Discussion Papers In Economics
And Business

A Comparison between Latent Class Model and
Mixed Logit Model for Transport Mode Choice:
Evidences from Two Datasets of Japan

Junyi Shen, Yusuke Sakata, and Yoshizo Hashimoto

Discussion Paper 06-05

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Comparison between Latent Class Model and
Mixed Logit Model for Transport Mode Choice:
Evidences from Two Datasets of Japan

Junyi Shen, Yusuke Sakata, and Yoshizo Hashimoto

Discussion Paper 06-05
January 2006

この研究は「2004－2006 年度科学研究費補助金(課題番号16203020)」より援助を受けた、記して感謝する。

Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, JAPANA Comparison between Latent Class Model and
Mixed Logit Model for Transport Mode Choice:
Evidences from Two Datasets of Japan

Junyi Shen a,#, Yusuke Sakata b, and Yoshizo Hashimoto a
Osaka School of International Public Policy, Osaka Universitya

1-3 Machikaneyama, Toyonaka City, Osaka 560-0043, Japan
School of Economics, Kinki Universityb

3-4-1 Kowakae, Higashi-Osaka City, 577-8502, Japan
January 2006

Abstract
This paper applies two recent stated choice survey datasets of Japan to investigate
the difference between the latent class model (LCM) and the mixed logit model (MLM)
for transport mode choice. A detailed comparison is carried out, focusing on comparing
values of time savings, direct choice elasticities, predicted choice probabilities andprediction success indices. Furthermore, a test on non-nested model is also utilized tohelp determine which model is superior to another one. The results suggest that the
LCM performs better than the MLM in both datasets.

Keywords: latent class model (LCM), mixed logit model (MLM), transport mode choice,predicted choice probability, prediction success index

JEL classification: C35, D12, R41# Corresponding author. Tel/Fax: +81-6-68505652
E-mail address: junyi@osipp.osaka-u.ac.jp

11. Introduction
In the recent thirty years, analysts have made a great endeavor on developing
different discrete choice models to relax the assumption of independence from irrelevantalternatives (IIA) in the fundamental multinomial logit model (MNL). Among thesemodels, the mixed logit model (MLM) is probably the most flexible one (see, for instance,
Revelt and Train, 1998; McFadden and Train, 2000; Bhat, 2003; Greene and Hensher,
2003; Bhat and Gossen, 2004, etc.). It generalizes a standard MNL by allowing its
parameter associated with observed variable to vary with a known population
distribution across individuals. Alternatively, the latent class model (LCM), which isfrequently applied in marketing research, assumes that a discrete number of latentclasses are sufficient to account for preference heterogeneity. Comparing with the mixed
logit model specification, the LCM has the advantage of being relatively simple,
reasonably plausible, and statistically testable. However, it is somewhat less flexible
than the MLM since the parameters associated with each variable in each class are
fixed. In contrast, the main disadvantage of the MLM is that the assumption made on
the distributions of parameters should be specified by the analysts. Due to that eachmodel has its virtues and limitations, it is meaningful to compare between these twoadvanced discrete choice models.
A recent study by Greene and Hensher (2003) compared the LCM with the MLM byusing a dataset of road type’s choice by car in New Zealand. After a detailed comparison
on value of travel time savings, direct share elasticities, choice sensitivities to 50%
increase in travel time, and choice probabilities, they concluded that although both themixed logit and latent class models offer attractive specifications than the multinomial
logit, it is inconclusive that which one is ‘completely’ superior to another despite somestronger statistical evidences support for the latent class model in their dataset. 1
Remained as a future study implication, they mentioned that “we encourage a greater
effort to compare and contrast such advanced models as one approach to searching forrules on stability in explanation and prediction” (Greene and Hensher 2003).
Strongly encouraged by their study, we will use two stated preference datasets oftransport modal choice (monorail, car and bus) in Japan to make a comparison between
the MLM and the LCM. Thus, the prime purpose of this paper is to seek for whether or
not the results of the comparison suggest that the latent class model is to some extent
superior to the mixed logit model as Greene and Hensher (2003) mentioned in theirstudy.
The inconclusiveness is due to the reason that these two models are non-nested,
therefore, normal Likelihood Ratio (LR) test can not be applied.

1

2

The rest of the paper is organized as follows. Section 2 provides a brief introduction
on the latent class and the mixed logit models. Section 3 compactly describes our two
stated preference datasets in Japan. Section 4 presents a comparison between these twomodels, and Section 5 draws conclusions of the paper.

