Comparison of Vehicle-Ownership Models

Abstract

Empirical studies on household car ownership have used two types of discrete choice modeling structures: ordered and unordered. In ordered response structures, such as the ordered logit and ordered probit models, the choice of the number of household vehicles arises from a unidimensional latent variable that reflects the propensity of a household to own vehicles. Unordered response structures are based on the random utility maximization principle, which assumes a household associates a utility value across different car ownership levels and chooses the one with the maximum utility. The most common unordered response models are the multinomial logit and probit models, but only the multinomial logit has been used in practical applications because of its simple structure and low computational requirements. Consensus among researchers on unordered or ordered structures is still lacking. Empirical studies have reported various models, including the multinomial logit, ordered logit, and ordered probit. An open question remains: Which model would better reflect households' car ownership choices? This paper compares multinomial logit, ordered logit, and ordered probit car ownership models through a number of formal evaluation measures and empirical analysis of three data sets: the 2001 National Household Travel Survey for the Baltimore [Maryland] Metropolitan Area, the 2005 Dutch National Travel Survey, and the 2000 Osaka [Japan] Metropolitan Person Trip Data. Results show the multinomial logit model should be selected for modeling the level of household car ownership.

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THIS IS A COPY OF THE EARLIER VERSION OF THE MANUSCRIPT. THE
PUBLISHED VERSION:
Potoglou, D. and Susilo, Y.O. (2008) Comparison of vehicle-ownership models.
Transportation Research Record, No. 2076, pp. 97 – 105.
Comparison of Vehicle-Ownership Models
Dimitris Potoglou, Ph.D.
(Corresponding Author)
Delft University of Technology
OTB Research Institute for Housing, Urban and Mobility Studies
P.O. Box 5030
2600 GA Delft
The Netherlands
Tel. +31 15 2785833
Fax. +31 15 2784422
E-mail: d.potoglou@tudelft.nl
Yusak O. Susilo, Ph.D.
Delft University of Technology
OTB Research Institute for Housing, Urban and Mobility Studies
P.O. Box 5030
2600 GA Delft
The Netherlands
Tel. +31 15 2782714
E-mail: y.susilo@tudelft.nl
Word Count: Text (5,586) + 5 Tables (1,250) = 6,836
Paper submitted for presentation and publication at the 87th Annual Meeting of the
Transportation Research Board, Washington, D.C., January 2008
July 2007

Potoglou and Susilo
2
Abstract
Empirical studies on household car ownership have used two types of discrete choice
modelling structures, the ordered and the unordered. In ordered structures such as the ordered
logit and ordered probit models, the choice of the number of household-vehicles arises from a
uni-dimensional latent index that reflects the propensity of a household to own vehicles.
Unordered response models, on the other hand, are based on the random utility maximization
principle, under which a household associates a utility value across different car ownership
levels and chooses the one with the maximum utility. The multinomial logit and probit
models are representatives of the unordered response models, but only the multinomial logit
has been used extensively because of its simple structure and low computational
requirements. Following Bhat and Pulugurta's (1998) comparative study between the
multinomial logit and ordered logit models, consensus among researchers is still lacking and
empirical studies have reported car ownership model based on the multinomial logit, ordered
logit as well as ordered probit models. It is apparent that there is still an open question to be
addressed: Which of the aforementioned models would reflect better households' car
ownership choices? This paper provides an empirical comparison of multinomial logit,
ordered logit and ordered probit car ownership models by introducing a number of formal
evaluation measures and using three datasets; the 2001 National Household Travel Survey for
the metropolitan area of Baltimore, the 2005 Dutch National Travel Survey and the 2000
Osaka Metropolitan Person Trip Data. Results show that the multinomial logit model is the
one to be selected for modelling the level of household car ownership over ordered logit and
ordered probit.
Keywords: car ownership, discrete choice models, automobile demand, multinomial logit,
ordered logit, ordered probit
1. INTRODUCTION
Car ownership is a key feature of modern life that to a great extent influences travel
behaviour and participation in out-of-home activities (1). Increasing utilization patterns and
high-levels of household car ownership have a direct effect on energy consumption and air
quality levels at local and global scales (2). It is therefore of interest to transport planners and
policy makers at all levels of governance to use models that are capable of explaining the
causal factors of car ownership, being sensitive to policy measures and forecast market shares
of automobiles. Such models can be used as stand-alone systems or as part of integrated land-
use and transportation models for simulating interactions between land-use and transportation
(3). Models of car ownership analysis can be distinguished into two broad categories:
disaggregate and aggregate. Disaggregate models focus on the household level, whereas
aggregate models consider car ownership as an accumulation of household decisions at
different geographical scales such the traffic analysis zone, region, state or country levels.
Disaggregated models have dominated over aggregate models mainly because of their
behavioural structure and improved capability in identifying causal relationships (4).
Moreover, disaggregate models have overcome deficiencies and limitations of aggregate
models such as mutli-collinearity across explanatory variables, large standard errors of

