Transportation Planning

Module IV

Dr. Ritvik Chauhan

Assistant Professor
Department of Civil Engineering
National Institute of Technology, Tiruchirappalli
Email: chauhan@nitt.edu
Course Content
• Mode Split Analysis - Mode split Models - Mode choice behaviour, competing modes, Mode split
curves, Probabilistic models.

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Modal Split
Process of separating person trips by mode of travel

Factors affecting modal split

• Characteristics of the trip

• Household characteristics
• Zonal characteristics
• Network characteristics
• Others-comfort, convenience, safety and prestige (difficult to quantify)

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Characteristics of the trip

TRIP PURPOSE TRIP LENGTH TIME OF THE DAY

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Household characteristics
Income

Car ownership

Family size and composition

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 Zonal characteristics
• Residential density
• Use of public transportation increases as residential density
increases
• Areas of high residential density are occupied by persons
with low income, less no. of vehicle ownership
• Concentration of workers
• Distance from CBD

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Network Characteristics
• Accessibility ratio
• Measure of relative accessibility of a zone to all other zones by means of mass transit
network
• Travel time ratio
• Ratio of travel time by public transport and travel time by private car
• TT for public transport includes
• Time spent walking to public transport vehicle at the origin
• Time spent for waiting for public transport
• Time spent in transfer from one vehicle to another
• Time spent walking from vehicle to destination
• Travel cost ratio
• Ratio of cost of travel by public transport and cost of travel by car

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Types of Modal Split Models
• Based on the type of analysis used, models may be
classified as:

 Aggregate model: Represents the average behaviour of a

group of travellers instead of a single individual (zonal
based)

 Disaggregate model: Models individual choice responses

as a function of characteristics of alternatives and socio-
demographic attributes of each individual

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Types of Modal Split Models
• According to the position of analysis in relation to travel forecasting process,
modal split models may be classified as:

 Trip-end modal split model

 Trip-interchange modal split model Trip Generation

Modal Split Trip Distribution

Trip Distribution Modal Split

Trip-end type Trip-interchange type

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 Types of Aggregate Models in Modal Split
• Pre-Distribution Modal Split
• Post-Distribution Modal Split
• Two Stage Modal Split Analysis

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 Aggregate Modal Split Models
• Used by early researchers (may be called as early generation models)

• Included both trip-end modal split models and trip-interchange modal split models

• Trip-end modal split models used socio-economic characteristics of trip makers as

the prime determinants (predominantly car ownership)

• Trip-interchange modal split models used service characteristics (TT, TC etc.) of

competing modes along with socio-economic characteristics of trip makers

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 Land use

Trip generation

Modal split model Trip distribution model

Trip ends by mode O-D volumes

Trip distribution model Modal split model

O-D volumes by mode O-D volumes by mode

Trip end Trip interchange

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 Trip end modal split model
• Modal split is considered prior to trip distribution stage
• Also called pre-distribution modal split
• Attraction has no impact on mode
• Separate MLR models are needed for each mode of transport
• Factors normally considered to influence modal choice
• Vehicle ownership
• Residential density
• Distance of the zone of origin from CBD
• Relative accessibility of the zone of the origin to the transport facilities
• Eg: Southern Wisconsin Model

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Trip end modal split model
• Advantages
• Less complicated and less costly
• Separate trip distribution pattern for public and private modes
• Disadvantages
• Factors considered are on area wide-basis
• Fail to reflect precisely the zone-to-zone combination
• Insensitive to future developments in inter-zonal travel

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Trip interchange modal split model
• Modal split is considered after the trip distribution stage
• Also called post-distribution modal split
• Attraction does impact mode
• Possible to incorporate wide range of system’s variables influencing mode choice
• Procedure gets complicated when number of zones are large
• Factors normally considered to influence modal choice
• Destination end characteristics
• Characteristics of the transport system
• E.g. Diversion Curve Model (Toronto Mode Split Model)

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Limitations
• Captive and choice transit riders were not identified and represented separately in the
models
• For this reason, models failed to reflect adequately the way choice transit riders react to
changes in transport system characteristics (Eg: change in fare, waiting time etc.)
• Data used were of zonally aggregated nature (Average doesn’t represent the reality)

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Southern Wisconsin Model
• Percentage of trip ends likely to use transit services from a
zone was related to
• Trip type
• Characteristics of trip maker
• Characteristics of the transportation system
• Trips were stratified as home-based work, home-based
shopping, home-based other and non-home-based trips
• The socioeconomic characteristics of trip makers are defined
on zonal basis in terms of average number of cars per
household in zone.

