RESTRICTED Z0NE

CH AP-T:ER

Modal Split
7.1 INTRODUCTION
The analysis of modal split can be made at trip generation stage or after trip generation as wel
as at or after trip distribution stage. O-D matrix or trip matrix derived from the trip distribution
model is finally converted into the number of matrices representing each mode of transport for
analysis with respect to mode choice model. Modal split is one of the most important aspects
of transportation planning. It is the process of separating person trips by the mode of travel. It
is usually expressed as the percentage of the total number of trips. It refers to the trips made
by private car and other private vehicles as opposed to public transport (road or rail).
Future modal split can only be accurately forecast if the mode choice behaviour of the
traveller is analysed ina scientific manner. There are many factors that govern the individual's
choice of modes which are very complex.
The issue of mode choice, therefore, is probably one of the most important elements in
transport planning and policy-making. It affects the general efficiency with which we can travel
in urban areas. In view of this, it is important to understand the rationale and develop mode
choice models which are sensitive to those travel attributes that influence individual choices ofl
mode. When we look at the trend of modal split in favour of public transport in Delhi given in
Table 7.1, it is surprising that the modal split of such a metropolitan city declines from 62%
to less than 50% from 20001 to 2008.

TABLE 7.1 Trend of Modal Split in Delhi [1]

Year Percentage of modal split
1975 40
2001 61-62
2008 <50 (Including metro)
128
 Modal Split 129

9 FACTORS AFFECTING MODAL SPLIT

There are a number of factors affecting the modal choice [2] of travellers. The following are
the primary factors affecting the modal choice of travellers:
1. Characteristics of the trip
2..Household characteristics
o3. Zonal characteristics
4. Transport system characteristics

Characteristics of trip
The characteristics of a trip-maker can be classified into the following which have aprofound
bearing on making trips:
1. Access to car or other vehicles
2. Ability to drive by possessing a driving license
3. Use of other transport by the trip-maker even if the car is available (for example,
many people prefer to use chartered bus due to convenience rather than driving in
a congested road).
4. Short trip or long trip (for example, short trip is generally performed by personalised
vehicles rather than public transport, if personalised mode is available to the trip
maker).
Household characteristics

1. Income: The income of a person is the direct determinant of the expenses incurred
on the journey. Higher income groups are able to purchase and use private cars or
other vehicles.
2. Car or vehicle ownership: Car/vehicle ownership is determined by the income
and for this reason, both income and car ownership are interrelated in the analysis
of modal choice. Families which own a car prefer private car for trips and families
without car prefer to travel through public transport.
3. Family size and composition: The number of persons in a family, number of
earners, unemployed and other socio-economic factors of family profoundly influence
the modal choice. Some of these factors are responsible for certain captivé trips in
public transport.
Zonal characteristics
l. Residential density: The use of public transport increases as the residential density
increases. This is due to the fact that the areas with the highest residential identity
are generally inhabited by the persons with variation in different ranges of income
group, dominated by low income group and middle income group. It is also found
that higher density areas are served well by public transport. High density area has
an advantage of creating transit-oriented development.
 Policies
Planning-Principles, Practices and
130 Transportation
Transport system characteristics
relative
It is a measure of the accessibility of that zone
1. Accessibility ratio:
to all
network and highway netweet
other zones with respect to mass transit
ratio: The ratio of the travel time by public transport to the travel
2. Travel time the attractiveness of that zone
private car gives ameasure of
time by
travel by public transport to the cost of
3. Travel cost ratio: It is the ratio of cost of vehicle ownership level os
private car and is a measure of income level or
travel by
mode.
the choice of travel
system is composed of
The travel time by public transport
transport vehicle at origin
(i) Time spent in walking to public
transport vehicle
(ii) Time spent in waiting for public
(ii) Time spent in public transport vehicle
transport vehicle to another
(iv) Time spent in transfer from one public
vehicle at destination
(v) Time spent in walking from public transport
The travel time by a private car is composed of
(i) Time spent in driving the car
(ii) Time spent in parking at destination
(iii) Time spent in walking from parked vehicle to the destination

7.3 TYPES OF MODAL SPLIT

There are four types of modal split models [3] and can broadly be divided into two categories,
ie., related to trip generation and trip distribution stage. Modal split related to trip generation
stage is generally called trip-end modal splitand when it is carried out at or after trip distribution
stage is known as trip interchange modal split. The details are presented in the subsequent
sections.

7.3.1 Trip-end Modal Split Models

One of the primary aims of transportation planning is to estimate the travel demand. In passenge
transportation, the travel demand can be classified into the demand related to private vehicle
passenger trips and public transport trips. In many situations, personal characteristics become
important for the selection of mode choice. Modal split models immediately after trip generation
is generally a preferred option for mode choice model. It is called trip-end modal split model.
In this way, different characteristics of a person could be preserved and used to estimate
the modal split. The modal split model of this type is related to the choice of mode and features
like income, residential density and car ownership. This is also called pre-distribution modal
split. There are two possibilities in pre-distribution modal splits:
1. At trip generation stage
2. After trip generation, but before trip distribution
 Modal Split 131
1. At trip generation stage itself, it is necessary to derive separate multiple linear
regression equation for each mnode of transport. The factors that are
considered to influence modal choice into this type of procedure are the car
normally
residential density and relative accessibility of the zone of the origin to theownership,
facilities.
transport
The multiple regression equation (Eq. 7.1) is an example of mode choice model
through which trips by public transport can be calculated at the trip generation stage.
Y= 10 + 0.29x1 + 0.44x) + 0.68x3
(7.1)
Le Yis the number of trips by public transport, x is the
the distance to central area and x3 is the accessibilitynumber
of dwelling units,
by public transport.
a When modal splits are carried Out after generation but before distribution, then the
trin generations are calculated on the assumption that the mode of travel
has no
nfuence of trip generation. After determining the total trips production and attraction,
these trips are allocated to public transport system and private car by considering the
relative attractiveness of each mode, as measured by variables considered to
govern
modal split. This type of modal split [4]was developed in the USA during 1950 and
1960. In this model, the percentage of zonal trips using public
against zonal car ownership or any other land use variable fromn transport
is plotted
which best fit line
is obtained, leading to the development of diversion curve.
Advantages
1. The advantage is that these models could be very
accurate in the short run, if public
transport is available and there is a little congestion.
2. They are less difficult and less costly as
compared to post-distribution methods.
3. The possibility of separate public transport and private car
this method is a desirable feature because of the distribution afforded by
differing trip lengths by car and
public transport.
4. This method reflects factors such as income, car
employment which are the characteristics affecting trip ownership, family structure,
generation.
Disadvantages
Lhese methods are strongly wedded to the existing and
ransport service. They are inappropriate to the studieshistorical levels of public
improvements to public involving planning of
service are contemplated. transport systems, where significantly different levels of
2. The
characteristics of the transportation system are fed on an
but this procedure fails to reflect the particular zone to zone
average area-wide basis
3. It combination.
4. It is
does not consider the trip
generation characteristics fully.
insensitive to the future developments in interzonal travel.
13.2 Trip
This is
the Interchange model;
Modal Split Models
ppost-distribution modal split is applied either while performing trip distribution
132 Transportation Planning-Principles, Practices and Policies

