public transport fares for striplos obviously
overestimated the fares significantly and a relatively
large difference persisted even after the correction for the
fares pertaining to internal trips in Oslo.
The difference between the LOS attributes in the two
data sets is a mixture of systematic differences in the
mean values and a “random” component. The extent of
the random component varies between the attributes and
is reflected in the ratio between standard deviation and
mean value of the differences and in R2 (given in the last
column) if we run a linear regression between the re-
spective attributes in the two data sets. The random com-
ponent is the most important for PT_wktm, PT_wait and
PT_xfers based on the R2.
5.2. Estimation Results
Since the models were formulated and reformulated in a
number of ways during the model building process, a
substantial body of empirical results was generated.
However, this section analyzes the results of the final
models with the best specification based on iterative
process of model building.
Table 3 summarizes the estimation results of the ECL
models on both the data sets. The estimation results of
the ECL model yielded the parameters for the standard
deviations of the error components in addition to the co-
efficients of the variables included in the systematic util-
ity functions of the models. The variance of the error
components related to nonmotorized modes was esti-
mated by normalizing the variance of the error compo-
nents of motorized modes to one because we can only
identify the sum of the variances in this particular for-
mulation. Contrary to the hypothesis, σnmt was not statis-
tically significant in all the models, likely indicating that
there is no significant common unobserved factors and
heteroscedasticity across the alternatives.
The estimation results of the “base case” on striplos
looked reasonably good. All the coefficients were statis-
tically significant and had the expected signs according
to theory and the previous results except the number of
transfers of public transport (PT_xfers). PT_xfers was
significant, but had the wrong sign. It was also the case
in the estimation of the national model that used the
whole sample (Madslien, et al., 2005). As a result, the
number of transfers was not included in the final model.
But we included it in this study in order to compare the
effects of different corrections to LOS attributes. The
implied value of time (VOT) of car driver seemed low
(Table 4). Without any further improvement of the LOS-
data, this model might have been re-estimated without
PT transfers in the model if the purpose of the study is
not to estimate the VOTs and the transfer vari- able is not
needed in the analysis. We tried this and the results were
good enough based on signs, significance and relative
values of the coefficients, and goodness-of- fit measures.
In the second model on striplos, we used the corrected
PT fare for the trips within Oslo instead of the fare esti-
mated from travel distance. However, the distance based
fare was still used for other combinations of origin-des-
tination although the actual fare system was based on
‘fare zones’ and the number of fare zones tranversed. All
the coefficients, except PT_xfers, were significant with
expected signs and reasonable magnitudes. PT_xfers had
still the wrong sign but significant at lower confidence
level. The VOTs in this estimation came close to ‘official
values’ used in cost benefit analyses in Norway. Sur-
prisingly, the model gave a poorer fit as measured by the
value of the log-likelihood function at maximum.
In Model 3, introducing both corrected public trans-
port fares and road tolls resulted in a further drop of
odel fit! The VOTs slightly decreased compared to the m
Copyright © 2011 SciRes. JTTS
Table 3. Estimation results of ECL models with different specifications of network-based LOS attributes.
Striplos Nylos
Base case (1) Corrected PT fares (2) Corr. PT fares + toll (3)Corrn 3 + add. variable (4)
Variable Est. t-stat. Est. t-stat. Est. t-stat. Est. t-stat. Est. t-stat.
