Hybrid Choice Modeling of New Technologies for Car Use in
Canada: A Simulated Maximum Likelihood Approach
PRELIMINARY
Please, do not quote or cite without the authors’ permission
by
Denis Bolduc1 , Nathalie Boucher, Ricardo Alvarez-Daziano
Département d’Économique
Université Laval.
Pavillon J.-A.-DeSève, QC G1V 0A6,
(418) 656-5427; Fax : (418) 656-2707
denis.bolduc@ecn.ulaval.ca (1 corresponding author)
nboucher@ecn.ulaval.ca
ricardo.alvarez-daziano.1@ulaval.ca
May 8, 2008
Abstract
In the last decade, a new trend in discrete choice modeling has emerged in which psychological factors are explicitly incorporated in order to enhance the behavioural representation of the choice process. In this context, hybrid choice models expand on standard
choice models by including attitudes and perceptions as latent (unobserved) variables.
The complete model is composed of a group of structural equations describing the latent variables in terms of observable exogenous variables, and a group of measurement
relationships linking latent variables to observable indicators. With a multinomial logit
model to describe the choice, the contribution of a given observation to the likelihood
function of the full system is an integral of dimension equal to the number of latent
variables in the model. Although the estimation of hybrid choice models requires the
evaluation of complex multi-dimensional integrals, simulated maximum likelihood is implemented in order to solve the integrated multi-equation model. In practice, we replace
the multidimensional integrals with a smooth simulator with good properties, thus leading to a maximum simulated likelihood (MSL) solution.
In this paper we apply the hybrid choice modeling framework to data from a survey
conducted by the Energy and Materials Research Group (EMRG) (Simon Fraser University, 2002-2003) of virtual personal vehicle choices made by Canadian consumers
when faced with technological innovations. The survey also includes a complete list of
indicators, allowing us to apply a hybrid choice model formulation. In our application,
the choice model is assumed to be of the logit mixture type, which increases the computational complexity in the evaluation of the likelihood function. The choice model
contains variables that are normally used in a travel choice model specification as well
as two transportation-related latent variables that we call EC (environmental concern)
and ACF (appreciation of car features). Our framework also makes it possible to tackle
the problem of measurement errors in variables in a very natural way. Our initial results
indicate that the quality of the information regarding income was questionable. We
therefore include in the choice model a third latent variable that we call (REV) which
represents the latent true income variable.
We conclude that the hybrid choice model is genuinely capable of adapting to practical
situations by including latent variables among the set of explanatory variables. Incorporating perceptions and attitudes as well as allowing for measurement errors lead to
more realistic models and give a better description of the profile of consumers and their
adoption of new private transportation technologies.
1
1
Introduction
In the current context of global warming, it is more relevant than ever to explore sustainable solutions to problems created by personal transportation. Technological innovation
and the use of cleaner alternative fuels are among the solutions that have traditionally
been proposed to contain, or at least alleviate, these problems. In this way it becomes
important to model the effect of introducing new technologies for car use on transportation choice behaviour in a more realistic and expanded way. The modeling challenge is
to develop transportation demand models that are not only able to adequately predict
individual preferences but also to recognize the impact of psychological factors, such as
perceptions and attitudes.
In this paper we analyze the practical implementation of hybrid choice models in order
to include perceptions and attitudes in a standard discrete choice setting. In section
2, we discuss the derivation of discrete choice modelling and their integration into a
hybrid model framework using latent variables. In section 3, we present the empirical
data on car choice that we use from the survey. In section 4 we discuss the results
of a multinomial logit (MNL) model estimation focusing exclusively on the car choice
dimension. In section 5 we expand this model emphasizing on the results of each partial
model that configures the hybrid model setting. In section 6, we present the main
conclusion of our work.
2
2.1
Hybrid Choice Modeling
Standard Discrete Choice Modeling
In discrete choice modeling, the most common approach is based on random utility theory. According to this theory, each individual has a utility function associated with
each of the alternatives. This individual function can be divided into a systematic part,
which considers the effect of the explanatory variables, and a random part that takes
into account all the effects not included in the systematic part of the utility function.