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3
estimated parameters and aggregation bias. Furthermore, the extensive use of disaggregate
models lies in their capability to conduct policy-sensitive analyses and compatibility with
contemporary agent-based approaches in transportation modelling (5).
Disaggregate models regard car ownership observations (i.e., 0, 1, 2, 3 or more cars)
either as ordinal or nominal discrete variables, thus giving rise to two types of choice models,
the ordered and unordered, respectively. Ordered response models assume that the choice of
the number of household-vehicles arises from a uni-dimensional latent index reflecting the
propensity of a household to own vehicles. On the other hand, unordered response models
follow the random utility maximization axiom, in which a household associates a utility value
across different ownership levels and chooses the one with the maximum utility.
A review of the recent literature on disaggregate car ownership models reveals that it
is not yet clear whether ordered response or unordered response models are the most
appropriate (see for example, 6). While Bhat and Pulugurta (7) argued that a multinomial
logit model (MNL) model would be more appropriate for modelling car ownership over an
ordered logit (ORL) model, subsequent empirical studies have developed ordered probit
(ORP) or ORL models claiming the discrete, ordered nature of the dependent variable (8,9) as
well as MNL models on the basis of their sound behavioural and theoretical nature (10-12).
In particular, comparing modelling results of MNL and ORL using several datasets, Bhat and
Pulugurta (7) found substantial differences in the elasticities of exogenous variables across
the choice probabilities of car ownership levels and identified misspecification problems
associated with the ORL that could lead to incorrect and inaccurate forecasts. Also, Potoglou
and Kanaroglou (12) found that a MNL model was a significantly improved model over the
ORL through a likelihood-ratio test between the two models using data from the metropolitan
area of Hamilton, Canada.
This paper offers a comprehensive comparison of car ownership models including
MNL, ORL and ORP. Two research questions are addressed in the paper. First, what
measures could be used in order to conduct a comparison between different discrete choice
model structures? And second, which is the most appropriate among the MNL, ORL and
ORP for modelling car ownership? We address these questions by developing a set of the
aforementioned car ownership models using three sources of data; 2001 U.S. National
Household Travel Survey (NHTS) of the Baltimore Metropolitan Area (13), the 2005 Dutch
National Travel Survey (14) and the 2000 Osaka Metropolitan Person Trip Data (15).
Following, we compute a number of comparison measures introduced in the econometrics
literature.
The reminder of the paper is organized as follows. First, we provide a brief
description on the structure and major assumptions of ordered and unordered models. Next,
we introduce a set of evaluation measures to be used in the comparison of models. Following
that, we present the data sets used and describe the construction of explanatory variables.
Next, we discuss estimation results of each model and report on the findings of the
comparative analysis as reflected by the evaluation measures. In the last section, we offer
some concluding remarks.
2. ORDERED AND UNORDERED MODELS: THEORETICAL BACKGROUND
Ordered and unordered models require different techniques for their respective analysis (16).
We briefly present the main characteristics and assumptions of ordered and unordered models
in the following subsections.

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4
2.1 Ordered Response Models: ORL and ORP
Ordered response models assume that the observed number of household cars (dependent
variable) is a discrete, ordinal variable that is mutually exclusive and collectively exhaustive.
Hence, the observed number of cars per household is assumed to be inherently ordered
implying that higher number of cars is ranked higher than the outcome associated with less
number of cars. Specifically, the ordered response models assume that the number of vehicles
of household n - denoted as (Yn) - arises from a dimensional latent index
*
n
y
, as follows :
n
K
1n nkk
*
nXy  