CK_00 –1.92 –8.83 –1.93 –9.03 –1.93 –9.01 –1.94 –9.02 –1.81 –7.94
CD_00 –2.61 –10.64 –2.56 –10.61 –2.55 –10.54 –2.54 –10.5 –2.54 –9.9
CP_00 –4.41 –14.58 –4.38 –14.76 –4.43 –14.83 –4.44 –14.85 –4.42 –13.64
PT_00 –0.756 –2.74 –0.931 –3.43 –1.03 –3.79 –1.05 –3.86 –0.872 –3.08
WK_dist –0.59 –13.45 –0.602 –14.34 –0.601 –14.25 –0.602 –14.27 –0.525 –12.02
CK_dist –0.186 –12.1 –0.194 –13.52 –0.194 –13.35 –0.194 –13.35 –0.178 –11.55
CD_time –0.031 –4.78 –0.044 –7.01 –0.0394 –6.25 –0.039 –6.09 –0.032 –5.65
GA_cost –0.045 –17.92 –0.044 –16.79 –0.0416 –16.82 –0.042 –16.82 –0.03 –10.02
PT_wktm –0.022 –4.99 –0.026 –5.71 –0.0261 –5.77 –0.026 –5.73 –0.027 –7.24
PT_invht –0.015 –3.33 –0.02 –4.42 –0.0208 –4.57 –0.021 –4.59 –0.015 –4.48
PT_wait –0.036 –7.32 –0.03 –6.35 –0.0264 –5.65 –0.026 –5.48 –0.032 –4.76
PT_xfers 0.417 6.11 0.147 2.51 0.113 1.96 0.112 1.93 –0.269 –3.54
CP_female 0.965 4.08 0.984 4.17 0.99 4.19 0.993 4.2 1.03 4.41
CD_pakgod 1.95 12.11 1.96 12.33 1.94 12.14 1.93 12.11 2.00 12.82
CD_pakfair 1.21 6.26 1.26 6.61 1.23 6.43 1.22 6.39 1.21 6.56
CK_winter –1.59 –7.06 –1.58 –7.1 –1.59 –7.1 –1.59 –7.1 –1.59 –7.05
CD_soj 0.558 4.61 0.554 4.66 0.564 4.75 0.576 4.82 0.569 4.94
CD_dbfem –1.09 –7.73 –1.1 –7.98 –1.1 –7.98 –1.1 –7.99 –1.17 –8.56
CP_time –0.054 –7.27 –0.066 –8.78 –0.0618 –8.28 –0.062 –8.24 –0.046 –7.32
CD_timf 0.0104 2.2 0.0107 2.26 0.011 2.33 0.0113 2.39 0.0131 3.44
PT_female 0.416 2.44 0.438 2.63 0.446 2.68 0.449 2.69 0.482 2.88
CD_tmrush - - - - - - –0.003 –0.9 - -
σnmt –0.388 –0.81 –0.221 –0.42 –0.236 –0.44 –0.235 –0.44 0.475 0.94
Summary Statistics
Number of observations 2,876 2,876 2,876 2,876 2,876
LL with zeros only –3888.29 –3888.29 –3888.29 –3888.29 –3888.29
LL at convergence –1904.15 –1936.06 –1939.65 –1939.24 –2050.82
51.0% 50.0% 50.0% 50.0% 46.6%
50.4% 49.6% 49.5% 49.5% 46.0%
previous estimation, PT_xfers had still the wrong sign,
but the t-value dropped to 1.96. Based on a prior expec-
tation about the weights of different travel time compo-
nents, it also seemed that the ratio of PT_walktm and
PT_waittm to PT_invhtm were on the low side. Ratio in
the range <1.5 - 2> is usually considered to be acceptable
for these coefficients.
In Model 4, an attempt was made to compensate for
low travel times during peaks by interacting car travel
time and a dummy variable (CD_tmrush) for traveling in
peak hours, it added statistically nothing to the model.
But the coefficient of the variable had the expected sign.
All the coefficients except PT_xfers were statistically
significant with expected signs and reasonable relative
magnitudes as earlier. PT_xfers was still positive with
further drop of the t-value to 1.94. VOTs also remained
more or less same as in model 3. Informal goodness of fit
measures such as 2
and 2
were almost the same
with all the models estimated on striplos.
As we see (Table 4 ), the VOTs changed due to a small
change in the specification of model and/or data.
We cannot use a log-likelihood ratio test (LRT) to
compare the models estimated on different versions of
striplos because the data are not identical. But we can use
an LRT to select between Model 3 and Model 4. Model 3
was chosen based on the log-likelihood ratio test. If
transfer variable is not needed for analysis, we can just
exclude this variable from estimation and estimate the
Model 3 without transfer. We can also estimate Model 4
without transfer but with CD_tmrush. In this case, the
Table 4. Implied values of time (NOK/hour (km).
striplos nylos
Categories of time 1 2 3 4
Car driving male 41.33 60.82 56.83 56.10 63.16
Car driving female 27.47 46.16 40.96 39.7637.30
Car passenger 72.00 90.82 89.13 89.0690.00
PT_access/egress time 29.33 35.48 37.64 37.59 53.49
PT_invktm 20.00 27.67 30.00 30.2230.00
PT_waitm 48.00 41.37 38.08 37.30 62.57
PT_xfers (NOK/xfers) –9.27 –3.36 –2.72 –2.708.85
WK_dist 13.11 13.74 14.45 14.5117.27
CK_dist 4.13 4.43 4.66 4.67 5.86
LRT is applicable.