In other words, choices are modeled using a structural equation (1) – the utility function – representing the individual preferences, where the explanatory variables are the
alternative attributes and individual characteristics. The observed choice corresponds
to the alternative which maximizes the individual utility function, a process represented
by a measurement equation (2). Because the utility function has a random nature, the
output of the model actually corresponds to the choice probability of individual n choosing alternative i. The set of equations describing the standard discrete choice setting is
given by:
Uin = Xin β + υin
(1)
2
yin =
1 if Uin ≥ Ujn , j 6= i
0 otherwise,
(2)
where Uin corresponds to the utility of alternative i as perceived by individual n; Xin is
a row vector of attributes of alternative i and socioeconomic characteristics of individual
n; β is a column vector of unknown parameters; υin is an error term and yin corresponds
to an indicator of whether alternative i is chosen by individual n or not.
Different choice models can be derived depending on the assumptions considered for
the distribution of the random error term (Ben-Akiva and Lerman, 1985). So far the
workhorses in this area have been the multinomial logit model (McFadden, 1974) and the
nested logit model (Ben-Akiva, 1973). Both offer closed forms for choice probabilities
but rely on restrictive simplifying assumptions. To gain generality, more flexible models
have been incorporated in practice. Indeed, one powerful modeling alternative is the logit
mixture model (Bolduc and Ben-Akiva, 1991 and Brownstone and Train, 1999), which
can approximate any random utility maximization model (McFadden and Train, 2000).
The main idea of this kind of model is to consider more than one random component,
allowing for the presence of a more flexible covariance structure. The estimation implies
the evaluation of integrals without a closed form solution, although it is possible to use
computer aided simulation techniques to approximate it.
In this way it can be seen that the development of discrete choice modeling has evolved
quickly and that powerful models can be used. However, under this whole approach,
discrete choice models represent the decision process as an obscure black box, where attitudes, perceptions and knowledge are neglected. This is why in the last decade discrete
choice modeling has evolved towards an explicit incorporation of psychological factors
affecting decision making (Ben-Akiva et al., 2002). According to 2002 Nobel laureate
Daniel Kahneman, there still remains a significant difference between economist modellers that develop practical models of decision-making and behavioural scientists who
focus on in-depth understanding of agent behaviour. Both have fundamental interests in
behaviour but each work with different assumptions and tools. McFadden (1986) points
out the need to bridge these worlds by incorporating attitudes in choice models. In his
2000 Nobel lecture, McFadden emphasized the need to incorporate attitudinal constructs
in conventional economics models of decision making.
2.2
Latent Variables and Discrete Choice: The Hybrid Choice
Model
The new trend in discrete choice modeling is to enhance the behavioural representation
of the choice process. As a direct result, the model specification is improved and the
model gains in predictive power. Econometrically, the improved representation model
as displayed in Figure 1 involves dealing with a choice model formulation that contains
3
unobserved psychometric variables (attitudes, perceptions, opinions) as latent variables
incorporated as explanatory variables.
Since the latent variables are not observed, they are normally linked to questions of a
survey: the indicators. These indicators can be continuous, binary or categorical variables expressed by responses to attitudinal and perceptual survey questions. The latent
variable model is composed of a structural equation, which describes the latent variables
in terms of observable exogenous variables, and a group of measurement relationships
(measurement model ) linking latent variables to indicators (Jöreskog and Sörbom 1984).
It is possible to integrate the latent variable model into the standard choice model setting, obtaining a group of structural and measurement equations leading to the Hybrid
Choice Model (HCM) framework (Ben-Akiva et al., 2002 and Walker and BenAkiva, 2002).
Figure 1: Latent Variables and discrete Choice.