analysis or after the distribution stage. In this method, we carry out modal split at or
distribution, but before assignment. When modal split exercise is caried out at trip distribution
function (5] of transport imped
stage, it considers the gravity model with an exponential
to estimate the amount of interzonal trips for each transport modes (Wlson, 1969). The modsl
asunder:
derived from the entropy maximisation method is given
1
Q,(1)
EO,(m) 1+e,(2)-0] (7.2)
O;1) is the estimate of number of trips from zone i to zone j by mode 1, i2) is the estimate
of number of trips from zone i to zone j by mode 2, e1S the travel impedance factor and
0 is the parameter to be calibrated from gravity model.
Trip interchange model dealing with allocation of trips after trip distribution is concerned
dependent variable. ie
with the application of multiple regression equation that specifies itsindependent variables ars
the proportion of trips from zone ito zone j by one transport. The
zonal land use variables which are concerned with either origin or destination zone and transpor
characteristics between the two. This type of model can be expressed as under:
T, (m) = k+ bxË + by + + bax3 (7.3)
E,T,(m)
where x, is the land use variable at origin end, x, is the land use variable at destination end.
constant b.
Xa is the land use variable associated with origin and destination zone k is the
b, and b, are coefficient, and TAm)/2T{m) is the proportion of trips between the two modes.
This model may also consider the form of diversion curve, apart from the multiple
regression equation [Eq. (7.3)]. The advantage of this type of model as against trip-end modal
split is that it can incorporate the effect of public transport system where there is a concern in
the improvement of public transport system.
Diversion curve
In the development of diversion curve [6], variables like relative transport cost, relative travel
time, and the ratio of total time spent in walking, waiting and transferring to public transport
against
to the time spent in parking, walking to and from motor car, etc. are taken into account
the share of public transport trips. This technique has been used in the conduct of transportation
studies carried out in Toronto. For working out the travel time ratio, the following are considered:
Travel Time Ratio (TTR): TTR is expressed as the ratio of door to door travel time by
public transport divided by door to door travel time by private vehicles.
(7.4)
TTR =

where, is the time spent in public transport vehicle, x is the time spent in changl" waiting at
spent in
public transport, vehicle, X, is the time spent in walking, xA is the time in driving a car, X)
origin, xs is the time spent in walking at destination, xG is the time spent
walking at destination.
is the time spent in parking at destination and xg is the time spent in
The travel time ratio can also be defined as under: (7.5)
CR =
Xo t 1 +0.5 X/m
 Modal Split 133

where, CR is the relative cost of travel, x, is the transit fare, Xyo is the cost of gasoline,
the cost of oil changes, xi2 is the parking cost at destination and mis the average car
Occupancy,
In addition to the above, relative travel service is also considered for the development
is characterised by the ratio of excess travel times taken by transit or a
ofdiversion curve. It
private vehicle.

SR = (7.6)

where, SR is the service ratio relative, x3 is the transfer time between transit vehicles, xj4 is
the time spent in waiting for transit vehicles, x1s is the walking time to atransit vehicle, xi6 is
the walking time from a transit vehicle, X17 is the time spent in parking and Xg is the walking
time from parking to destination.
The mode choice version of diversion curve analysis relates to the ratio of travel time,
say Turunsit/ (automobile) as Can be seen from Figure 7.1.

100

50

1 2
Percentage of users R
using transit
FIGURE 7.1 Diversion curve.

The graph indicates the percentage of users that will choose transit on the basis of R
value which is calculated from the above ratio. The technique can also use travel cost rather
than travel time for calculating the diversion ratio. It is primarily based on the empirical
vUservations and its improvement with respect to more correctness of users travel time data
can lead to a better
prediction.
Advantages
l. The advantage of this kind of modal slit model is that the characteristics of the journey
and the alternative modes available can be included in the formulation of this model.
Apart from this, policy decisions can also be tested.
2. This is beneficial for long-term
decision-making.
t is useful in situations where serious consideration is given to the public transport
planning.
T he method makes it possible to develop modal split based on a wide range of
tansport system variables influencing the modal choice.
134 Transportation Planning-Principles, Practices and Policies

5. The method considers private car and public transport

instead of zonal basis as in pre-distribution methods. usage on
zone to 20ne
Disadvantages basis
1. Trip interchange model is more complex,
especally if the number of zones
2. It also has one major drawback that the total person trip
distribution
out before any modal choice) ignores the different lengths of is (which
public transport. journey by carcarrianded
7.4 TWO-STAGE MODAL SPLIT MODEL
For the separation of captive and choice riders, a
two-stage modal split
developed. This model works ith the identification of trip ends with respectmodel can also k
to both
riders separately. The choiceproduct
riders iare
on
and attraction for transit captive riders and choice transit
allocated to a transit or a car according to the choice model. Figure 7.2
procedure of modal split made between the different modes of shows the step-wige
motorised modes are segregated against the other trips. In the transport. In the first stage, non
public transport trips and private trips are made. This may be second stage, apportionment of
ratio or travel cost ratio. The ratio of travel time by public carried out by using travel time
may be considered to develop a diversion curve, as shown in transport to the travel time by car
Figure 7.2.