2. The latent class and mixed logit models2
2.1 The latent class model
The latent class model, unlike the MLM which specifies the random parameters tofollow a continuous joint distribution, assumes that a discrete number of classes are
sufficient to account for preference heterogeneity across classes. Therefore, theunobserved heterogeneity is captured by these latent classes in the population, each ofwhich is associated with a different parameter vector in the corresponding utility. The
LCM has often been used in marketing research instead of ML model, while there arefew studies in other fields such as transportation.
The choice probability that individual q of class s chooses alternative i from aparticular set J, which is comprised of j alternatives, is expressed as:
J

Piq|s = exp(β s′ X iq ) / ∑ exp(β s′ X jq )s = 1,..., S

(1)

j =1

where β s′ is the parameter vector associated with the vector of explanatory variables

Xiq. Note that Eq. (1) is a simple MNL specification in class s .
Additionally, one can construct a classification model as a function of someindividual-specific attributes to explain the heterogeneity across classes. The LCM
model simultaneously estimates Eq. (1) for S

classes and predicts the probability Hqs

as individual q being in class s . Then, the unconditional probability of choosing
alternative i is given as:
S

Piq = ∑ Piq|s H qs

(2)

s =1

An issue to be noted is the choice of S, the number of classes. Since this is not aparameter, hypotheses on S cannot be tested directly. However, as Louviere et al. (2000,
chap. 10) mentioned that a number of methods to decide S have been used based on the
Akaike Information Criterion (AIC) and its variants. AIC and Consistent AIC (CAIC),
which are given in Eqs. (3) and (4), are used to guide model selection.
2 Since Greene and Hensher (2003) have provided a detail description on the latent classmodel and the mixed logit model, therefore, we just give a brief introduction on these
two models. For the other literature on the MLM and LCM, see Revelt and Train (1998),
Louviere et al. (2000), McFadden and Train (2000), Bhat and Gossen (2004), etc.
3

AIC = −2( LL( βˆ ) − S ⋅ K s − ( S − 1) K c )(3)

CAIC = −2 LL( βˆ ) − ( S ⋅ K s + ( S − 1) K c − 1)(ln(2 N ) + 1)

(4)

where LL (θˆ) is the log likelihood at the estimated parameters βˆ , Ks is the number of
elements in the utility function of the class-specific choice models, Kc is the total numberof parameters in the classification model, and N is the number of observations in thesample. The value of S that minimizes each of the measures of AIC and CAIC suggests
which model should be preferred (Louviere et al. 2000, chap. 10).
2.2 The mixed logit model
The mixed logit model allows for a heightened level of flexibility by specifying taste
coefficients to be randomly distributed across individuals. Additionally, superior to LCM,
MLM can account for potential correlation over repeated choices made by eachindividual by imposing a first-order autoregressive (AR1) process3.
The model is a generalization of the MNL model, summarized as below:
J

Piqt = exp(α ′ + β ′X iqt + ϕ ′Fiqt ) / ∑ exp(α ′ + β ′X jqt +ϕ ′F jqt )

(5)

j =1

where

α′

is a vector of fixed or random alternative-specific constants (ASCs) associatedwith i = 1,..., J alternatives and q = 1,..., Q individuals, and one of these ASCs
should be identified as 0.

β′
ϕ′is a vector of non-random parameters.

Xiqt

is a vector of individual-specific characteristics and alternative-specific attributes

is a parameter vector that is randomly distributed across individuals.

at observation t, and is estimated with random parameters.

Fiqt

is a vector of individual-specific characteristics and alternative-specific attributes
at observation t, and is estimated with fixed parameters.
In this specification, a subset or all of α ′ and the parameters in the β ′ vector

can be assumed to be randomly distributed across individuals 4 . These randomparameters can then be defined as a function of characteristics of individuals and/or
other attributes that are choice invariant. Based on these defined attributes, the mean
3 Greene and Hensher (2003) mentioned that the latent class model does not readilyextend to autocorrelation, therefore, this aspect is left for future research.
4 The distributions of random parameters can be considered, for example, normal
distribution, lognormal distribution, and triangular distribution, etc.
4and standard deviations of specified random parameters and contributions from thesechoice invariant attributes to random parameters are estimated by using Maximum
Simulated Likelihood (MSL) method. The MLM is sufficiently flexible that it provides
the modeler a tremendous range to specify individual unobserved heterogeneity. To
some extent, this flexibility offsets the specificity of the distributional assumptions(Greene and Hensher 2003).