The hybrid choice model that we consider may be written as follows:
Structural equations
x∗n = Bwn + ζn ,
ζn ∼ N (0, Ψ),
Un = Xn β + Cx∗n + υn ,
(3)
(4)
Measurement equations
In = α + Λx∗n + εn ,
yin =
εn ∼ N (0, Θ)
1 if Uin ≥ Ujn , j 6= i
0 otherwise,
4
(5)
(6)
where x∗n is a (L × 1) vector of latent variables; wn is a (M × 1) vector of explanatory
variables affecting the latent variables; B is a (L × M ) matrix of unknown parameters
describing the effects of the explanatory variables wn on the latent variables; and Ψ is
a (L × L) variance covariance matrix which describes the relationship among the latent
variables through the error term. The choice model in equation (4) is written in vector
form where we assume that there are J alternatives. Therefore, Un is a (J × 1) vector of
utilities; υn is a (J ×1) error vector assumed to be independent and identically distributed
(i.i.d.) Type 1 extreme value distributed. Xn is a (J × K) matrix with Xin designating
the ith row. β is a (K × 1) vector of unknown parameters. C is a (J × L) matrix of
unknown parameters associated with the latent variables present in the utility function,
with Ci designating the ith row of matrix C.
In the set of measurement equations, In corresponds to a (R × 1) vector of indicators
of latent variables associated with individual n; α is a (R × 1) vector of constants and
Λ is a (R × L) matrix of unknown parameters that relate the latent variables to the
indicators. The term εn is a (R × 1) vector of independent error terms. This implies
that Θ is a diagonal matrix with variance terms on the diagonal. Finally, we stack the
choice indicators yin ’s into a (J × 1) vector called yn .
If the latent variables were not present, the choice probability would correspond exactly to the standard choice probability that we denote P (yn |Xn , β ). In a setting with
given values for the latent variables x∗n , the choice probability would be represented by
P (yn |x∗n , Xn , θ ) where θ contains all the unknown parameters in the choice model of
equation (4). Since latent variables are not actually observed, the choice probability is
obtained by integrating the latter expression over the whole space of x∗n :
Z
P (yn |Xn , wn , θ, B, Ψ) =
P (yn |x∗n , Xn , θ )g(x∗n |B, wn )dx∗n ,
(7)
x∗n
which is an integral of dimension equal to the number of latent variables in x∗n and where
g(x∗n |B, wn ) is the density of x∗n defined in equation (3).
Indicators are introduced in order to characterize the unobserved latent variables, and
econometrically they permit identification of the parameters of the latent variables. Indicators also provide efficiency in estimating the choice model with latent variables,
because they add information content. The variables yn and In are assumed to be correlated only via the presence of the latent variables x∗n in equations (4) and (5). Given
our assumptions, the joint probability of observing yn and In may thus be written as:
Z
P (yn , In |Xn , wn , δ) =
P (yn |x∗n , Xn , θ )f (In |Λ, x∗n )g(x∗n |B, wn )dx∗n ,
(8)
x∗n
where f (In |Λ, x∗n ) is the density of In defined in equation (5). The vector δ designates
the full set of parameters to estimate.
5
Few applications of the hybrid choice model are found in the literature. While BenAkiva and Boccara (1987) develop the idea of hybrid modeling in the context of a more
comprehensive travel behaviour framework, Walker and Ben-Akiva (2002) and Morikawa,
Ben-Akiva and McFadden (2002) extend this development, showing how the model can
be estimated and implemented in practice. The contribution of Bolduc, Ben-Akiva,
Walker and Michaud (2005) is the first example of the analysis and implementation of
a situation characterized by a large number of latent variables and a large number of
choices. The work of Ben-Akiva, Bolduc and Park (2008) is a recent application of the
Hybrid Choice setting applied to the freight sector.
2.3
Estimation
In practice, with a large number of latent variables (more than 3), we replace the multidimensional integral with a smooth simulator which has good properties. The number
of latent variables has an impact on the computation of the joint probability in equation
(9). Indeed, if υn is i.i.d. extreme value type 1 distributed, then conditional on x∗n the
probability of choosing alternative i has the multinomial logit form, which leads to the
following expression:
Z
P (yn , In |Xn , wn , δ) =
x∗
exp(Xin β + Ci x∗n )
P
f (In |Λ, x∗n )g(x∗n |B, wn )dx∗n .