The wrong sign of PT_xfers might be attributed to se-
rious coding errors of this variable with striplos. This
may imply that it is very difficult to correct for such
types coding errors. We can simply estimate the model
excluding PT_xfers if this variable is not a variable of
particular interest in the analysis. It is possible to correct
for “known errors” such as coding of road tolls on the
toll cordon.
All the coefficients including PT_xfers were signifi-
cant with correct signs and reasonable relative magni-
tudes when the same model was estimated on nylos. The
VOTs of different aspects of time were also reasonably
accurate. The implicit weights on walking and waiting
time of public transport also had the expected magnitude.
The transit assignment algorithm of the network model
used to produce LOS-data for public transport in nylos
has a slight tendency to overestimate in-vehicle time and
to underestimate waiting time. This is probably also re-
flected in the estimated parameters of PT_invht and
PT_waitm, biasing the coefficients of PT_invht down-
ward and PT_waitm upward (in absolute values). On the
other hand, the assignment algorithm used to derive the
LOS attributes for public transport in striplos tends to
underestimate PT_invhtm and overestimate PT_waitm
when multiple paths are used. This might also have been
reflected in the parameter estimates. In addition, it is
suspected that more routes were un-coded with striplos.
With nylos, some local routes in periphery of the
Oslo-region were un-coded. Surprisingly, the model es-
timated on nylos resulted in lower goodness of fit meas-
ures such as 2
and 2
compared to that of the mod-
els estimated on striplos despite nylos presumably being
relatively more accurate than striplos. In terms of model
fit and statistical significance, models estimated on
striplos looked better than the model with nylos.
The results are generally plausible, but with a rather
variable pattern of significance of variables across the
different levels of accuracy of LOS attributes. The t-
statistics of the estimated parameters do not show any
general tendency. The t-statistics of some coefficients
increase and some decrease when with different versions
of striplos and change from striplos to nylos. Similarly,
the relative magnitudes of the coefficients, as evident by
the VOTs, do not remain the same. The most notable
improvements with nylos were the correct sign of PT_
xfers and consistency of the relative magnitudes of coef-
ficients with prior expectations.
We had hypothesized that there were some common
unobserved factors and heteroscedasticity across some
alternatives in the choice set. However, it depends on the
choice set, data used in the estimation of the models, and
the specification of systematic utility functions. If the
systematic utility function is adequately specified that
include major factors influencing the choice, there might
not be room for the error components. This might be case
with our models. The goodness of fit measures such as
likelihood ratio index and adjusted likelihood ratio index
are reasonably high with our models. This might be one
of the reasons of the error components being insignifi-
cant. Additionally, this is actually a matter of empirical
question whether the error components are significant or
not. Moreover, it is reasonable that the error component
of each model was not significant because the choice set
and the specification of systematic utility function was
identical and the data used in estimation were marginally
different across the different models. Further, we also
explored the various possible specifications of the ECL
models and we reported the results of the best identified
5.3. Aggregate Forecasting
Table 5 summarizes the predicted market shares on the
same data set that was used in model estimation by
modes under different scenarios, viz., increasing car
driving cost by 10% (scenario 1), increasing PT fare by
10% (scenario 2) and reducing PT wait time by 10%
(scenario 3).
As we see in Table 5, the predicted market shares
were almost identical in each scenario in each model
irrespective of the specification of network LOS attrib-
utes in the model. Each model predicted as intended ac-
cording to theory. Each model predicted that an increase
in car driving cost and PT fare and a reduction of PT
waiting time did not have any impact on the market
shares of CK and WK. The prediction of market shares is
consistent with previous studies, theory, and expectation.