[1]
where,
*
n
y
reflects the propensity of a household to own vehicles, k (to be estimated) is a set
of parameters associated with a set of k explanatory variables (Xnk). The distribution of the
error terms
n

marks the difference between the ordered logit and the ordered probit models.
In general, the observed level of automobile ownership of a household (Yn) equal to i
( = 0, 1,…M) number of cars is assumed to be related to the latent auto ownership index as
follows (17):
iallfor,,0,,M,...,1,0i,yifonlyandifiY i1i0i1i
*
n1in  
[2]
where  are cut-offs points for discriminating between successful automobile ownership
levels on the underlying latent scale. Cut-off points are estimated along with the 
coefficients in one-step procedure (see, 18). Hence, the probability of household n to own i
number of cars is as follows:
)x()x(P]iY[P n1ininin 
[3]
where (.) is the standard cumulative normal distribution, which gives rise to the ordered
probit model. Alternatively, (.) can be replaced with the Gumbel distribution, (.),
resulting into the ordered logit model. With regard to the selection of the cumulative
distribution function and hence, the choice between ordered logit and probit models, Greene
(18) pointed out that "it is difficult to justify the choice of one distribution over the other on
theoretical grounds…in most applications, it seems not to make much difference".
A significant assumption in the estimation of ordered response models (ordered probit
and logit) is that of parallel slopes. This assumption implies that the estimated coefficient of
an explanatory variable affecting the probability of a household to own a number of cars
would be equal for all outcomes (i.e., i = 1, 2, 3 or more cars) (16). If the parallel slopes
assumption is invalid and coefficients associated with a particular variable are different
across different levels of car ownership, then the ordered response mechanism is no longer
appropriate. In that case, the model should be estimated using an unordered response model.
As Borooah (16) suggested "the validity of the parallel slopes assumption can be tested by
estimating a multinomial logit model on the data…while the ORL model estimates K
coefficients, the MNL model estimates K(M-1) parameters…if the LL1 is the likelihood
function value from the ORL model and LL2 is the likelihood value from the MNL model,
then one can compute 2*(LL2-LL1) and compare with 2(K(M-2))". This test is only
suggestive implying that a "very large" 2 value would provide grounds for concern, a
moderately "large" value would not (16).

Potoglou and Susilo
5
2.2 Unordered Response Models: MNL and MNP
In the case of the unordered response models, the information conveyed by the ordinal nature
of the observed car household ownership is discarded. Hence, the probability of a household
to own a given number of automobiles is based on the utility maximization principle, in
which a household n associates a utility value to each car ownership level and chooses the
one with the maximum utility. Assuming that a household is perfectly informed and the
decision is completely rational and consistent, the random utility maximization framework
implies that:
n,inn,in,i XU 
[4]
where Ui,n represents the true utility of a household n owning i number of cars, i,n is a vector
of parameters to be estimated and i,n is the random component that captures the unobserved
utility or uncertainty from the point of view of the observer/analyst. Again, if the error terms
i,n in Equation 4 are identically and independently distributed (IID) with a Type I Extreme
Value (or Gumbel) distribution, the probability of owning a number of cars i takes the form
the MNL expressed as follows (19):





n
Cj nn,j
nn,i
n)xexp(
)xexp(
)i(P
[5]
The computational simplicity of the MNL model has permitted its wide use in empirical
studies of car ownership. Nevertheless, the MNL has an undesirable property known as the
"independence of irrelevant alternatives" (IIA). The IIA property implies that the ratio of the
probabilities of two alternatives is independent from any other available alternatives. Should
this assumption is violated then the MNL is unsuitable for use in any application in which the
random components of utility are correlated across alternatives and observations of choices
(20). Alternatively, the assumption of error terms i,n being multivariate normal distributed
with mean zero and covariance matrix n leads to the Multinomial Probit (MNP) model. As
opposed to the MNL, the MNP model is more flexible because it relaxes the IIA assumption
of IID errors and thus, allows for correlations of the error terms of different alternatives (20).
In the MNP model, the probability of a household choosing a certain number of cars i is
given as follows:
 
inn1n2nm
VV VV VV
n,in ddd...d
~
)i(P n
in
n1inin
n1
n2inin
n2
mninin
mn
    









[6]
where
n,i
~

is a vector of error differences
nJii1nn,i ~
,...,
~~ 
over all alternatives except i,
with density function
 
n,i
~

.
As shown in Equation 6, the required integrations are computationally burdensome,
especially when the number of alternatives increases. As a result, the use of the MNP model
has been limited in empirical studies involving discrete choice models. Several simulation
methods (see, 21) have been introduced to overcome this problem, however, there remain
considerations with regard to the applicability of the MNP model. Weeks (22) concluded that
the estimation of the MNP entails several estimation, specification and identification issues.
Also, Horowitz (23) argued that the MNP model involves problems such as the proliferation