All trips

Trips on foot and

trips on bicycles Trips by other
transport modes

Trips by private
vehicles Trips by public
modes

Trips by buses
Trips by railways
FIGURE 7.2 Two-stage modal split.
7.5 MODAL SPLIT MODEL ON
BEHAVIOURAL BASIS
The types of modal split models discussed so far are primarily
concerned with the aggregate
 Modal Split 135

zonal It would be interesting to understand and incorporate the choice behaviour of

level.
or individuals while selecting the mode in the development of mode choice model. In order
theincorporate the choice behaviour of the individuals in the model, the concept of disutility
to
generalised cOst of travel has to be understood first. The concept of disutility model is
or
described here.
A utility nodel or function measures the degree of satisfaction that people derive from
their choices. A disutility function represents the generalised cost that is associated with each
choice.
In modalsplit, the characteristics of the trip also bear a relationship to the utility associated
with choosing a particular mode of travel.
The utility (or disutility) [7] function is expressed as a linear weighted sum of the
independent variables of their transformation:
(7.7)
where Uis the utility derived, x*z, and x, are the attributes denoting travel and socio-economic
parameters of travellers and a denotes parameters.
In mode choice, Uis disutility and negative. This is because typical independent variables
include travel times and cost that are perceived as losses.
There can be a separate utility function for different types of modes. For example, the
following three utility functions are expressed with respect to car, auto-rickshaw and bus:
Ucar =3.1 + 2.lx, + 2.5x3 + ayx4 (7.8)
auto-rickshaw = 4.5 + 3.lxj+ 2.6x, + 2.8x + 1.1x4 (7.9)
Upus = 5.7 + 1.lx + 2.8x, + 1.8x, + 1.7x4 (7.10)
These are called mode specific utility models because same attributes are given different
weights for different modes, though it is not essential to add same variables for all modes. For
example, the utility equation for a car does not have variable x, as against the other modes. Let
us assume that xË, *2, , and x4 represent access plus egress time, waiting time, line-haul time
and out of pocket cost in rupees, respectively. Therefore, the waiting time for the car does not
arise. Accordingly, it is not reflected in the utility equation for the car.
Let us demonstrate an example of developing mode specific utility model based on the
recent study conducted at Gandhinagar, Gujarat[18]. Model inputs for mode choice set are car,
twO wheeler, auto and bus, while the variables used are income, travel time, travel cost, and
Tequency. Table 7.2 presents mode specific utility model for the above mode choice.

TABLE 7.2 Mode Specific Utility Model Output

Mode Variable Coefficient b/St. Er.
Standard error P[lz| > Z]
Intercept -1.612 0.975 -1.653 0.987
Income 0.839 0.412 2.037 0.008
Car Travel time -0.131 -2.417
0.054 0.013
Travel cost 0.465 0.190 2.445 0.006

Frequency 0.000 ...Fixed parameter)..

136 Transportation Planning--Principles, Practices and Policies

Variable Coefficient Standard error b/St. Er.

Mode
0.897
P[lzl >Z)
4.137 4.612
Intercept 0.000
Income -0.137 0,068 -2.013 0.054
0.889 0.579 L536
Two wheeler Travel time 0,000
-0.756 0.215 -3.5 16
Travel cost 0.000
0.000 ..(Fixed parameter)...
Frequency
2.298 1.857 1.237 0.899
Intercept
Income -0.137 0.059 -2.320 0.009
-2.138 0.990 -2.159 0.014
Auto Travel time
Travel cost -0.218 0.045 -4.812 0.001
0.250 0.079 3.174 0.057
Frequency
-4.822 0.974 -4.953 0.191
Intercept
-0.695 0.380 -1.829 0.022
Income
-3.157 0.579 -5.453 0.000
Bus Travel time
Travel cost -8.064 2.410 -3.346 0.000
-0.403 0.188 -2.146 0.061
Frequency

Final utility equations

=-l.612 + 0.839 x Income - 0.131 x Travel tÉme + 0.465 x Travel cost
Ucar) =4.137 0.137 × Income + 0.889 x Travel time - 0.756 x Travel cOst
U(two-wheeler)
= 2.298 0.137 x Income -2.138 x Travel time 0.218 × Travel cost + 0.250
Ulauto)
x Frequency
Ubus) =-4.822 - 0.695 x Income - 3.157 x Travel time 8.064 x Travel cost -
0.403 x Frequency
Table 7.3 presents the statistics as a part of the model output.

TABLE 7.3 Statistics as a Part of the Model Output

Number of Chi-squared R squared Adjusted R
Model a Log squared
likelihood parameters value
function
-713.670 4
Constant only 0.625
-249.005 20 151.249 0.651
Constant, income, time
cost, frequency
that
based on the assumption
On the other hand, the abstract utility equation derived is their attributes, each of which
of
people perceives goods and services or make choices in terms mode choice
model can
of abstract
is weighted identically across the choices [8]. An example
be shown as under: (7.11)