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Southern Wisconsin Model
• The characteristics of the transport system relative to a given
zone are defined by an accessibility index Modal split surface

𝐴𝑐𝑐 = 𝐴𝑓

𝐴𝑐𝑐 = Accessibility index for zone i,

𝐴 = Number of attraction in zone j,
𝑓 = Travel time factor for travel from zone i for the particular

• 𝐴𝑐𝑐𝑒𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜 =

Percentage transit usage from zone plotted against the

accessibility ratio and zonal average number of cars per
household
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Example
• Accessibility index for zone i 𝑨 𝟐 = 𝟏𝟓𝟎
𝑨 5 = 200 2
𝐴𝑐𝑐 = 𝑎𝑓 20/25 15/20
5
1
10/15 25/30
Car accessibility index for zone 1=𝟏𝟓𝟎 ∗𝟏𝟓−𝟐 +𝟐𝟓𝟎 ∗𝟐𝟓−𝟐+
𝟏𝟎𝟎 ∗𝟏𝟎−𝟐 +𝟐𝟎𝟎 ∗𝟐𝟎−𝟐 = 2.567 𝑨 𝟑 = 𝟐𝟓𝟎
𝑨 𝟒 = 𝟏𝟎𝟎 4 3
Transit accessibility index for zone 1 = 𝟏𝟓𝟎 ∗𝟐𝟎−𝟐 + 𝟐𝟓𝟎 ∗
𝟑𝟎−𝟐 + 𝟏𝟎𝟎 ∗𝟏𝟓−𝟐 + 𝟐𝟎𝟎 ∗𝟐𝟓−𝟐=1.417
Accessibility ratio = 2.567/1.417 = 1.81 10 = Travel time by car (min.)
15 = Travel time by transit (min.)

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Diversion Curve Model
• Basic hypothesis underlying this model developed for Metropolitan Toronto (Canada) was as
follows:
• Total number of people moving between an origin-destination pair constitute a travel
market where various modes compete
• Competing modes secure position as per their relative competitiveness expressed in
terms of relative travel time, relative travel cost, relative travel service, and economic
status of trip maker

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Toronto Mode Split Model
Relative travel time (RTT) by competing modes is expressed by the ratio of door travel time by public transit and car

𝑎+𝑏+𝑐+𝑑+𝑒
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑟𝑎𝑣𝑒𝑙 𝑡𝑖𝑚𝑒 =
𝑓+𝑔+ℎ
a = in –vehicle travel time, b= transfer time between transit vehicles, c = waiting time for transit service, d= walking time to
transit service, e= walking time from transit service, f = personal vehicle driving time (i.e. car or two-wheeler), g= parking
delay, h= walk time from parking to destination

Relative travel cost (RTC) is defined as the ratio of out of pocket travel costs by public transit and car
𝑖
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑟𝑎𝑣𝑒𝑙 𝑐𝑜𝑠𝑡 =
1
𝑗 + 𝐾 + 0.5𝑃 𝑚
i =Transit Fare, j = Cost of Fuel, K = Cost of lubricants, P = Parking Cost at Destination, m = Average Car Occupancy

Relative travel service (RTS) is characterized by the ratio of the excess travel times (other than in-vehicle TT) by transit and car.
𝑏+𝑐+𝑑+𝑒
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑟𝑎𝑣𝑒𝑙 𝑠𝑒𝑟𝑣𝑖𝑐𝑒 =
𝑔+ℎ

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Toronto Mode Split Model
• For a particular cost ratio and income group, different diversion curves were developed for
different service ratio.
100
SR1
% Public Transit Usage

80 SR2
SR3
60

40

20

0
0 1 2 3
Public Transport Travel Time/Car Travel
Time

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Two Stage Mode Split Models
• In this approach, the “Transit Captive” and “Transit Choice” are identified to develop trip production
and trip attraction as follows
qp = hi rq
i
qp = Trip productions in zone i by q trip makers
i
hi = Number of households in zone i
rq = Trip production rate for type being a function of the economic status of a zone and
average no. of employees per household