3. Data
We use two survey datasets, which are recently collected in Osaka of Japan, tocompare the LCM with the MLM. The first survey is based on a stated choice
experiment carried out in July 2005 on transport mode choices by the residents in the
Saito and Onohara Area of Northern Osaka (hereinafter, called Saito survey). A prime
purpose of this experiment is to investigate whether or not individual environmental
consciousness is one of the determinants in transport modal choice. The transportmodes in the choice set faced by each respondent consist of monorail, car and bus. Thisdataset is composed of 467 individuals with each answering 8 choice sets, therefore, thetotal observations are 3736 (i.e. 467∗8 observations). Five attributes are used in thestated choice experiment as follows.
A. In-vehicle time including delay time caused by traffic jam (in minutes)
B. Access time (in minutes)
C. Frequency (in minutes)
D. Travel cost (in JP yen)
E. Negative impact on the environment caused by transport modes
For each attribute, we adopted a 2-level design expect for access time and frequency
in car and negative impact on the environment in monorail. Then, 32 choice sets wereconstructed by a fractional factorial design to reduce the number of choice sets to a
manageable level. These 32 choice sets were further blocked into 4 versions avoiding adominant selection. Each sampled individual was asked to answer one version. An
example of the choice sets is provided in Table 1. Further details on the survey are given
in Shen et al. (2005).
The second dataset is based on another stated choice survey on transport mode
choice of the residents in Eastern Osaka (hereinafter, called Eastern Osaka survey),which was also carried out in July 2005. Different from the first one, this survey focused5Table 1
An example of choice set in Saito survey
Monorail

Car

Bus

15

40

50

15
10

almost 0
at any time

3
15

360

800

280

Negative impact on the environment(such as CO2 emission)Low

3 times asmonorail

2.5 times asmonorail

Please choose one most preferable
transport mode and ✔ in □

□

□

□

In-vehicle time including delay timecaused by traffic jam (minutes)
Access time (minutes)
Frequency (minutes)
Generalized cost (JP yen)

Table 2
An example of choice set in Eastern Osaka survey

Average in-vehicle time for 1 section(minutes)
Average delay time due to congestion(minutes)
Average cost (JP yen)Frequency (numbers/hour)
Local natural environment
Network accessibility
Please choose one most preferable
transport mode and ✔ in □Monorail

Car

Bus

3

4

10

0

8

10

100
4
Worse thancurrent state
Only monorail200
at any time
Worse thancurrent state
Only monorail60
10Worse thancurrent state
Only monorail

□

□

□

on both impacts of local natural environment and network accessibility on transport
modal choice. Same experimental design strategy as that in Saito survey was used,
except that the local natural environment and network accessibility were treated as acommon condition in each choice set, i.e. they were allowed to vary across choice sets
but not across alternatives. A total of 453 valid responses, each with 8 choice sets,

6

produce 3624 observations (i.e. 453∗8 observations). Table 2 shows an example of the
choice sets, and Sakata et al. (2005) provides further details on this survey.

4. A comparison between LCM and MLM
Tables 3 and 4 summarize the estimated results of the two datasets with thespecifications of MNL, MLM and LCM5. We have specified a number of individual
socio-economic characteristics and added them into the estimated model. However, tosave space, we omit these results in the tables.
With respect to the mixed logit model, we have defined all time-associatedattributes as random parameters and selected a Normal distribution for them.
Specifying a given parameter to follow a Normal distribution is equivalent to making apriori assumption that both positive and negative values for this parameter may exist
in the population. Concerning the possible positive signs of time-associated parameters,
Hess et al. (2005) have noted that “a negative measure for VTTS [value of travel timesavings] for a given individual in effect suggests that this individual would be willing to
pay for increases in travel-time. At first sight, this is counter-intuitive. However, several
recent papers discuss zero (Richardson, 2003) or positive (Redmond and Mokhtarian,2001) elasticity with respect to travel-time. There are interesting statements like: ‘I’drather have an hour-plus commute than a five-minute commute. In the morning, it
gives me a chance to work through what I’m going to do for the day. And it’s my
decompression time.’(Sipress, 1999, cited by Redmond and Mokhtarian, 2001)”. This
citation indicates that if an individual is more satisfied with longer time-associatedattributes due to some individual-specific reasons, the positive sign of time-associatedattributes could be possible.6
Akaike Information Criterion (AIC) and Consistent AIC (CAIC) given in Eqs. (3)and (4) were used to select the number of classes in the latent class model. As a result,both AIC and CAIC were the lowest ones in three latent classes for both datasets.
Therefore, three-class LCMs were estimated for both Saito and Eastern Osaka surveys.
From the results in Tables 3 and 4, based on the log likelihood values, the hypothesisthat the MNL model is in favor of either the MLM or the LCM can be safely rejected.
With respect to the comparison between MLM and LCM, we focus on contrasting
5 All the results were estimated by NLOGIT 3.0 (Econometric Software, Inc., 2003).
6 We have also estimated the MLM with a specification of triangular distribution on