U= 2.4 + 3.2x; + 2.7x, +4.lx3

 Modal Split 137

It is a single equation to measure utility. The values of utilities for different modes of
travel can be worked out on the basis of the magnitudes of the attributes of x of those competing
with each other. If one mode is efficient than the other modes, then it will be reflected in the
calculated utilities. Though attributes abstract mode choice formulation appears to be stronger
than the mode specific choice formulation, but the first constant term in Eq. (7.11), which is
supposed to capture the effect of the variables, is not explicitly incorporated in the model. In
view of this, it is advisable to capture the unexpressed differences by calibrating the alternative
specific constants in the attribute specific mode choice formulation. For example, the equation
representing the above facts can be expressed as under (Eq. 7.12).
U = ay + 3.2x + 1.7x, + 0.9x, (7.12)
Eor different modes, the values of a, will be different.
A recent study[18] (conducted at School of Planning and Architecture for developing
Smart Mobility Plan for Gandhinagar, Gujarat was successful in developing an abstract utility
model where a number of new transport modes were contemplated. Since metro is already
proposed in the study area, an abstract logit model has been developed using NLOGIT Software
from base year data so as to predict the horizon year modal split which has an advantage
of predicting utility equation of any new mode to be incorporated for future as in this case.
Variables considered for predicting modal split are income, travel time, travel cost and frequency.
Coefficients and statistical figures are presented in Table 74.
TABLE 7.4 Abstract Logit Model Output
Variable Coefficient Standard error b/SL,Er. P(z > ZÊ
Income 0.233 0.104 -2.251 0.003
Cost 0.547 0.093 -5.894 0.000
Time 0.140 0.064 2.205 0.006
Frequency 0.125 -0.077 1.632 0.005
ASC, car 0.688 ...(Fixed parameter)..
ASC, two wheeler 1.148 ...Fixed paraneter)..
ASC, auto -0.811 ...(Fixed parameter)...
ASC, bus -1.026 ...(Fixed parameter)...
Statistical tests
Log likelihood Number of Chi-squared R squared Adjusted R
function parameters value squared
-321.3894 8.000 621.470 0.595 0.581

Oniity equations derived are used to calculate probability for different modes to be used
for travel.
For
observed mode purpose
of using the model for horizon year, comparison between estimated and
split by developing mode and specific mode choice model is undertaken for
validation of the model. The estimated shares for cars, two wheelers, auto-rickshaw and public
transport are 21.3%, 46.8%, 11.3% and 20.6% as against observed 23%, 52%, 8% and 17%
Tespectively. It can be seen that the mode-wise differences are insignificant, thus generating
confidence to predict future travel pattern.
 Planning--Principles, Practices and Policies
138 Transportation

7.6 LOGIT MODEL

deterministic
believed that the stochastic model is better than the deterministic model, as the
It is to the real-life situations. On the other
model of choice may be confined in its replication the judicious rules of choice exactly.
hand, behaviour of individuals may not always consider the deterministic model, Ir
predicted from
Also, the random behaviour of a traveller cannot be information about the transportation
is also true that the potential travel may not have correct
modes to be selected. It can be said
system and the availability of the number of alternatives
a random function which takes
that a good model is the one where choice functions consider
diferent values with certain probabilities. random
The perceived utility curve U.) can be called random function and expressed as
utility model, as given under:
Ui) =V(i) + e(i)
where U)) is the choice function for the alternative i, V) is the deterministic function of
the attributes of (i) and e) is a stochastic component, a random variable that follows some
distribution.
It may be said that the individual will select an alternative () if the perceived Ui) of
alternative (i) is the largest of all such values. Therefore, the probability that (i) is chosen can
be given as
P() = P[U) > U)] for all j
It may be further written as
P()) = P[V) + e(i) > V) + ei), for all j i]
P()= P[eý) < V(i) - Vù) + e()), for all j # )
P() = [F[V) V) + e()] for all jil f(0)-do (7.13)
where F() is the joint distribution function [4] of [ei), ei), ...] terms of the alternatives and
fAØ) is the marginal density function of e().
Using Eq. (7.13), logit model can be developed. Random components of a choice utility
function (as expressed above) are all independent. The expression of Logit model can also be
derived from Gumbel distribution.

Fe =ete 0> 0; -<x< a (7.14)

Using the Gumbel distribution, the following
expression is derived:

j=l

e)

j=1'
 Modal Split 139
logit model and also referred to as
Thisis known as multinomial (MNL) when more than two
alternatives are considered, as explained in the
for its mathematical subsequent section.
Logit model offers numerous
advantages
than that of the
manipulation.
multinomial
Its parameter estimation and
application [9] are
easier probit model. In statistics, logistic
known as logit model) isconsidered to be used for the prediction of regression (usually
of an
event. For example, if we wish to probability of occurrence
predict mode choice behaviour of a person from
the knowledge of person':'s age, sex and socio-economic background, logit
regression model may be used for this purpose. This model model or logistic
medical and social sciences. The concept of this
[10] has been extensively used
logistic function can be described from
the explanation of logistic function whose probability always ranges
(Figure 7.3). This can also be expressed as between zero and one

f()=
1+e

0.5

0
6 -2 0 4 6
FIGURE 7.3 Logistic function with v; on the horizontal axis and
fv) on the vertical axis.
A logistic function or logistic curve is a
common
purpose. It can accept any input from negative infinitysigmoid curve used for the prediction
produced in the range between zero and one. Here, the to positive infinity. The output is
variable
described earlier. As logit model is simply a log ratio of the V is the disutility of travel, as
to the probability of not selecting a probability of selecting a mode
mode, it can also be expressed as:

As defined earlier, V, is the disutility of

using travel mode. Therefore,
V;= d + ajX + ayy t . + a,X,
P
log 1-P,

Pa =ei PeVi
P(1 + ea) = ea
P, =
This als0 (1+e)
expresses the logit model for estimating the probability of selecting a mode.
140 Transportation Planning- -Principles, Practices and Policies
7.7 PROBIT MODEL
Probit analysis [11, 12] is a type of regression used to
It transforms the sigmoid dose-response curve to a analyse binomial
straight line
regression either through least squares or through the maximumthat can then response varivables.
be
the relationship of response to dose was sigmoid in
linear data. nature and likelihood. earanlaileyrsetdimes,
regression
In
was only
by
The probit model considers the percent
response with
used on
cumulative normal distribution. The normal distribution in respect to log dose
other probability distributions, influences the predicted this probit method, as with the
of possible doses. It has alittle response rate at the high against the
influence near the middle. The and low ends
using this sigmoid curve is carried out comparison
using response rates of 50%. The of
dif erentmodel is
formulated as under: drugs
probit
P= a+ B[log1o(Dose)]
As can be seen from Eq.
binomial (7.15), probit analysis is a specialised
response variables. Regression is a method regression model of
compare the relationship of the response variable or of fitting a line to the data in order to
variable X. The final form of Eq. (7.15) can be dependent variable Ywith the independent
expressed as under:
Y= a+ bX +e
where a is the y-intercept, b is the slope of (7.16)
the line and e is an error term.
Warner[13], Lisco[14] and
statistical analysis technique calledLave[15]
probit
developed binary modal choice models including
analysis. This concept is based on the premise that
the choice trip-makers that respond by
type of relationship. This shows the choosing a particular mode of
transport will follow the
proportions of trip-makers that would
the difference between the
generalised cost of using public transport and carusetransport
private cars as
Lave[14] worked out varies.
from a set of 1956 data forEq.the(7.17) for estimating the probability of bus-car modal patronag®
Chicago area using
probit analysis.
Y=-2.08 + 0.00759kWAT +0.0186AC -
R= 0.379 0.02541DCc + 0.0255A (7.17)