Model 3 estimated on striplos gave a better fit than the
model estimated on nylos. We re-estimated the model
without transfers as would be natural in estimation if a
model that gives a wrong sign for a coefficient. Table 6
Copyright © 2011 SciRes. JTTS
Table 5. Predicted market shares by modes in different sce-
Travel modes WKCK CD CP PT
Actual market shares 8.26.3 51.6 4.9 29.0
Predicted market shares
Model 1_S 8.36.5 49.8 5.3 30.1
Model 2_S 8.26.5 49.9 5.3 30.1
Scenario 1 Model 3_S 8.26.5 49.7 5.3 30.2
Model 4_S 8.26.5 49.7 5.3 30.2
Nylos 8.26.4 49.9 5.1 30.3
Model 1_S 8.36.6 52.9 5.2 27.0
Model 2_S 8.36.5 52.8 5.2 27.3
Scenario 2 Model 3_S 8.36.5 52.7 5.1 27.3
Model 4_S 8.36.5 52.7 5.1 27.3
Nylos 8.36.5 52.6 5.1 27.5
Model 1_S 8.26.3 51.1 4.8 29.7
Model 2_S 8.26.3 51.1 4.8 29.6
Scenario 3 Model 3_S 8.26.3 51.2 4.8 29.6
Model 4_S 8.26.3 51.2 4.8 29.5
Nylos 8.26.3 51.1 4.8 29.6
Table 6. Implied demand elasticities—simulated on sample.
Direct Cross
Striplos 3 without xfers –0.32 0.46
Scenario 1
Nylos –0.31 0.48
Striplos 3 without xfers –0.60 0.22 Scenario 2
Nylos –0.54 0.20
Striplos 3 without xfers –0.17 0.06
Scenario 3 Nylos –0.19 0.08
presents implied direct and cross- elasticities respectively
with the models estimated on both nylos and striplos.
Both the models yielded direct and cross elasticities as
expected according to theory, i.e., negative direct elastic-
ity and positive cross elasticity for the attributes consid-
ered. Both the direct and cross elasticities are inelastic
and just the opposite in scenario 2. The cross elasticities
of CD cost were significantly higher than the own elas-
ticities with scenario 1. The implied demand elasticities
were almost similar in each scenario. The main differ-
ence was a moderately lower both direct and cross elas-
ticities of PT waiting time of the model estimated on
striplos. The models should thus give the similar conclu-
sions for policy purposes.
6. Summary and Conclusions
The need for travel demand models is growing world-
wide. Obtaining reasonably accurate LOS attributes of
transportation system for different travel modes, the ma-
jor factors shaping the travel demand, is not a trivial task.
The objective of the paper was therefore to investigate
the effects of using LOS attributes measured at different
levels of accuracy on the results of disaggregate travel
mode choice models. The case study in this paper is an
example of what might happen practically when we cor-
rect for ‘known errors’ in the data set or switch to the
data set with better quality. The sensitivity of model re-
sults including goodness of fit measures, VOTs and ag-
gregate forecasting were compared by estimating ECL
models for travel mode choice on the two data sets of
LOS attributes. The difference between the LOS attrib-
utes in the two data sets was a mixture of systematic dif-
ferences in the mean values and a random component.
The extent of the random component varied between the
Striplos yielded generally better fit and reasonably
satisfactory models statistically. But number of transfers
had wrong sign and VOTs were generally low without
any correction. The correction helped to get VOTs of
reasonable magnitudes. Model estimated on nylos on the
other hand had all the significant coefficients with cor-
rect sings including number of transfers, the reasonable
relative magnitude of coefficients of public transport
travel components and reasonably plausible VOT esti-
mates except slightly less model fit compared to the
model on striplos. Models estimated on both striplos and
nylos gave almost similar aggregate forecasting and ag-
gregate elasticities on the same data set used in estima-
tion. During the model building process, it was also ob-
served that the VOTs changed significantly due to a
small change in the specification of model and data im-
plying that utmost care must be taken for specification of
data and model if the purpose of the study is to estimate
The lack of peak hour driving time in striplos appeared
less important for parameter estimates than it was ini-
tially expected. This may not hold true in general since
having a model that accounts for congestion correctly
ought to give better results in an urban setting.
All the models predicted well implying that specifica-
tion of LOS attributes matters less for prediction as long
as the predictions are done with the same data. The re-
quirement of data accuracy depends on the purpose of
developing a model since the model with relatively in-
accurate data also predicts reasonably well. Measuring
data as accurately as possible is presumably more im-
portant if the purpose of the study is to estimate VOTs.
7. Acknowledgements
I am thankful to Odd I. Larsen, John K. Dagsvik and
Copyright © 2011 SciRes. JTTS
anonymous reviewers for their help and compliments on
earlier draft of this work. The author is fully responsible
for any errors and omissions.
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