time-associated parameters. However, we did not find large differences between normal
distribution and triangular distribution specifications on the estimated parameters,
value of time savings, and choice elasticities, etc.
7

Table 3
Estimated results for Saito survey (t statistics in parentheses)
Attribute

Alternative

In-vehicle time
Access time
Frequency
Travel cost
Negative environmental

All
All
All
All
All

impactMonorail constant

MLM

LCM
Class 1

Class 2

Class 3-0.0758-0.1668-0.0653-0.1160-0.0858(-25.45)(-17.12)(-4.05)(-36.34)(-11.47)-0.0265-0.0575-0.0270-0.0642-0.0088(-2.08)(-2.59)(-3.78)(-3.48)(-2.94)-0.0155-0.0247-0.0228-0.0232-0.0097(-3.57)(-3.21)(-2.04)(-4.63)(-2.82)-0.0027-0.0049-0.0019-0.0056-0.0014(-9.87)(-10.13)(-3.30)(-15.42)(-3.50)-0.7066-0.5100-3.1898

0.3882-3.1662(-2.78)(-3.06)(-2.52)(1.273)(5-5.97)-0.7612-1.7252

19.3000-2.0457

0.9842(-3.19)(-3.22)(0.02)(-7.90)(1.71)-1.3935-3.4679

0.4838-18.5697

4.1862(-4.41)(-4.92)(0.00)(-0.02)(5.48)

Latent Class

0.14175

0.585200.27305

probability(7.15)(20.30)(10.781)

Car constantIn-vehicle time

Monorail

MNL

Car
All

0.1039standard derivation
Access time

(11.17)All

0.2109standard derivation
Frequency(14.79)All

0.0848standard derivation

Log-likelihood
Pseudo- R

2(12.12)-2853.062-2320.686-1954.913

0.1844

0.3366

0.4460indicators of willingness to pay, e.g. values of time savings, choice elasticities, predictedchoice probabilities of each transport mode, and prediction success index, respectively.
In addition, a test on non-nested choice models which is based on the AIC proposed by
Ben-Akiva and Swait (1986) is applied to help determine which model is relatively more
superior in the two datasets applied in this study.
Tables 5 and 6 summarize the estimated values of time savings (VOTS). For bothdatasets, the mean estimates of VOTS by the MLM specification differ substantiallywith the three latent classes for LCM, although in Saito survey, VOTS of in-vehicle time
is similar to that in class 1 and VOTS of access time is similar to that in class 2. Overall,

8

Table 4
Estimated results for Eastern Osaka survey (t statistics in parentheses)
Attribute

Alternative

In-vehicle time
Delay time
Frequency
Travel cost
Monorail constant
Bus constant
Local natural

All
All
All
All
MonorailBus
Monorailenvironment
Network accessibility
Local natural

Monorail
Bus

MNL

MLM

LCM
Class 1

Class 2

Class 3-0.1251-0.2669-0.1365-0.2825-0.1915(-8.65)(-10.23)(-5.51)(-8.62)(-3.55)-0.0606-0.1338-0.0672-0.1522-0.0501(-8.10)(-8.94)(-5.10)(-10.36)(-2.10)-0.0328-0.1101-0.0710-0.0913-0.0377(-3.18)(-8.67)(-3.97)(-5.94)(-2.21)-0.0050-0.0083-0.0157-0.0062-0.0022(-13.29)(-15.52)(-13.19)(-10.70)(-2.55)1.35642.0211

1.06472.1905-0.1073(7.25)(7.04)(2.42)(6.64)(-0.18)0.39300.98440.64290.3326-1.3832(1.95)(3.43)(1.43)(0.77)(-1.54)0.41500.4396-0.9100