∗
exp(Xjn β + Cj xn )
(9)
j
Taking advantage of the expectation form, we can replace the probability with the following empirical mean:
S
1 X exp(Xin β + Ci x∗s
n )
P
P̃ (yn , In |Xn , wn , δ ) =
f (In |Λ, x∗s
n ),
S s=1
exp(Xjn β + Cj x∗s
)
n
(10)
j
where x∗s
n corresponds to a random draw s from its distribution. This sum is computed
over S draws. This simulator is known to be unbiased, consistent and smooth with respect to the unknown parameters. Replacing P (yn , In |Xn , wn , δ) with P̃ (yn , In |Xn , wn , δ)
in the log likelihood leads to a maximum simulated likelihood (MSL) solution. We thereN
P
fore consider the following objective function: max
ln P̃ (yn , In |Xn , wn , δ).
δ
n=1
In the past few years, a lot of progress has been made regarding MSL estimation. Train
(2003) gives an in-depth analysis of the properties of MSL estimators. Recent results,
mostly attributable to Bhat (2001), suggest that simulation should exploit Halton draws.
Halton type sequences are known to produce simulators with a given level of accuracy using many fewer draws than when using conventional uniform random draws (Ben-Akiva
et al. 2002; Munizaga and Alvarez-Daziano 2005). Simulated maximum likelihood is now
6
well known and has been applied in numerous circumstances. The logit probability kernel
present in equation (10) makes the simulated log likelihood fairly well behaved. Asymptotically, meaning as S → ∞ and as N → ∞, the solution becomes
PN identical to a solution
arising from maximizing the usual log likelihood function: n=1 ln P (yn , In |Xn , wn , δ ).
Regarding the measurement model, we assume that each equation that links the indicators and the latent variables corresponds to a continuous, a binary, or a multinomial
∗
ordered response. A measurement equation r in the continuous case is given by Irn = Irn
with:
∗
(11)
= αr + Λr x∗n + εrn , εrn ∼ N (0, θr2 )
Irn
In the binary case, we rather get instead:
1
Irn =
0
∗
≥0
if Irn
otherwise,
(12)
while in the multinomial ordered case with Q responses, we obtain:

∗

1
if γ0 < Irn
≤ γ1


 2
∗
if γ1 < Irn ≤ γ2
Irn =
..

.


∗
 Q
≤ γQ ,
if γQ−1 < Irn
(13)
where Irn and εrn are the rth element of In and εn respectively. θr2 is the rth element
on the diagonal of Θ, and Λr denotes row r of Λ. In the multinomial cases, the γq ’s
are estimated. By convention, γ0 and γQ are fixed to −∞ and ∞ respectively. We
assume that Θ is diagonal, which implies that the indicators are not cross-correlated.
For identification, the constant terms αr must be set to 0 in the non continuous cases.
Given our assumptions, the density f (In |Λ, x∗n ) that we denote as f (In ) to simplify,
corresponds to:
R
Y
f (In ) =
f (Irn ).
(14)
r=1
If measurement equation r is continuous, then
1
Irn − αr − Λr x∗n
f (Irn ) = φ
,
θr
θr
(15)
where φ denotes the probability density function (pdf) of a standard normal. If the
measurement equation r corresponds to a binary response, then
f (Irn ) = Φ
αr + Λr x∗n
θr
Irn 1−Φ
7
αr + Λr x∗n
θr
(1−Irn )
,
(16)
where Φ denotes the cumulative distribution function (cdf) of a standard normal. Finally,
if measurement equation r corresponds to a multinomial ordered response, then
γq−1 − Λr x∗n
γq − Λr x∗n
−Φ
.
(17)
f (Irn = q) = Φ
θr
θr
Except for the continuous case, the variances θr cannot be estimated. They are fixed to
1 automatically.