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Disaggregate Modal Choice Modeling
• Simple or Multiple Regression Techniques
• Utility based approach: Deterministic or Random utility
• Probit Model
• Logit Model

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Disaggregate Modal Choice Modeling
Advantages over Aggregate Models
• Disaggregate approach explains why an individual makes a particular choice given the circumstances
and is better able to reflect changes in choice behaviour due to changes in individual characteristics
and/or attributes of alternatives
• Because of their causal nature, they are likely to be more transferable to a different point in time
and to a different geographic context (a critical requirement for prediction)
• More suited for proactive policy analysis since they are causal, less tied to estimation data and more
likely to include a range of relevant policy variables
• More efficient in terms of model reliability per unit cost of data collection whereas, aggregation leads
to considerable loss in variability, thus requiring much more data to obtain same level of model
precision

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Concept of Utility
• Utility function measures the degree of satisfaction that people derive from their choices
• Magnitude of utility depends on the characteristics of alternatives and that of the individual
• The utility (or disutility) function is typically expressed as the linear weighted sum of the independent variables
𝐔 = 𝐚𝟎 +𝐚𝟏𝐗𝟏 +𝐚𝟐𝐗𝟐 + ⋯+ 𝐚𝐫𝐗𝐫
• where, U is the utility derived from a choice defined by the magnitudes of the attributes X in the choice weighted by
the model parameters a
• In mode choice context, U is disutility and is negative since independent variables are travel times, out-of-pocket expenses,
etc.
• Early attempts to describe utility of travel modes calibrated a separate utility function for each mode.
• This type of formulation is known as a mode-specific or choice-specific model because same attributes are assigned
different weightsfor different modes
• This hypothesis causes a problem when a new mode is introduced because of lack of data required for calibration of its
utility function
• To resolve this, a new approach called choice-abstract or attribute- specific approach was proposed
• As per this approach, when making choices, people perceive goods and services indirectly in terms of their attributes
weighted identically across choices

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Probabilistic Utility Models
• Probabilistic utility models capture the differences between the utility values estimated by the analyst and the
utility values used by the traveller
• The utility function can be written as
U=V+e
where, U = True utility function, V = Utility function specified by analyst or deterministic component, e = Random
component or error term
• The deterministic component (V) is what the analyst can measure or estimate
• Error term (e) is the difference between unknown utility used by the individual and the utility estimated by
analyst and is represented by a random variable
• As the true utilities (U) of the alternatives are also random variables, it is not possible to state with certainty
which alternative has the maximum utility
• The most an analyst can do is to predict the probability that an alternative has the maximum utility
• In general, probability that a particular alternative is chosen increases when the deterministic component of
its utility increases, and decreases when the deterministic component decreases

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Probability Distribution of Error Term
• How to estimate e? 1
• Make assumption about the probability distribution
function of e. P(1)
• Error terms are unobserved and unmeasured which
could be represented by a wide range of
distributions
• Consider 2 modes, 0.5
U 1 = V1 + e 1
U 2 = V2 + e 2
• When V1 = V2, 50% chance of choosing mode 1 and 2
• When V1 > V2, everybody should choose mode 1
• Probability of choosing mode 1 0
-10 -5 0 5 10

V1 < V2 V1 = V 2 V1 > V2
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Probability Distribution of Error Term
• Mode choice is not strictly based on deterministic part but it also includes the error part (nature of individuals)
• What is the shape of the curve? Can it be associated with some known distributions?
• Based on research, considering simplicity, it was found that Gumbell or double exponential distribution is suited
for fitting random utility term.
𝑈
𝑝 𝑗 =
∑ 𝑈

• When we assume Gumbell distribution for error terms,

𝑒
𝑝 𝑗 =
∑ 𝑒
• Also named as logit model of mode choice.