0.98951.3309(1.85)(2.19)(-1.55)(2.74)(2.24)

0.77050.99240.72491.28601.5493(3.33)(2.60)(1.16)(3.66)(2.44)

0.23960.1647-0.9972-0.1079-5.9485(0.87)(0.42)(-1.70)(-0.14)(-1.61)0.79901.06380.8712-0.1265

5.8119(2.91)(2.60)(1.40)(-0.16)(4.48)

Latent Class

0.35625

0.52661

0.11714

probability(12.60)(18.02)(6.43)

environment
Network accessibility
In-vehicle time

Bus
All

0.2799standard derivation
Delay time

(12.16)All

0.1620standard derivation
Frequency(9.95)
All

0.1993standard derivation

Log-likelihood
Pseudo- R

2(14.37)-2791.523-2390.553-1714.392

0.08920.22000.4406

the results from the latent class model indicate the fact that for either in-vehicle time,
access time and frequency in Saito survey or in-vehicle time, delay time and frequency
in Eastern Osaka survey, three segments of low, medium and high VOTS can be found.
This evidence supports the claim in Greene and Hensher’s (2003) study that the latent9

Table 5
Values of time savings for Saito survey (JP yen per hour)
MNLTime type

MLM

LCM

(mean)Class 1

Class 2

Class 3In-vehicle time

1684

2042

2062

1243

3677

Access time

589

704

853

688

377

Frequency

344

302

720

249

416

Table 6
Values of time savings for Eastern Osaka survey (JP yen per hour)Time type

MNL

MLM

LCM

(mean)Class 1

Class 2

Class 3In-vehicle time

1501

1929

522

2734

5223

Delay time

727

967

257

1473

1366

Frequency

394

795

271

884

1028

influences are to some extent related to an individual’s VOTS.
Summaries of the probability weighted choice elasticities for common attributes(in-vehicle time and travel cost) in two surveys are provided in Tables 7 and 8. The
choice elasticities differ substantially between the MLM and the LCM, especially in
Eastern Osaka survey. For response to changes in in-vehicle time, the LCM suggests
less sensitivity for monorail and car but more sensitivity for bus than the MLM in bothdatasets, whilst the magnitude of sensitivity is relatively larger in Saito survey. With
respect to changes in travel cost, the MLM predicts less sensitive response for almost all
the modes than the LCM in both datasets with the exception of car in Eastern Osaka
survey.
A comparison of predicted choice probability between the LCM and the MLM for
two surveys starts from the kernel density estimators of their ratios for each mode thatare listed in Figures 1 and 2. From these figures, we may find that for both datasets, thedistribution around 1 is skewed to the right for monorail and to the left for car and bus.

10

Table 7
Direct choice elasticities for Saito survey (probability weighted)
MNL

MLM

LCM

Monorail-0.510-0.586-0.446Car-1.304-1.367-1.361Bus-1.418-1.343-1.374

Monorail-0.397-0.400-0.423Car-0.955-1.001-1.056Bus-0.375-0.398-0.455Time typeIn-vehicle time

Travel cost

Table 8
Direct choice elasticities for Eastern Osaka survey (probability weighted)
MNL

MLM

LCM

Monorail-0.181-0.237-0.179Car-0.276-0.398-0.306

Bus-0.676-0.666-0.776

Monorail-0.243-0.263-0.313Car-0.993-0.988-0.869Bus-0.331-0.419-0.785Time typeIn-vehicle time

Travel costThis evidence indicates that at the individual level, the choice probability of monorailpredicted by the LCM is relatively larger than that predicted by the MLM, whilst the
choice probabilities of car and bus are relatively smaller than those predicted by the
MLM. It is consistent to the result at the aggregate choice probability level for the
sampled population. The respective aggregate probabilities for monorail, car and bus
are in Saito survey LCM: 0.6784, 0.1881, 0.1335 and MLM: 0.6586, 0.1889, 0.1525, and11

Figure 1
Kernel density estimate for probability ratio of LCM to MLM in Saito survey

density0.51(i) Monorail

0

1

2

3
p_ratio

4

5

6

0

.2

.4

density.6.81(ii) Bus

0

1

2

3
p_ratio

4

5

6

4

5

6

0

.5

density11.5(iii) Car

0

1

2

3
p_ratio12

Figure 2
Kernel density estimate for probability ratio of LCM to MLM in Eastern Osaka survey