Potoglou and Susilo
6
of random effects and parameters as well as specification testing. Proliferation can
complicate forecasting as well as adds to the complexity of estimation because it requires a
higher number of covariance matrix elements to be estimated. Regarding specification
testing, Horowitz (23) claimed that "… a misspecified model can create non-IID random taste
variation or additive random components in the error terms of the model". In such case, it
may appear that a MNP model with random taste variation or non-IID additive random utility
components fits the data set better that a MNL model, when the real problem is that the
systematic component of the logit utility function is misspecified. As a result, the use of MNP
for car ownership models may present several difficulties, while also estimation results may
not be directly comparable with those of a MNL.
TABLE 1 Main characteristics of common ordered and unordered models
Ordered Models
Unordered Models
ORL
ORP
MNL
MNP
Behavioural Context
No
No
Yes
Yes
Distribution of Error Terms
Gumbel
Normal
IID - Gumbel
Normal
Parallel Slopes Assumption
Yes
Yes
No
No
IIA Property
No
No
Yes
No
Computational Requirements
Low
Low
Low
High
3. EVALUATION MEASURES OF DISCRETE CHOICE MODELS
The likelihood ratio
2

and the adjusted likelihood ratio indices
2

are the most common
measures of goodness-of-fit used with discrete choice models and are given as follows (20):
)C(LL
)
ˆ
(LL
1
2

[7]
)C(LL
K)
ˆ
(LL
1
2

[8]
where
)
ˆ
(LL 
and
)C(LL
are the log-likelihood function values at convergence and sample
shares, respectively. K is the number of parameters estimated in the model, excluding any
constants as well as cut-off parameter values in the case of ordered models.
The difference [
K)
ˆ
(LL 
] is also known as the Akaike Information Criterion (AIC),
which is another measure of goodness-of-fit of a model given as (24):
K2)
ˆ
(LL2AIC 
[9]
To correct for small samples Hurvich and Tsai (25) proposed the AICc criterion, which can
be used regardless of sample size:
)1KN(
)1K(K2
K2)
ˆ
(LL2AICc


[10]

Potoglou and Susilo
7
where N is number of observations. AIC and AICc allow for a better comparison across
models because they account for goodness-of-fit as well as include a penalty that is an
increasing function of the number of parameters.
Another measure for model comparison is the Bayesian Information Criterion (BIC),
also known as Schwarz Criterion (SIC) (26):
)Nln(K)
ˆ
(LL2BIC 
[11]
The BIC can be used to compare models that are non-nested as is the case with MNL, ORL
and ORP models. Given any estimated models derived from the same sample, the model with
the lower value of AICc or BIC is the one to be preferred because this model is estimated to
be the "closest" to the unknown true model. Compared with AIC, the BIC penalizes free
parameters more strongly than the AIC.
Another consistent criterion as opposed to the non-consistent AICc and BIC is the
Hannan and Quinn Information Criterion (HQIC) criterion (27):
))Nln(ln(K2)
ˆ
(LL2HQIC 
[12]
AICc, BIC and HQIC indices take into account model parsimony. That is, other things equal,
given two models with equal log-likelihood values, the model with fewer parameters is
better. Finally, a comparison between two non-nested models may be performed with Ben-
Akiva and Lerman's (20) adjusted log-likelihood ratio test, which determines if the adjusted
likelihood ratio indices between two non-nested models are significantly different. Under the
null hypothesis that model 1 is a better representation than model 2, the following holds
asymptotically:
 
 
5.0
12
2
1
2
2)KK()C(LLz2)zPr( 
, z > 0 [13]
where (.) is the standard normal cumulative distribution function. As Bhat and Pulugurta
(7) argued a small value of the probability in Equation 13 indicates that the difference z is
statistically significant and the model with the higher value of adjusted likelihood ratio index
is to be preferred.
Finally, another goodness-of-fit statistic is "the percent correctly predicted", which is
calculated by identifying the highest probability for each decision-maker in the sample. The
"the percent correctly predicted" is the portion of decision-makers in the sample for which the
alternative with the highest probability and the actually chosen alternative are the same.
However, as Train (21) argued, this contradicts with the notion of probability. A model
provides enough information in identifying the probability of choosing each alternative,
however, it is incapable of determining repeatedly the actual choice. Hence, this measure will
not be considered further in the evaluation of models.
4. SOURCES OF DATA
The data sets used in this paper were obtained from three sources: the 2001 US NHTS (13),
the 2005 Dutch NTS (14) and the 2000 Osaka Metropolitan Person Trip Data (15). The US
NHTS has been conducted by the US Bureau of Transport Statistics (BTS) and the US
Federal Highway Administration (FHWA). The objective of this survey is to gain a better
understanding of travel behaviour in the US. The data are used by the US Department of
Transportation to assess program initiatives, to review programs and policies, to study current
mobility issues, and to plan for the future. In this paper, the analyses used data from the