where Y is the binary variable with positive

magnitudes denoting transit riders and negative
magnitudes denoting car riders, kWAT is the time
trip-makers wage rate and his marginal preferencedifference between the modes multiplied by
for leisure time, IDCc is a binary valued
comfort variable multiplied by income and trip distance. (Tt is the
the alternative modes.) A is the age of difference of cost between
trip-maker and AC is the comfort variable.
7.8 BASIC
MODELS ASSUMPTIONS/REQUIREMENTS OF LOGIT AND PROBIT
1. The observations based on dependent variable Yare assumed to be randomly
sampled
from the populationof interest (even for stratified samples or choice-based samples).
2. Y is caused by or associated with the Xs.
 Modal Split 141

There is an uncertainty in the relation between Y and the Xs, as reflected by a

3. scattering of observations around the functional relationship.
distribution of error terms must be assessed to determine if a selected model is
4. The
appropriate.

Inputs for Logit and Probit Models

7.8.1
Discretevariable Yis the observed choice or classification such as brand selection, transportation
mode selection etc. For grouped data, where choices ar observed for homogeneous experimental
units or observed multiple times per experimental unit, the dependent variable is proportion of
the choices observed. Input to this type of model is one or more continuous and/or discrete
variables X (variables represent the attributes. of the choice maker or event).

Models
Z.8.2 Outputs of Logit and Probit
1. Functional form of relation between Yand Xs
2 Strength of association between Y and Xs (individual Xs and collective set of Xs)
3. Confidence in predictions of future/other observations on Y given X
As mentioned, an alternative to the logistic regression analysis can be made using probit
analysis. These analyses (i.e., logit and probit) are quite similar to one another. Logit analysis
is based on log odds, while probit analysis uses the cumulative normal probability distribution.
Figure 7.4 shows a cumulative normal distribution.

04
Cumulative normal distribution

0.5

FIGURE 7.4 Probit curve.

functioniShaped
as shown incurve runs7.3.
Figure fromThezero
twoto procedures
one. It is very
are sosimilar
similarto that
the graph
one canof easily
the logit
be
confused with one another. The bottom line is that logistic regression and probit analysis
produce predicted probabilities. An example of predicted probabilities for logit and probit
analyses is shown in Figure 7.5.
142 Transportation Planning-Principles, Practices and Policies

14 Predicted logit and probit probabilities

Logit

0.5
Probit

-2 2
-1
Utility value
FIGURE 7.5 Logit and probit curves.

7.9 MULTINOMIAL LOGIT MODEL

The multinomial logit (MNL) model is the most commonly applied model to explain and
forecast discrete choices due to its ease of estimation and foundation in utility theory. The MNI
model is a general extension of the binomial choice model to more than two alternatives. The
universal choice set is C, which contains j elements and a subset of C for each individual C
that defines its restricted choice sets. It should be noted that it is not a difficult task to define
restricted choice sets for individuals.
The concept of derivation of the MNL model has been already expressed in Section 7.6.
eVn
P,()=
c en
In this expression,
1. Utility for traveller n and mode i= Ui, = Vin + Ein
2. P,) is the probability that traveller nchooses mode i.
3. Numerator is the utility for mode i for traveller nand denominator is the sum of
utilities for all altemative modes C, for traveller n.
4. The disturbances E, are independently and identically distributed.
5. The disturbances are Gumbel distributed with location parameter F and a Sedlo
parameter u > 0.

7.9.1 Incremental (or Pivot-point) Logit Model

The MNIL model gives Eq. (7.18).
(7.18)
Px =
to
alternatives belonging
policies
It gives the probability of choosing alternative K, given the utilitiesofof a combinationof
the choice set. Consider the general case whereas a consequence
 Modal Split 143

of one or more alternatives are changed. Let AU, represents

utility function, utilities
the
in
change in the utility of alternative x. By applying Eq. (7.18) to calculate the new share of
the it yields
each alternative,
P=

By dividing
the numerator and denominator by Eexp(U,), we get
P(K) x eAUk
Pk) =
E, P(r)eAU
me the revised probability P of choosing K due to the changes in the utilities of one or
nre alternatives can be incrementally computed by pivoting about the baseline probabilities
P.. The baseline probabilities do not need to be calculated by the MNL model; they may be
btained from surveys of the existing conditions. We take a situation where the utilities of
cat, bus and auto-rickshaw are Ua) = -0.625, Ub) = -0.1530 and U = -0.070, respectively
derived from the abstract utility function [8], Uk=a - 0.025 - 0.032X, 0.015X, 0.002X4
and their probabilities work out to be 0.489, 0.198 and 0.313, respectively. If auto-rickshaw fare
is changed from ? 75 to ? 150, then the change in the utility of auto-rickshaw will be -0.002
x75 =-0.15 according to the utility function discussed here. If this is taken intoconsideration,
the new probability of bus can be worked out using the following expression.
P, =
0.198x exp(0) =0.207
0.489x exp (0) + 0.198x exp(0)+0.313x exp(-0.15)
Similarly, new probability of car, P = 0.511 and probability of auto-rickshow Par= 0.282.
Therefore, the change of utility of auto-rickshaw will definitely affect the probability of
bus and car.