1

0

.5

density

1.52(i) Monorail0

12
p_ratio

3

4

0

.5

density11.52(ii) Bus

0

1

2

3

4

5

3

4

5

p_ratio

0.5density11.5(iii) Car0

12
p_ratio13

Table 9
OLS regressions of predicted probability estimated by the LCM and MLM
Saito survey

Eastern Osaka survey

Monorail

Car

Bus

Monorail

Car

Bus

Constant-0.03118-0.01796-0.0473-0.1205-0.03407-0.04991

P_MLM

1.132968

1.012928

1.07295

1.253378

1.175096

1.046462

0.395

0.448

0.456

0.384

0.340

0.277

R

2

Note: Dependant variable is P_LCM. All the parameters are significant at 99.9% level.

Table 10Prediction success indices for Saito and Eastern Osaka surveys
MNL

MLM

LCM

Saito survey

0.10490.14400.3259Eastern Osaka survey

0.04350.06220.2218in Eastern Osaka survey LCM: 0.5759, 0.1216, 0.3025 and MLM: 0.5369, 0.1456,
0.3175.
OLS regressions are further applied to investigate the relationship between the
LCM probability and the MLM probability. The results of OLS regressions are provided
in Table 9. From the relatively low R

2

for OLS regression, we may conclude that therelationship between the predicted choice probabilities under the LCM (for three latentclasses) and the MLM (a normal distribution on the random parameters) is relatively
weak at the individual level.
The prediction success indices suggested by McFadden (1979) are calculated andsummarized in Table 10. From these indices, we found that in both datasets the LCM
has more predictive capability than the MLM.
Finally, we apply a test on non-nested choice models which is based on the AIC
proposed by Ben-Akiva and Swait (1986).The test is carried out as follows. Suppose
there are two non-nested models 1 and 2. Model 1 explains choices using K1 variables,
while model 2 explains the same choices using K2 variables. Assume that K1 ≥ K2 and14either the two models have different functional forms or the two sets of variables aredifferent by at least one element. Define the fitness measure for model j, j=1, 2:ρ 2j = 1 −Lj − K j
L(0)(6)

where Lj is the log likelihood at convergence for model j and L(0) is the log likelihood forconstants only. Ben-Akiva and Swait (1986) show that under the null hypothesis thatmodel 2 is the true model, the probability that the fitness measure in Eq. (6) for model 1
will be greater than that of model 2 is asymptotically bounded by a function given in Eq.
(7):

Pr(| ρ 22 − ρ12 |≥ Z ) ≤ Φ(− − 2ZL(0) + ( K1 − K 2 ))(7)

where Z is the difference of the fitness measures between model 1 and model 2 andassumed larger than zero, Φ is the standard normal Cumulative Distribution
Function (CDF). Therefore, Eq. (7) sets an upper bound for the probability that one
incorrectly selects model 1 as the true model although model 2 is the true model.
Using the above definition, we calculate that the probabilities in Eq. (7) for Saito
survey and Eastern Osaka survey are P ≤ Φ ( −27.039) ≈ 0 and P ≤ Φ ( −36.773) ≈ 0
respectively, assuming that the MLM is model 1 and the LCM is model 2. Therefore, we
may conclude that in both datasets to which we applied the test, the LCM is superior to
the MLM.

5. Conclusions
This paper provides a detail comparison between two advanced specifications of
discrete choice model, i.e. a latent class model and a mixed logit model. Following thestudy of Greene and Hensher (2003), the paper compares the values of time savings,
direct choice elasticities, and predicted choice probability derived from these two models.
In addition, the prediction success indices and a non-nested model test are further
applied to investigate the difference between these two models, while these results
indicate that the LCM performs statistically better than the MLM in our two datasets.
Although our results are consistent with that one concluded from Greene andHensher (2003), which claims that the latent class model is supported by stronger
statistical behaviors than the mixed logit model in their dataset, we still can not makethis evidence as a conclusive suggestion that the LCM is definitely superior to the MLM
in all cases. More and more studies on comparison between these two specifications
should be appreciated in the future, since either a systematical meta-analysis or Monte

15

Carlo simulation can be, only after a number of accumulated studies, considered to seek
for some rules on concluding which model specification is better or not.

Acknowledgement
The authors would like to appreciate the financial support from Japanese Ministryof Education, Culture, Sports, Science and Technology (Grand-in-Aid for Scientific
Research A(2) 16203020). All the views expressed in this paper and any errors are thesole responsibility of the authors.

References
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