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Binary Logit Model
• Simplest form of mode choice
• Travel choice between two modes is considered
• The traveler will associate some value for the utility of each mode. Utility function measures
the degree of satisfaction that people derive from their choice.
• If the utility of one mode is higher than the other, then that mode is chosen.
• Disutility – generalized cost of travel

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Generalised cost of travel
• It is often convenient to use a measure combining all the main attributes related to the disutility of a journey
and this is normally referred to as the generalised cost of travel
• Considered in terms of distance, time or money units
• Typically a linear function of the attributes of the journey weighted by coefficients which attempt to represent
their relative importance as perceived by the traveller.

t vij is the in-vehicle travel time between i and j;

twij is the walking time to and from stops (stations) or from parking area/lot;
ttij is the waiting time at stops (or time spent searching for a parking space);
tnij is the interchange time, if any;
Fij is a monetary charge: the fare charged to travel between i and j
φj is a terminal (typically parking) cost associated with the journey from i to j;
δ is a modal penalty, a parameter representing all other attributes not included in the generalized measure so far, e.g.
safety, comfort and convenience;
a1 . . .6 are weights attached to each element of cost

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Binary Logit Model
• Simplest form of mode choice
• Travel choice between two modes is considered
• The traveler will associate some value for the utility of each mode. utility function measures
the degree of satisfaction that people derive from their choice.
• If the utility of one mode is higher than the other, then that mode is chosen.
• Disutility – generalized cost of travel
• If 𝐶 − 𝐶 is positive, then mode 1 is chosen
• If 𝐶 − 𝐶 is negative, then mode 2 is chosen
• If 𝐶 − 𝐶 is zero, then both modes have equal probability

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Binary Logit Model
• Relationship is normally expressed by a logit curve

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Binary Logit Model
• Choice of a mode is expressed as a probability distribution
• Proportion of trips by mode 1 is given by
𝑇
𝑃 =
𝑇
P1 =
𝑒
𝑃 =
𝑒 +𝑒

Pij1 : Probability of choosing Mode 1 for trips between zones 𝑖 and j

𝑐𝑖𝑗1 and 𝑐𝑖𝑗2 are the generalized costs (which may include factors like travel time, fare, comfort, etc.) for
Modes 1 and 2, respectively.
𝛽 is a calibration parameter, known as the sensitivity parameter, that adjusts how sensitive the mode
choice is to changes in cost.

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Problem
• Let the number of trips from zone i to zone j is 5000, and two modes are available which has
the characteristics given below.

Car 20 - 18 4
Bus 30 5 3 9
0.03 0.04 0.06 0.1
In-vehicle walking transfer
Cost factor Fare
travel time time time

• Compute the trips made by mode bus, and the fare that is collected from the mode bus. If
the fare of the bus is reduced to 6, then find the fare collected.

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Solution
• Cost of travel by car, Ccar = 0.03 × 20 + 18 × 0.06 + 4 × 0.1 = 2.08
• Cost of travel by bus, Cbus = 0.03 × 30 + 0.04 × 5 + 0.06 × 3 + 0.1 × 9 = 2.18
• Proportion of trips by mode 1

• Probability of choosing mode car

.
. . 0.52
• Probability of choosing mode bus
.
. . 0.475

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Solution
• Proportion of trips by car = 𝑇 = 5000×0.52 = 2600
• Proportion of trips by bus = 𝑇 = 5000×0.475 = 2400
• Fare collected from bus = 𝑇 × Fij = 2400×9 = 21600
• When the fare of bus gets reduced to 6,
• Cost function for bus= Cbus = 0.03 × 30 + 0.04 × 5 + 0.06 × 3 + 0.1 × 6 = 1.88
• Probability of choosing mode bus
.
𝑃 = . . = 0.55
• Proportion of trips by bus = 𝑇 = 5000×0.55 = 2750
• Fare collected from the bus = 𝑇 × Fij = 2750×6 = 16500

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Multinomial logit model
• If more than 2 modes are there
𝑒
𝑃 =
∑ 𝑒
• Let the number of trips from i to j is 5000, and three modes are available which has the
characteristics given in Table. Compute the trips made by the three modes and the fare required to
travel by each mode.