3
The Data
The data for this study are from a survey conducted by EMRG (Energy and Materials
Research Group, Simon Fraser University) in 2002-2003 on 1500 Canadian consumers living in urban areas with populations over 250,000 people (Horne, Jaccard, and Tiedman,
2005). Survey participants were first contacted in a telephone interview for personalizing a detailed questionnaire that was then mailed to them. The telephone conversation
allowed general information to be gathered on the socioeconomic characteristics of the
participants and their households, as well as on their automobile fleet.
The mailed questionnaire consisted in:
• Part 1: Transportation options, requirements and habits
• Part 2: Virtual personal vehicle choices made by Canadian consumers when faced
with technological innovations (stated preferences experiment)
• Part 3: Transportation mode preferences
• Part 4: Views on transportation issues
• Part 5: Additional information (gender, education, income)
The stated preferences (SP) hypothetical car choices in Part 2 considered four vehicle
types:
• A conventional vehicle (operating on gasoline or diesel) (SGV)
• A natural-gas vehicle for alternative fuel vehicle (AFV)
• A hybrid vehicle (gasoline-electric) (HEV)
• A hydrogen fuel cell vehicle (HFC)
8
The characteristics of the vehicles were depicted as:
• Capital Cost: purchase price
• Operating Cost: fuel cost
• Fuel Available: percentage of stations selling the proper fuel type
• Express Lane Access: whether or not the vehicle would be granted express lane
access
• Emissions Data: emissions compared to a standard gasoline vehicle
• Power: power compared to their current vehicle
Under the SP experimental design of the survey, each participant was asked to make up
to four consecutive virtual choices while the features of the vehicle were modified after
each round. The sample has 866 completed surveys (77% response rate) and since each
respondent provided up to four vehicle choices, after some clean up, there remains 1877
usable observations. The various values assumed for the characteristics of the vehicles
that were used in the experimental design of the SP survey are set out in Table 1 on
the next page. The basis of comparison of the experimental design refers to the motor
vehicle that is the most frequently used by the respondent.
4
Multinomial Logit Results
We first apply a standard multinomial logit model, using as variables the list of attributes
for the vehicle choice. The choice model is depicted in Figure 2, while in Table 2 we
present the estimation results, which are equivalent to those reported by Horne, Jaccard,
and Tiedman (2005).
The estimates of the standard multinomial logit model show that the SP experiment
was well designed in the sense that it allows one to estimate a significant effect of
each experimental attribute. Signs are also correct: costs are perceived as negative
attributes, while Fuel Available, Express Lane Access and Power are considered good
characteristics. The magnitude of each estimated parameter permits one to rank the
impact of an attribute on the choice probability. For example, power appears to be
much more important than accessibility to an express lane. The alternative specific
constants (ASC) allow for reproducing the experimental market shares.
9
TABLE 1 SP Design
FIGURE 2 Basic Choice Model.
10
ASC AFV
ASC HEV
ASC HFC
Capcost
Fuelcost
Fuelavail
Expaccess
Power
Number of observations
Final log-likelihood
Adjusted rho-square
Estimates
-4.500
-1.380
-2.100
-0.856
-0.826
1.360
0.156
2.700
1877
-1984.55
0.234
Student t
-6.81
-2.18
-3.26
-4.07
-4.18
7.32
2.29
4.12
TABLE 2 Multinomial Logit Results
5
Hybrid Choice Model
5.1
Definition of the Latent Variables
The first step to build a hybrid choice model is to define the latent variables involved.
In the survey, people answered several questions. We conduct our analysis focusing on:
Question 26 : What is your level of support for/opposition to the following government
actions that would influence your transportation system? Degree of support: 5 levels
from Strongly Opposed to Strongly Supportive.
1. Improving traffic flow by building new roads and expanding existing roads
2. Discouraging automobile use with road tolls, gas taxes and vehicle surcharges
3. Making neighbourhoods more attractive to walkers and cyclists using bike lanes
and speed controls
4. Reducing vehicle emissions with regular testing and manufacturer emissions standards
5. Making carpooling and transit faster by giving them dedicated traffic lanes and
priority at intersections
6. Making transit more attractive by reducing fares, increasing frequency, and expanding route coverage
11
7. Reducing transportation distances by promoting mixed commercial, residential and
high-density development
8. Reducing transportation needs by encouraging compressed workweeks and working
from home
Question 29 : Thinking about your daily experiences, how serious do you consider the
following problems related to transportation to be? Degree of seriousness of problem:
5 levels from Not a Problem to Major Problem.