Potoglou and Susilo
8
Baltimore Metropolitan Area, which consist of 3,496 households, 8,744 persons, and 32,359
trips. The Dutch NTS is a cross-sectional travel-diary of households and data collection has
been conducted continuously by Statistics Netherlands since 1978. For each year up to 1993,
the NTS recorded data for approximately 10,000 households, 20,000 individuals (and more
than 80,000 journeys). During 1994 and 1995 the NTS was extended to include substantially
more respondents and households each year and also to include children younger than 12,
who were previously excluded from the survey (14).
Finally, the Osaka metropolitan area person-trip survey is a conventional large-scale
household travel survey conducted in the Osaka metropolitan area of Japan in 1980, 1990 and
2000, with sampling rates of 2.4% to 3.0%. The survey collected travel patterns as well as
home and work locations of the respondents on the observed day. It also collected the socio-
demographics and household characteristics (15).
5. ESTIMATION RESULTS AND EVALUATION OF MODELS
Car ownership models were estimated considering four car ownership levels: zero, one, two
and three or more cars. All estimations were performed using the program NLOGIT Ver. 3.0
(28) and final models are reported in Tables 2, 3 and 4. There are some key features to be
addressed at this point. First, parameters of the MNL models were estimated for three
alternatives (i.e., one, two and three or more cars), whereas the zero-cars alternative was
considered as base alternative for identification purposes. Second, the parameters of the MNL
models indicate propensity to own one, two or three or more vehicles in such way that
positive values increase the probability and negative values decrease the probability of
owning a particular number of cars. Similarly, the coefficients in the ordered response models
indicate propensity to own more cars and thus, positive values of coefficients indicate
propensity of households to own higher number of cars. Finally, it is worth noting that MNP
models of car ownership did not reach convergence with any of the aforementioned datasets,
and therefore MNP model estimated are not reported in this comparison.
With regard to the Baltimore dataset, the single-family house attribute was used as
proxy for parking-space availability at the place of residence. The coefficient of this variable
was significant in all models, except in the utility of owning one car. Thus, in the case of
MNL model, households living in single family dwellings were more likely to own two and
three-or-more cars. In the ORL and ORP models, the positive sign of the Single Family
House attribute implied the increased propensity of households to own cars. This finding is in
line with findings reported in Potoglou and Kanaroglou (12), Bhat and Pulugurta (7) and Chu
(8). Furthermore, socio-economic variables such as number of workers, total household
income and race of the head of the household had positive coefficients implying an increased
probability of owning vehicles in the MNL as well as an increased likelihood of owning more
vehicles in the case of ORL and ORP models, respectively. Furthermore, as shown in Table
3, parameter signs of the number of workers and income variables were consistent with
estimation results using the 2005 Dutch NTS.
The household life cycle reflected the influence of the composition of the household
on the number of cars owned. In all datasets, we used as reference class the household
composition "single" (households with one adult only). As shown in Table 2, the MNL model
captures non-linear effects between household life cycle and the probabilities of car
ownership. Specifically, a household comprised of two adult members ("couple") is less