Coefficient 0.03 0.04 0.06 0.1 0.1

Car 20 - - 18 4
Bus 30 5 3 6 -
Train 12 10 2 4 -

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Solution
• Cost of travel by car = Ccar = 0.03 × 20 + 18 × 0.1 + 4 × 0.1 = 2.8
• Cost of travel by bus = Cbus = 0.03 × 30 + 0.04 × 5 + 0.06 × 3 + 0.1 × 6 = 1.88
• Cost of travel by train = Ctrain = 0.03 × 12 + 0.04 × 10 + 0.06 × 2 + 0.1 × 4 = 1.28
• Probability of choosing mode car
.
𝑃 = . . . = 0.1237
• Probability of choosing mode bus
.
𝑃 = . . . = 0.3105
• Probability of choosing mode train
.
𝑃 = . . . = 0.5657

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Solution
• Proportion of trips by car, 𝑇 = 5000×0.1237 = 618.5
• Proportion of trips by bus, 𝑇 = 5000×0.3105 = 1552.5
• Proportion of trips by train, 𝑇 =5000×0.5657 = 2828.5
• Fare collected from the mode bus = 1552.5×6 = 9315
• Fare collected from mode train = 2828.5×4 = 11314

Coeff 0.03 0.04 0.06 0.1 0.1 - - - -

Car 20 - - 18 4 2.8 0.06 0.1237 618.5
Bus 30 5 3 6 - 1.88 0.15 0.3105 1552.5
Train 12 10 2 4 - 1.28 0.28 0.5657 2828.5

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Independence of Irrelevant Alternatives (IIA)
• IIA property of MNL model states that for any individual, ratio of probabilities of choosing two alternatives is
independent of the availability or attributes of any other alternatives in the choice set
• Consider an MNL model of choice between drive alone, carpool and bus, probabilities of choosing drive alone and
carpool:

New option only affects the overall

probabilities, not the relative preference
• The ratio of these probabilities is: between two original options

Ex: 70% vs 30% probabilities

• This ratio is independent of the attributes and availability of bus i.e., the ratio remains the same regardless of
whether bus is an available alternative or not
• An improvement in bus service would be predicted by an MNL model to draw travellers from drive alone and carpool
in proportion to the original shares of these modes

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Limits on Applicability of MNL Model due to IIA
The Red Bus/Blue Bus Paradox
• Let modes available for travel between home and work are drive alone and a bus (Red Bus or RB)
• Assume the attributes of drive alone and red bus are such that 𝐕𝐃𝐀 = 𝐕𝐑𝐁; then P(DA) = P(RB) = 0.5 as per
binomial logit formula
• Suppose, a competing bus operator starts operating a blue bus on the same route as the red bus
• Except the colour, the two buses are otherwise identical
• The blue bus runs exactly on the same schedule, and serves exactly the same stops as the red bus
• Assuming that the colour of the bus does not affect the mode choice, the existing bus riders should divide
evenly between red bus and blue bus
• Addition of blue bus should not have effect on travellers who choose to drive alone because it does not
affect the relative service quality of drive alone and bus
• The choice probabilities due to the introduction of blue bus should be: P(DA) = 0.5, P(RB) = 0.25, P(BB) =
0.25

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Limits on Applicability of MNL Model due to IIA
• Consider prediction made by MNL model
• 𝐕𝐑𝐁 =𝐕𝐁𝐁 (RB and BB are identical);
• 𝐕𝐃𝐀 = 𝐕𝐑𝐁 by assumption; therefore,
• 𝐕𝐃𝐀 = 𝐕𝐑𝐁 = 𝐕𝐁𝐁 = 𝐕
• Then, for any of the three modes

• Introduction of blue bus causes the share of drive alone to decrease from 1/2 to 1/3 of the travellers
• The result is both inconsistent and unreasonable
• Red bus/ blue bus paradox provides an important illustration of possible consequences of IIA property of logit
models

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Nested Logit (NL) Model
• A possibility to reduce the counterintuitive implication of IIA property of MNL model is to
employ a nested (or hierarchical) structure where similar alternatives are clustered together

Choice
Choice

Transit Car
Metro City Bus Car

Metro City Bus

MNL structure
Nested Logit structure

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Nested Logit (NL) Model
• MNL places these modes on a single level resulting in undesirable IIA condition
• Nested structure groups bus and metro rail together as sub-choices of the transit modes where a greater
degree of choice substitution is allowed within nests than between/among nests
• Top-level decision is whether to travel by car (C) or transit (T) using:

where 𝐕 𝐓 = f ( 𝐕 𝐁 , 𝐕 𝐌 )