1.9.2 Independent of Irrelevant Alternatives (l A) Property

mtinomial logit model, if x and y are the alternative modes, then the ratio of the probability
aSSOciated with the two alternatives can be expressed as Eq. (7.19).

P (7.19)
Po)
in theeen trom the expression that the two probabilities are the function of the difference
For
utilities of the two alternatives. This is not affected by the utility of any other alternative.
example, if we look at the example mentioned above with respect to the three alternative
modes that include car, bus and auto-rickshaw, the ratio of the probabilities of the first two
alternat2.47.ive Themodes, 1.e., car and bus which are 0.489 and 0.198, respectively, works out to
be
probabilities ofchange
car andin the
bus, utility of the alternative, ie., auto-rickshaw results in the new
ie., 0.5ll and 0.207, respectively. If we take the ratio of the
utpriolhbabi
ty oflitianes, alternative
this works out to be 0.247. It, therefore, demonstrates that the change in the
does not
have any infiuence on the remaining two alternatives. In other
144 Transportation Planning--Principles, Practices and Policies
of two altermative moder
words, we can say that there is no change in the ratio of probabilitie
of situation is known
though there is a change in the utility of the other mnode. This type
independent of irrelevant alternatives.
7.9.3 Demand Elasticity Using MNL
P(m1 = Di: I2. C C2)= D), then the
If the probability of the major mode is expressed ascalculated
mode 1is by
price elasticity of demand for travel by
E(1:C) = (0D,(.)/0C) x C/D()
computing modes can be calculated h..
Similarly, the extent of this relationship between the describes the percentage chanoe in
demand, which
the concept of cross price elasticity of change in the price of travel of anothes
amount of travel by one mode following a percentagetravel by mode l with respect to the
demand for
mode. Thus, the cross price elasticity of
of mode 2 is measured by
E(2:C,) = (0D,()/0C) x C/D,)
for a binary mode choice model can then h
The expressions for direct and cross elasticity
derived as E(1:X) = (l - Pml)X
and
E(2:X) = -a -[Pm2)]X
to variable X, E(2:X) is the cross elasticity
where E(1:X) is the direct elasticity with respect
respect to variable X, a, is the model parameter for attribute, Pm) is the probabilityof
with choosing mode 2.
choosing mode 1and Pm2) is the probability of split model through a household
Chari [17]conducted a study on developing a modal elasticity of mode choice using
developed
study interview in Ahmedabad metropolitan city. He elasticities. Table 7.5 presents the results of
logit model by considering both direct and cross
ownerships and occupations. The values in Table 7.5,
the mode choice elasticities for allmode
the competing mode for one percent change
show the percentage change in the probability of
Table 7.5 that the increase in travel cost relative to the
in the travel cost. It can be seen from
demand of car and scooter usage as compared
alternative mode has a little influence on the
to bicycle and walk groups.
TABLE 7.5 Mode Split Elasticities of Work Trips
1% change in time 1% change in cost
Group Mode owned Cross
Cross Direct
Direct elasticity
elasticity elasticity
elasticity 3.53
0.99
Car 2.44 8.68 0.094
Employed 3.41 0.035
Scooter 1.26
5.67
Bicycle 0.547
6.09 0.318
Walk 1.53 0.149
Car 0.824 1.75
|Self-employed 2.88
0.36
Scooter 1,44
8.2
Bicycle 0.96 5.93
Walk 3,88
 Modal Split 145

EXAMPLE 7.1 Given the utility expression

U,= A - 0.05T, -0.04T, - 0.02T, - 0.01C
the access time, T, is the waiting time, T, is the riding time Ug is the utility, A
where T, is
the constant
value, and C is the out of pocket cost
is
Annly the logit model to calculate the division of usage between the motorised two
wheeler mode (A7 =0.005) and bus (A = -0.05) (data is as per Table 7.6).
i) Estimate the shift of patronage that would result from doubling the bus out of pocket
COst.

TABLE 7.6 Data of Travel Attributes of Motorised Two Wheeler and Bus
Mode T min T mìn F min CRs
Motorised two wheeler 10 45 150
Bus 20 20 60 100

Solution Part (i) is solved by substituting the given values into the utility function and solving
the logit model equation. The calculations and results for part (i) are shown in Table 7.7.
TABLE 7.7 Calculations and Results of Part (i)
Mode T T, Ag P
Motorised two wheeler 10 45 150 0.0050 -2.95 0.055 0.753
Motorised two wheeler 20 20 60 100 -0.05 4.005 0.018 0.247
0.073 1.00

Part (ii) is essentially identical to part (i) except for the change in the out of pocket cost
tor bus travel. Its calculations and results are shown in Table 7.8.
TABLE 7.8 Calculations and Results of Part (ii)
Mode T, C Ag P
Motorised two wheeler 10 45 150 -0.0050 -2.95 0.055 0.896
Bus 20 20 60 200 -0.05 -5.05 0.0064 0.104
0.0614 1.00

ASgnificant number of bus riders are predicted to shift to the automobile.

(24-10) x 100 = 58%
24
The increase in automobile use will be
(89 - 75) x100 = 15.7%
89
EXAMPLE
abus in the 7.2 We have estimated the modal share of two modes, i.e., automobile car and
urban area whose abstract utility equation is given. What will be the modal share
146 Transportation Planning-Principles, Practices and Policies

of all mnodes of transport when metro is introduced in the later stage? Further,
modal share of bus, where the fare of metro is increased to 75? what will be
U, = ap- 0.027x - 0.033x - 0.017x, - 0.004x,
where x, is the access time, x, is the waiting time, x, is the line-haul and x4 is the
cost. Table 7.9 shows the attributes along with the values of X|, 2, Xa and x. out of pocket
TABLE 79 Data of Travel Attributes of Automobile and Local Bus
Attribute
Automobile 10 25 105
Local bus 15 20 45 55

Solution
a = 0, ag= -0.1
U, =0 -0.027 x 10 0.033 × 5 - 0.017× 25 - 0.004 x 105
= -1.28
UR =-0.1 0.027 x 15 -0.033 x 20 - 0.017 x 45 0.004 × 55
=- 2.15
e.28
Pay = (e-l.28 = 0.705
+e2is)
-2.15
e
P) = e-l +e215) = 0.295

Assuming the total number of trips to be 6000.