Potoglou and Susilo
9
likely to own one car and more likely to own two or three-or-more cars. It is demonstrated in
this case that unordered models such as the MNL placed no restrictions on the effect of an
explanatory variable across car ownership levels. This finding agrees with the theoretical
claim of Bhat and Pulugurta (7).
Also in Table 2, the pattern of switching parameter signs of the variable "couple"
across car ownership levels cannot be captured in ORL and ORP models where the parameter
value is restricted to a unique (positive) parameter. Similarly, the "couple with children"
variable had no effect in the probability of owning one car, however, it did affect positively
the probability of owning two-or-more vehicles. Furthermore, the single parent household
structure had no effect at all levels of car ownership; that was also the case of "retired"
households and the probability of owning one car. For all other types of household structure,
coefficients were statistically significant and their signs agreed across MNL, ORL and ORP
models as well as with a priori expectations.
TABLE 2 Parameter estimates of the Baltimore Dataset
MNL
ORL
ORP
Variable
1
2
3 +
Constant
0.504
(1.94)
-2.695
(-8.00)
-6.746
(-12.52)
-0.374
(-2.32)
-0.191
(-2.09)
Type of Dwelling: Single Family House
0.275
(1.49)
1.118
(5.53)
1.778
(7.38)
0.763
(8.36)
0.452
(8.77)
Number of Workers
0.509
(4.13)
1.212
(8.65)
2.175
(13.77)
1.035
(17.15)
0.574
(17.15)
Household Income (>$30,000)
REFERENCE
Household Income ($30,000 - $80,000)
1.683
(10.80)
2.401
(13.18)
3.178
(11.16)
1.413
(15.44)
0.806
(15.82)
Household Income (> $80,000)
2.013
(4.91)
3.708
(8.80)
4.659
(9.82)
1.906
(16.61)
1.100
(16.91)
Household Life Cycle: Single
REFERENCE
Household Life Cycle: Couple
-0.573
(-2.46)
1.872
(6.91)
1.950
(4.73)
1.243
(10.41)
0.669
(9.84)
Household Life Cycle: Single Parent
-0.333
(-1.49)
-0.070
(-0.21)
-0.254
(-0.42)
-0.080
(-0.48)
- 0.053
(-0.55)
Household Life Cycle: Couple w. Children
-0.460
(-1.81)
2.082
(7.14)
2.350
(5.51)
1.383
(10.97)
0.751
(10.49)
Household Life Cycle: Retired
0.011
(0.06)
1.864
(8.07)
2.620
(6.73)
1.310
(11.83)
0.733
(11.60)
Race: Caucasian
1.066
(7.95)
1.636
(9.45)
2.007
(8.45)
0.939
(10.53)
0.531
(10.56)
Residential Density
-0.00025
(-6.62)
-0.00046
(-10.85)
-0.00063
(-11.63)
-0.00025
(-12.82)
-0.00015
(-13.02)
Threshold Parameters

(for identification 0=0)
1
3.087
(52.76)
1.726
(53.49)
2
6.263
(74.16)
3.520
(79.60)
Log-likelihood at convergence
-2949
- 3081
-3092

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10
TABLE 3 Parameter estimates using the 2005 Dutch NTS Dataset
MNL
ORL
ORP
Variable
1
2
3 +
Constant
-1.051
(-20.24)
-5.649
(-47.67)
-9.090
(-23.50)
-1.065
(-24.36)
-0.590
(-23.20)
Number of Workers
0.964
(22.09)
1.559
(31.19)
2.120
(27.62)
0.888
(38.74)
0.480
(37.52)
Household Income (>€20,000)
REFERENCE
Household Income (€20,000 - €60,000)
0.800
(21.72)
1.593
(22.88)
1.312
(5.30)
0.885
(27.38)
0.500
(27.47)
Household Income (>€60,000)
1.693
(15.76)
3.269
(26.61)
3.475
(12.94)
1.791
(39.26)
1.020
(39.48)
Household Life Cycle: Single
REFERENCE
Household Life Cycle: Couple
1.073
(20.83)
2.757
(28.14)
1.534
(5.27)
1.256
(31.29)
0.700
(31.06)
Household Life Cycle: Couple w. Children
1.425
(18.04)
3.596
(31.64)
1.904
(6.23)
1.722
(39.12)
0.951
(38.64)
Household Life Cycle: Extended family
0.687
(8.95)
2.779
(24.29)
3.298
(11.60)
1.856
(36.93)
1.030
(37.17)
Household Life Cycle: Retired
0.137
(2.88)
0.577
(4.71)
0.416
(0.97)
0.159
(3.78)
0.09
(3.52)
Reside in very highly urbanised area
REFERENCE
Reside in high urbanised area
0.631
(12.36)
1.026
(12.95)
1.550
(6.35)
0.616
(14.79)
0.350
(14.91)
Reside in moderately urbanised area
0.904
(16.25)
1.557
(18.85)
2.199
(9.01)
0.911
(21.01)
0.520
(21.23)
Reside in low urbanised area
1.195
(20.63)
1.987
(23.73)
3.049
(12.81)
1.168
(26.933)
0.670
(27.22)
Reside in non-urbanised area
1.306
(20.29)
2.258
(25.09)
3.209
(13.07)
1.301
(28.17)
0.740
(28.36)
Threshold Parameters