1. Traffic congestion you experience while driving
2. Traffic noise you hear at home, work, or school
3. Vehicle emissions which impact local air quality
4. Accidents caused by aggressive or absent-minded drivers
5. Vehicle emissions which contribute to global warming
6. Unsafe communities due to speeding traffic
Question 6 : What importance did the following factors have in your family’s decision
to purchase this vehicle? Degree of importance: 5 levels from Not at All Important to
Very Important.
1. Purchase Price
2. Fuel Economy
3. Horsepower
4. Safety
5. Seating Capacity
6. Reliability
7. Appearance and Styling
Considering answers to those questions as indicators we identify two travel related latent
variables:
• Environmental Concern (EC): related to transportation and its environmental
impact (x∗1n )
12
• Appreciation of new car features (ACF): related to car purchase decisions
and how important are the characteristics of this new alternative (x∗2n )
Our model also includes a third latent variable called (REV) to account for the measurement error problem in quantifying the income variable. The hybrid model setting that we
consider is represented in Figure 3, where the complete set of structural and measurement
equations is sketched, depicting the relationships between explanatory variables and each
partial model. Indeed, we can distinguish the choice model, which is centered on the
utility function modeling; the latent variables structural model, which links the latent
variables with the characteristics of the traveller and the latent variables measurement
model, which links each latent variable with the indicators.
FIGURE 3 Hybrid Choice Model.
13
5.2
Car Choice Model
The set of equations for the mode choice model alone are given by:
USGV n
UAF V n
UHEV n
UHF Cn
=
=
=
=
VSGV n + c1,2 ACFn + υSGV n
VAF V n + c2,1 ECn + c2,2 ACFn + υAF V n
VHEV n + c3,1 ECn + c3,2 ACFn + υHEV n
VHF Cn + c4,1 ECn + c4,2 ACFn + c4,3 REVn + υHF Cn ,
(18)
(19)
(20)
(21)
where Vin = Xin β, denotes the deterministic part of the utility expression given in
equation (1). It contains the variables listed in Table 2. The utility specifications also
contains the effect of the latent variables. The latent variable related to environmental
concern (EC) was not considered on the standard gasoline vehicle (SGV). On the basis
of several attempts, the latent income variable (REV) was included only in the Hydrogen
fuel cell vehicle (HFC) alternative. In Table 4, we report the results of the choice model.
ASC AFV
ASC HEV
ASC HFC
Capcost
Fuelcost
Fuelavail
Expaccess
Power
Latent Variables
ACF on SGV
EC on AFV
ACF on AFV
EC on HEV
ACF on HEV
EC on HFC
ACF on HFC
REV on HFC
Number of individuals
Final global function
Adjusted rho-square
Number of Halton draws
Hybrid Choice Model
MNL
Estimates Student t Estimates Student t
-6.626
-5.162
-4.500
-6.81
-4.383
-5.688
-1.380
-2.18
-6.403
-8.750
-2.100
-3.26
-0.943
-4.369
-0.856
-4.07
-0.849
-3.917
-0.826
-4.18
1.384
7.096
1.360
7.32
0.162
2.229
0.156
2.29
2.710
3.985
2.700
4.12
3.160
0.798
2.810
0.770
2.810
1.085
3.054
0.456
1877
-57624.26
0.236
500
25.984
2.695
30.708
3.965
30.708
5.620
31.048
3.373
TABLE 4 Car Choice Model Results
14
1877
0.234
-
-
Common parameters with the standard multinomial logit model have the same sign and
magnitude, except for alternative specific constants. In addition, the significance of the
latent variable parameters shows that they have a significant effect on the individual
utilities. The latent variables all enter very significantly and positively into the choice
model specification. EC has the highest effect on the HFC alternative.