Oa = 0.705 x 6000 = 4230 trips for automobiles
QR = 0.295 x 6000 = 1770 trips for local bus
Attributes of metro to be introduced are shown in Table 7.10.
TABLE 7.10 Attributes of Metro to be Introduced
Attribute:o.
Metro 15 10 35 80

We assume the new mode, metro is to be introduced whose attribute specific constant
value is -0.08. The utility function for rail can be written as under:
Uz = -0.08 0.027 × 15 0.033 x 10 - 0.017 x 35 - 0.004 × 80
=-1.73
el.3
PR = = 0.31
(eo-1.73 +el.28 +e215)
el28
PA) = (e-173 +e-125 +e215) =0,486
 Modal Split 147
p2.16

Pp = = 0.204
(e -1.73 +e L.28 te 215)
Op = 6000 × 0.310 = 1860
OR = 6000 × 0.486 = 2916
OR = 6000 x 0.204 = 1224

Let the
increase in fare be 75 cent for metro
AUR = -0.004 x 75 = -0.3
P(K)xAUk
Piky = E,P(r)eAU,
0.204¢º
PB) 0.489e +0.313 x(-0.3) + 0.198e
=0.344

tcan be seen that an increase in the fare of metro would result in the shift in patronage of
the bus.

EXAMPLE 7.3 Ahmedabad and Vadodara are connected by expressway (92 km long 4 lane
divided carriageway) and National Highway-8 (110 km long, converted from 4 lane to 6 lane
divided carriageway in December, 2015). Average operating speed of cars on expressway is
85 kmph and that on NH is 95 kmph. Before December, 2015 average operating speed of cars
on NH was 60 kmph (Mileage=12 km/litre) and payable toll was 50. Now, after December
2015, cars are able to maintain uniform speed for majority of travel resulting into I5% more
tuel efficiency compared to expressway. On an average, car runs 12.5 km for l litre of petrol
R60fitre). Toll charge payable per trip on expressway is 95, whereas it is raised 160 from
*50 on NH-8. Based on the travel behaviour study, utility function is developed as under:
U, = A - 0.18TT- 0.14TC
A=0 for expressway and -0.397 for National Highway. If the annual average daily car
Taric is 11,675, estimate the shift in car traffic among these two highways comparing pre
Docember 2015 and post-December 2015 periods on annual basis considering other parameters
COnstant.
Solution
Up= A -0.18TT - 0.14TC
On expressway,
Travel time = 92/85
= 1.08 hrs
Travel COst = fuel
consumption +toll tax
= 92/12.5
={7.36
Iravel cost =(7.36 x 60) + 95
=536.60
 Practices and Policies
148 Transportation Planning-Principles,
Pre-December on NH,
Travel time = 110/60
= 1.83 hrs
Travel cost = 50 + (110/12 x 60)
=600
Pre-December 2015, the shift in car traffic is shown in Table 7.11.

TABLE 7.11 Shift in Car Traffic in Pre-December 2015

Highway A; Travel time Travel cost U

NH-8 -0.397 1.833 600 -84.72 1.60 x 10
Proportion
8.16 x105
Expressway 1.08 536.6 -75.31 1.96 x 10-33 0.999

Post-December on NH,
Travel time = 110/85
= 1.15 hrs
Travel cost = 160 + (110/12 x 0.85)
= 627.5
Post-December 2015, the shift in car traffic is shown in Table 7.12.

TABLE 7.12 Shift in Car Traffic in Post-December 2015

Highway Travel time Travel cost U Proportion
NH-8 -0397 1.115 627.5 -88.44 4.00 × 10-39 2.04 x 106
Expressway 0 1.08 536.6 -75.31 1.96 x 10-33 0.999

Though after implementation, stillthe utility difference between expressway and NH-8 is
high. Thus, more vehicle will continue to go through expressway as utility difference increase.
EXAMPLE 74 Proportion of passengers carried by rail and road transport modes along
an industrial corridor of 200 km length is 0.4 and 0.6 respectively. The regional travel mode
choice study has obtained following utility function:
V;= -0.16 t 0.12 C7 0.35 w
where, tt is travel time in hours per trip by mode k, C is out of pocket cost in rupees per trip
by mode k and w; is waiting time for mode k in minutes.
()) Average journey speed by road drops from 50 kmph to 30 kmph due to bottleneck
created by closure ofa two-lane bridge along the corridor, what will be the effect of
this on mode shares of railways and roads?
(ii) If total daily passenger movement is 1,18,400 along the corridor, estimate the chang
in VKT and PKT by road considering average vehicle occupancy by cars as 2
Solution
(i) V = 0.16 t¡ -0.12 C7 -0.35 w
 Modal Split 149
bus,
V, for base case for
X =0.12 C7 -0.35 w
=.200/50 = 4 hrs
t
= 0.16 x 4) + X
V, for design case
t = 200/30 = 6.67 hrs
=(-0.16 x 6.67) + X
Change in utility
= (-0.16 x 6.67) - (0.16 x 4)
= -0.4272
pt =(0.6 x e22y(0.6 xe0.4272 + 0.4e)
= (0.3913)/(0.79)
= 0.494 by road.
Therefore,
Share by road = 0.494
Share by rail = 1 0.494 = 0.506
() Total daily passenger movement is 1,18,400
Share by road = 0.494 x 1,18,400 = 58490 passengers
Share by rail = 0.506 × 1,18,400 = 59910 passengers
Average vehicle occupancy by cars as 2.5
Vehicle occupancy by car = 58490/2.5
= 23396
In base case,
0.6 x 1,18,400 = 71040 passengers
Vehicle occupancy by cars = 2.5
Total cars = 71040/2.5
=28416 passengers
Now, change in VKT =28416 23396 = 5020 VKT
Change in PKT = 71040 - 58490 = 5020 PKT
7.9.4 Nested Logit Model
e multinomial logit model works on the basis of independence from irrelevant alternatives
(IA) property, which asserts that the ratio of any two alternatives is independent of the presence
OT absence of any other
alternatives.
The IIA property implicitly implies that if in a city there are two modes operating -bus
and mmetro. The introduction of a new modes, the auto-rickshaw would not have any impact
on the
Theprroportion
of passengers which use bus and the
metro.
nested logit model, partially relaxes the property of the IIA simply because it is
believed that the utility of a mode is not restricted to the observed partjourney time, fare,
rtheilsiabiunobser
lity, etc.,ved but also
about the unobserved part like comfort, convenience, etc. Therefore,
part need to be addressed.
The nested logit model, thus defines the utility of the function as:
150 Transportation PlanningPrinciples, Practices and Policies