(for identification 0=0)
1
3.870
(153.13)
2.19
(169.49)
2
7.145
(162.78)
3.95
(185.95)
Log-likelihood at convergence
-22941
-23255
-23254

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TABLE 4 Parameter estimates using the 2000 Osaka Metropolitan
Area Dataset
MNL
ORL
ORP
Variable
1
2
3 +
Constant
-0.397
(-14.53)
-1.541
(-35.89)
-2.318
(-35.08)
0.520
(21.77)
0.325
(23.93)
Household Life Cycle: Single
REFERENCE
Household Life Cycle: Couple
0.912
(29.59)
0.252
(6.77)
-1.235
(-18.74)
-0.356
(-18.59)
-0.211
(-18.30)
Household Life Cycle: Single parent
-0.871
(-19.10)
-2.843
(-25.00)
-4.388
(-16.21)
-1.953
(-45.65)
-1.154
(-45.02)
Household Life Cycle: Couple w.
Children
0.687
(34.88)
0.011
(0.46)
-1.373
(-34.62)
-0.465
(-35.52)
-0.272
(-35.24)
Household Life Cycle: Extended family
1.164
(81.37)
1.092
(69.87)
0.835
(48.35)
0.299
(36.01)
0.190
(39.82)
Household Life Cycle: Retired
-1.061
(-85.54)
-2.195
(-118.0)
-3.305
(-105.86)
-1.898
(-184.89)
-1.088
(-186.24)
Reside in CBD area
REFERENCE
Reside in mixed area
0.564
(20.30)
0.577
(13.09)
0.586
(8.58)
0.484
(19.85)
0.267
(19.27)
Reside in autonomous area
1.458
(41.19)
3.212
(66.16)
4.200
(59.87)
2.631
(101.21)
1.499
(100.93)
Reside in suburban area
1.270
(46.46)
2.011
(46.72)
2.362
(35.61)
1.452
(60.97)
0.824
(60.95)
Reside in non-urbanised area
1.792
(22.75)
3.398
(39.19)
4.624
(45.99)
2.804
(69.53)
1.609
(68.43)
Threshold Parameters

(for identification 0=0)
1
2.375
(531.86)
1.400
(555.86)
2
3.877
(659.11)
2.265
(710.88)
Log-likelihood at convergence
-350228
-355634
-355820
Finally, we specified a full set of alternative specific constants in the MNL models
corresponding to one, two and three-or-more-cars options in order to capture the systematic
influence of omitted variables, namely car ownership costs, in the utility functions of the
model (8).
5.1 Behavioural Comparisons across the American, Dutch and Japanese Datasets
Comparing the estimated coefficients across the Baltimore, Dutch and Japanese
datasets, it is clear that estimates present some discrepancies, which may be explained by the
contextual/cultural differences in the sampled population and also, by the different
explanatory variables available in the dataset. For example, while in the Baltimore dataset
(Table 2) we used residential density to measure the influence of land-use on car ownership,
we used the degree of urbanisation in the Dutch (Table 3) dataset and urban-functions in the
dataset of Osaka metropolitan area (Table 4). Moreover, unlike the other two datasets, the
Osaka metropolitan area dataset did not include household income and information on the
number of workers, which is a crucial variable for car ownership decisions.