5.3
Structural Model
The set of equations for the latent variables’ structural model is given by the following
expressions, while the estimation results are showed in Table 5:
ECn = B1,1 Intercept + B1,2 user car + B1,3 user carpool + B1,4 user transit
+B1,5 gender + B1,6 HighInc5 + B1,10 EDU C5 + B1,11 AGE2
+B1,12 AGE3 + B1,13 AGE4 + ς1n
(22)
ACFn = B2,1 Intercept + B2,2 user car + B2,5 gender + B2,6 HighInc5
+B2,10 EDU C5 + B2,11 AGE2 + B2,12 AGE3 + B2,13 AGE4 + ς2n
(23)
REVn = B3,1 Intercept + B3,10 EDU C5 + B3,11 AGE2 + B3,12 AGE3
+B3,13 AGE4 + ς3n
(24)
The structural equations link consumers’ characteristics to the latent variables. Based
on the results presented in Table 5, we can conclude that environmental concern is more
important for transit users than for car pool users. We also observe a negative parameter
for a driving alone user.
High education level has a significant positive effect on the REV variable while the effect
is positive but not significant on both the EC and ACF variables. The effect of age on
EC increases as the individuals get older. The effect of age on ACF is the highest for
people between 41 to 55 years old. Not surprisingly, the effect of age on REV is small
and not significant for people older than 55 years of age.
Note that we also estimate the elements of the covariance matrix. As shown in Table 6,
the elements on the diagonal of the Ψ matrix are significant and show the presence of
heteroscedasticity. In this version, we assumed that the latent variables are uncorrelated.
15
16
TABLE 5 Structural Model Results
EC
ACF
REV
Estimates Student t Estimates Student t Estimates Student t
Intercept
2.434
9.660
-3.094
-18.495
1.293
7.374
Driving Alone User : user car
-0.020
-0.428
-0.118
-2.244
Car Pool User : user carpool
0.097
1.135
0.100
0.938
Transit User : user transit
0.204
2.572
Gender (Female Dummy)
0.258
7.392
0.283
6.474
High Income Dummy (>80,000$)
-0.011
-0.294
-0.001
-0.017
Education level 5 (University)
0.064
1.712
0.008
0.170
0.598
9.522
Age level 2 (26 to 40 years)
0.187
2.279
0.328
3.961
0.592
5.363
Age level 3 (41 to 55 years)
0.262
3.105
0.621
6.657
0.889
7.952
Age level 4 (56 years & more)
0.332
3.702
0.525
5.278
0.228
1.840
Var(EC)
Var(ACF)
Var(REV)
Estimates Student t
0.553
20.934
0.708
23.410
0.449
3.336
TABLE 6 Latent Variables Variances
5.4
Measurement Model
The latent variable measurement model links the latent variables to the indicators, and
a typical equation for this model has the form:
q26ind2 = αq26ind2 + λ1,q26ind2 ECn + λ2,q26ind2 ACFn + ε26ind2 .
(25)
In this example, we can see that the effects on the second indicator of question 26
are measured using a constant and the two latent variables. We have considered 21
indicators, so it is necessary to specify 21 equations. Their relations with the latent
variables are depicted in Table 7 and the estimation results are displayed in Table 8.
As explained before, this model measures the effect of the latent variables on each indicator. Some interesting conclusions can be seen from the results presented in Table 8.
For example, the effect of EC on the indicator related to the support of expanding and
upgrading roads is negative. This sign reflects the idea that car priority in the context
of rising road capacity is negatively perceived because of the negative impact on the
environment.
On the one hand, we see that the effect of EC on the indicator related to the support of
applying road tolls and gas taxes is positive, indicating a perceived positive environmental impact of measures allowing a rational use of the car. Note also that the effect on
the same indicator of the ACF, the other transport related latent variable considered, is
negative although not significant. This sign can be explained because of the perceived
negative impact of this kind of car use restrictions, especially if the user is considering
buying a new car. A similar analysis can be done for the other indicators. For example,
the positive sign of the effect of both transport related latent variables on the support for
reducing vehicle emissions with regular testing and manufacturer emissions standards:
it is perceived with a positive environmental impact but also it is positively perceived
by consumers as a good attribute of a potential new car.