where, U; is the utility for mode i, V, is the observed part of

the utility and is
as a weighted linear combination of variables which explain the travellers
unobserved part of the utility.
generally expressed
choice and e is the
Difference between multinomial logit modelling and nested logit
The main difference between the nested logit and the multinomial
logit
logit partially is not very sensitive property of the independence from model is that the nested
(IA) property and relaxes it by allowing groups of alternatives to be irrelevant
similar to eachalternatives
an unobserved way. other
Concept of nests in nested logit model
The nested logit model allows the analyst to specify a
share some common characteristics into nests, where each
structure that groups alternatives which
one and only one nest. Within each nest, the unmeasured partsalternative is allowed to belong to
of the utilities are allowed to
correlate, but not across nests. Thus, it allows the IIA property to hold within
across nests. nests, but not

Mathematical formulation of the nested logit model

Suppose we have,
Alternatives of mode to be = 1, 2, 3, ...,j
And nests be = 1, 2, 3, ... n
These n alternatives can be partitioned into n nests.
Probability of choosing alternative i nest m is given as:
P; = Pm x Pim
where, Pm is probability of choosing nest m and Pim is probability of choosing alternative i
and given nest m is chosen.
It is given by:
exp)
Pim =
Lre,exp)
where the log of the denominator represents the total utility of the whole choice set and is
called the logsum.
Logsum is expressed as:
In= In E;emexp"
Pm is the upper model and represents the probability that nest m is chosen. It is expresseu
as:

exp"t4L)
P

jel
or
where, I, is the logsum or expected maximum utility and um is the logsum parameter
structural parameter for nest m.
 Modal Split 151
As discussed, the best practice approach to rectifying the counterintuitive implication of
property of the MNL mode is to employ a nested structure where similar alternatives
ILA
the clustered together compares the MNL and a nested structure involving three mode choices:
areautomobile, local bus service and rail transit. The MNL places
these modes on the single
the
resulting in the usually undesirable IIA condition.
level An appreciation of the structure of nested logit model can be made from Figure 7.2, where
two-stage modal split structure has been shown, indicating the split between automobile and
public transport in the first stage. In the next stage, the split between the two types of public
shown.
transport has been
This structure permits a change in the utility of one of the composite transit mode to
modes.
effect the share of the other transit
Nested logí structure
Approach of the nested logit model dealing with the automobile (A) or transit (T) gives
expa)
[exp" +exp"']
exp)
Pr [exp) +exp"a]
where the composite transit utility V, = fV, V,).
By moving to the lower transit level, the conditional probabilities of choosing bus (B) or
rail (R), given the decision to travel by transit, become
exp)
PBI) [exp+exp]
To calculate the unconditional probabilities of choosing bus or rail, use Eqs. (7.20) and (7.21)
given below:
PB = P(BIT) X P) (7.20)
PR = PRIT) X P) (7.21)
The utility of composite transit model can be made using the characteristics of all transit sub-
modes (i.e., bus and rail1). This is normally accomplished by including the logsum variable
(defined as the natural log of the denominator) multiplied by its calibration coefficient in the
transit utility expression.
The logsum = In fexp") + exp}
transit utility expression takes the following form:
a, x X, + 0x
. + the
V,=a,+ fromn logsum
The value of the logsum coefficient model provides information about the nearness
of the
selected nesting structure.
152 Transportation Planning- -Principles, Practices and Policies
If theestimated value of 0 is 0, the transit utility is independent of the utilities of
modes. Consequently, the primary choice between the trans1t the ek
by the changes in the utilities of the sub-modes. Any such and the automobile not affected
is
of the sub-modes primarily between them. In this case, the
change reorganises the market sharoe
sub-modes are considered to be e
perfect substitutes of each other.
If the estimated value of works out to be greater than 0 but
selected nested structure is considered acceptable. A value of exactly less than 1, then the
it presents an equivalent MNL model which is equally equal to 1 means that
whereas a value greater than 1indicates that the selected appropriate (1.e., the IIA property holds)
nesting structure is not correct and
other structures need to be examined. It is fairly easy to
0 is equal to 1, an equivalent MNL equation can be demonstrate mathematically that when
sub-choices as follows:
obtained by modifying the utilities of the
yMNL Nested
Subchoice = aTt .** + a, X X, + VSubchoice
Application of theory
Suppose there are two destinations A and B as shown in Figure 7.6 which can be
reached by
modesCar and PT (public transport). Then there are four alternatives which are as follows:
1. Destination A can be accessed by Car
2. Destination B can be accessed by Car
3. Destination A can be accessed by PT
4. Destination B can be accessed by PT
The options (1) and (2) have the same unobserved factors as
both have
transport. Similarly for options (3) and (4). Thus alternatives (1) and (2) can becar as mode of
one nest called Car nest, while (3) and (4) can be grouped into one nest, grouped into
the PT nest.

Car
PT

Zone A Zone B Zone A Zone B

Alternative 1 Alternative 2 Alternative 4
Alternative 3
FIGURE 7.6 Example of nested logit model.
Since alternatives (1) and (2) are in the sanme nest. it
for implies that erroCar, where
l-uCar, where
alternatives 1 and 2 are correlated with the measure of corelation given by