• By moving to the lower transit level, the conditional probabilities of choosing bus (B) or metro (M), given
decision to travel by transit are as:

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Nested Logit (NL) Model
• Unconditional probabilities of choosing bus and metro are given by:

• Utility of transit mode needs to capture characteristics of all transit sub-modes (i.e., bus & metro)
• This is normally accomplished by including Logsum variable (defined as natural log of the denominator of
conditional probabilities equation) multiplied by its calibration coefficient in the transit utility expression

• Transit utility expression takes the form

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Nested Logit (NL) Model
• The logsum parameter, θ is a function of underlying correlation between the unobserved components for pairs
of alternatives in that nest, and it characterizes the degree of substitution between those alternatives
• The value of the logsum parameter is bounded by zero and one to ensure consistency with random utility
maximization principles
• If θ > 1 or θ < 0, it is not consistent with theoretical derivation and other nesting structures need to be
investigated
• θ = 1 implies zero correlation among mode pairs in the nest, so the NL model collapses to the MNL model
• 0 < θ < 1 implies non-zero correlation among pairs. This range is appropriate for the nested logit model.
Decreasing values of θ indicate increased substitution between/among alternatives in the nest.
• θ = 0 implies perfect correlation between pairs of alternatives in the nest. That is, the choice between the
nested alternatives, conditional on the nest, is deterministic

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Example
Estimation of nested logit structure for a mode choice model as shown in the previous figure found that 𝐕 𝐓
= 𝐚 𝐓 + 𝛉 𝐥 𝐨 𝐠 𝐬 𝐮 𝐦 with 𝐚 𝐓 = −0.56 and θ = 0. For a particular interchange, modal utilities calculated were as
𝐕 𝐂 = −𝟎. 𝟑 , 𝐕 𝐁 = −𝟎. 𝟗 and 𝐕 𝐌 = −𝟎. 𝟕 𝟓. Calculate the corresponding mode shares and the effect of a policy
that is expected to cause a increase in 𝐕 𝐁 by -0.20.
Nest Level
Mode (m) V 𝐞𝐱𝐩𝐕 P(m/T)
Given, 𝐕 𝐓 = 𝐚 𝐓 + 𝛉 𝐥 𝐨 𝐠 𝐬 𝐮 𝐦 = −𝟎. 𝟓 𝟔 + 𝟎 𝐱 𝐥𝐧(𝟎. 𝟖 𝟕 𝟗 ) = −𝟎. 𝟓 𝟔 Bus -0.90 0.407 0.46
Metro -0.75 0.472 0.54
Sum 0.879 1.00

Primary Choice Level

Mode (m) V 𝐞𝐱𝐩𝐕 P(m/T)
Car -0.30 0.741 0.56
Transit -0.56 0.571 0.44
Sum 1.312 1.00

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Example
• After change in𝐕𝐁 = -0.20, the corresponding probabilities are
Nest Level
Mode (m) V 𝐞𝐱𝐩𝐕 P(m/T)
Bus -1.10 0.333 0.41
Metro -0.75 0.472 0.59
Sum 0.805 1.00

• 𝐕 𝐓 = −𝟎. 𝟓 𝟔 + 𝟎 𝐱 𝐥𝐧 𝟎. 𝟖 𝟎 𝟓 = −𝟎. 𝟓 𝟔
• Primary choice level remains the same i.e., P(C) = 0.56 and P(T) = 0.44

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Class activity
• Estimation of nested logit structure for a mode choice model as shown in figure found that 𝐕 𝐓 = 𝐚 𝐓 +
𝛉 𝐥 𝐨 𝐠 𝐬 𝐮 𝐦 with 𝐚 𝐓 = -0.7 and θ = 0. For a particular interchange, modal utilities calculated were as 𝐕 𝐂 =
−𝟎. 4 ,𝐕 𝐁 = −1. 1 0 and 𝐕 𝐌 = −𝟎. 80. Calculate the corresponding mode shares and the effect of a policy that
is expected to cause a increase in 𝐕 𝐁 by -0.30.

Choice

Transit Car

Metro City Bus

Nested Logit structure

23-Oct-24 CE604 Transportation Planning 50