Potoglou and Susilo
12
Nevertheless, comparison of the datasets reveals interesting differences. For example,
except for the extended family case, the Dutch and Osaka metropolitan respondents tend to
have two cars rather than three or more cars, which is different than Baltimore respondents.
Presumably this is because of the different needs for car usage. Dutch people tend to walk
and to bike in their daily travel (29), while the Osaka metropolitan area has a very dense and
well developed public transport network (15) compared to Baltimore area. Yet, despite the
differences in describing the land-use influences to the household car ownership, results in all
datasets are in line with the hypothesis that higher densities or proximity to the activity
locations reduces the probability of a household owning a car.
Furthermore, examining the influence of household structure to household car
ownership, we found that - all else being equal - while Baltimore couples were less likely to
own one car, Dutch and Osaka's couples were more likely to own one and three cars than
zero cars. Also, single-parent households residing in Baltimore and Osaka had a higher
probability of owning one car and lower probability of owning three cars. On the other hand,
Dutch single parents were more likely to own one car and less likely to posses three cars. As
shown in Tables 2, 3 and 4, couples with children also present differences across the dataset
estimates. In particular, couples with children living in Baltimore were less likely to own one
car and more likely to own three cars, as opposed to Dutch and Osaka's households that
would be more likely to own one car. Interestingly, Baltimore's retirees had a higher
probability to own cars as opposed to Osaka's where the negative coefficients imply that the
probability of owning any number of cars would be less than owning no cars. Again, these
discrepancies are because of differences in public transport availability and high usage of
non-motorized modes across Baltimore, the Netherlands and Osaka. It is worth mentioning
here that these discrepancies are also reflected in the estimates of the ORL and ORP models.
5.2 Comparison of MNL, ORL and ORP Models
All models performed well as indicated by the relatively high values of rho-squared. Also,
likelihood ratio tests were used to test the null hypothesis that all parameters in each model -
except the alternative specific constants - were zero. As shown in Table 5, chi-square values
of the likelihood ratio indices in all models reject the null hypothesis and indicate that all
models were statistically significant. The adjusted likelihood values lend support to the MNL
model as the best for modelling car ownership because it exhibits the highest value of the
index. Also, the values of AICc, BIC and HQIC indices clearly demonstrate the superiority of
the MNL against the ORL and ORP. Finally, Ben-Akiva and Lerman's (20) adjusted log-
likelihood ratio test was used for testing the non-nested hypothesis that the adjusted log-
likelihood values of the MNL, ORL and ORP were statistically different. The last three rows
of Table 5 present the upper bound of the probability of erroneous choosing the incorrect
model, which however, had the highest adjusted likelihood index. In other words, this
hypothesis states that the estimated differences in the adjusted likelihood ratio index values
between the MNL, ORL and ORP models could have occurred by chance. The estimated
probability values of the aforementioned hypothesis showed that the adjusted likelihood ratio
index of the MNL is significantly different than those of the ORL and ORP models and
therefore, the MNL is the preferred model. Similarly, the ORL model should be preferred as
opposed to the ORP model in the Baltimore case, whereas there is no difference between the
ORL and ORP models in the Dutch and Japanese datasets.

Potoglou and Susilo
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14
6. CONCLUSION
Car ownership is a key element in the study and simulation of urban systems. Hence, it is of
interest to develop models of car ownership that are capable of explaining and predicting
households' choices. To date, empirical studies have focused on two types of disaggregate
models, the ordered and unordered. The first type refers to ORL and ORP whereas the second
is mainly represented by the MNL. While a previous comparison suggested the MNL as more
appropriate for car ownership modelling over an ORL (7), subsequent empirical analyses
have adopted both MNL and ORL as well as ORP models. Thus, it has not been clear, which
of the aforementioned models would be more suitable for car ownership modelling.
The objective of this paper has been to evaluate the MNL, ORL and ORP models for
car ownership based on a number of data fit measures. We approached this task by
empirically studying household car ownership levels using as explanatory variables the
household's life-cycle stage, income, race, type of dwelling and number of workers per
household. In addition, we included residential density as a measure of urban form assuming
that higher densities would discourage households to own more vehicles. The results of
model estimations confirm previously published findings highlighting the importance of
socio-demographic and economic characteristics of households as well as the type of
dwelling and urban form in explaining household car ownership.
A key difference between ordered and unordered models is that unordered models,
namely the MNL, are based on the utility maximization principle, whereas ordered models
(ORL, ORP) are not. This difference makes the MNL more appealing over ordered models,
because findings are based on a solid behavioural framework and not a single continuous
propensity measure. Furthermore, a quick glance in the estimation of parameter reveals that
the MNL model is more flexible because it allows for alternative-specific effects of
explanatory variables across car ownership levels. On the other hand, ordered models are
constrained to a unique coefficient per explanatory variable. Finally, comparison tests of data
fit among the MNL, ORL and ORP models suggest that the MNL model should be the
preferred model structure for household car ownership.
ACKNOWLEDGEMENTS
An earlier version of this paper was presented at the 9th NECTAR Conference held in
Porto, Portugal in May 2007. The authors are grateful to Professors Yoram Shiftan of
Technion-Israel Institute of Technology and Gerard de Jong of Institute of Transport Studies
at University of Leeds for their constructive comments and suggestions. Also, the authors
would like to thank Nam Seok Kim, Ph.D. Candidate at the OTB Research Institute of Delft
University of Technology, for his help in identifying the Baltimore data for this analysis and
the Kinki Branch Office of the Japanese Ministry of Land, Infrastructure and Transportation
for providing Osaka's dataset.
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