It is worth noting that such results permit us to establish a consumer profile in a way not
possible with standard discrete choice models. Using simple questions we can enrich the
model and obtain better knowledge about the user’s characteristics and his behavioral
attitudes and perceptions.
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Table 7 Indicators and Latent Variables
18
Question 26
EC on Expanding & Upgrading Roads
EC on Road Tolls & Gas Taxes
ACF on Road Tolls & Gas Taxes
EC on Bike Lanes & Speed Controls
EC on Reducing Car Emissions
ACF on Reducing Car Emissions
EC on High Occupancy Vehicules & Transit Priorities
EC on Improving Transit Service
EC on Promoting Compact Communities
EC on Encouraging Short Work Weeks
Question 29
EC on Traffic Congestion
EC on Traffic Noise
EC on Poor Local Air Quality
ACF on Poor Local Air Quality
EC on Accidents Caused by Bad Drivers
EC on Emissions & Global Warming
EC on Speeding Drivers in Neighborhoods
Question 6
ACF on Purchase Price
ACF on Fuel Economy Importance
ACF on Horsepower Importance
ACF on Safety Importance
ACF on Seating Capacity Importance
ACF on Reliability Importance
ACF on Styling
Income Class
REV on rev
Estimates
Student t
-0.392
0.581
-0.091
0.532
0.478
0.295
0.606
0.491
0.206
0.396
-5.405
6.600
-1.389
8.507
7.944
7.856
8.143
8.352
2.994
7.159
0.735
0.901
1.000
-0.061
0.837
1.113
1.107
9.154
9.495
-1.416
14.472
16.200
15.790
-0.004
0.259
0.433
1.000
0.684
0.537
0.371
-0.087
5.008
7.220
11.563
16.241
6.660
1.00
-
TABLE 8 Structural Model Covariates
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6
Conclusion
In the last decade, discrete choice modeling has evolved towards an explicit incorporation
of psychological factors affecting decision making. Traditionally, discrete choice models
represented the decision process as an obscure black box for which attributes of alternatives and characteristics of individuals were inputs and where the observed choice made
by the individual corresponded to the output of the system. The new trend in discrete
choice modeling is to enhance the behavioral representation of the choice process. As
a direct result, the model specification is improved and the model gains in predictive
power. Econometrically, the improved representation – called the hybrid choice model
– involves dealing with a choice model formulation that contains latent psychometric
variables among the set of explanatory variables. Since perceptions and attitudes are
now incorporated, this leads to more realistic models.
In this paper we have described the hybrid choice model, composed of a group of structural equations describing the latent variables in terms of observable exogenous variables,
and a group of measurement relationships linking latent variables to certain observable
indicators. We have shown that although the estimation of hybrid models requires the
evaluation of complex multi-dimensional integrals, simulated maximum likelihood can
be successfully implemented and offers an unbiased, consistent and smooth estimator of
the true probabilities.
Using real data about virtual personal vehicle choices made by Canadian consumers when
faced with technological innovations, we showed that hybrid choice is genuinely capable
of adapting to practical situations. Indeed, the results provide a better description of the
profile of consumers and their adoption of new private transportation technologies. We
identified two travel related dimensions with a significant impact: environmental concern
and appreciation of new car features. We also successfully included in the choice model
a latent income variable to account for the measurement errors associated with the
reported income classes. A valuable positive feature of hybrid choice is the fact that
enriching the model is quite easy: people are used to rating exercises from marketing
surveys, and responses to such questions are simple to include in econometric studies.
Further research will include enriching the model specification through specification testing – taking advantage of the complete information provided by the survey – and analyzing the results of a prediction and simulation exercise, which will permit us to compare
the predictions of a hybrid choice model versus those obtained from a conventional choice
model.
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