Urban Travel Forecasting

CME 508
Choice Modeling

Kouros Mohammadian
Department of Civil, Environmental, and
Materials Engineering
University of Illinois at Chicago

1
Urban Transportation Modeling System
Population &
Employment Forecasts

Trip Generation

Trip Distribution

Transportation
Mode Split Network & Service
Attributes

Trip Assignment

Tij,auto
Link & O-D Flows,
Times, Costs, etc. I Mode Split J
Tij,transit 2
Mode Split Modeling

• Trip-End Models
• Trip-Interchange Models
• Explanatory Variables
• Modes
• Decision Structures
• Logit Models

3
Trip-End Models

• It is possible to develop trip-end mode split models,

which are applied prior to trip distribution (i.e., they
split the “trip ends” estimated by the trip generation
model).
• Essentially these are mode-specific trip generation
models, and take on the same form as normal trip
generation models (e.g., regression or cross-
classification).

4
Trip-End Models - ii

• Trip-End mode split is a function of socio-economic

variables such as income, auto ownership, etc.
• Cannot include modal level-of-service attributes
(travel time, cost, etc.) since do not yet have O-D
flows
• Trip-end models are suitable for small urban areas
where transit is basically a “social service”, or in
developing countries where mode choice is almost
completely determined by income & auto
ownership

5
Trip-Interchange Models

• Trip-Interchange mode split models are applied

after trip distribution (i.e., they split the “trip
interchanges” or O-D flows computed by the trip
distribution model)
• Since O-D flows are known, we can compute travel
times, costs, etc. for the competing modes
• Trip-interchange models generally applied in
medium to large urban areas where transit actively
competes with automobile

6
Trip-Interchange Models - ii

• Since trip-interchange models are sensitive to travel

times, etc. they can be used to assess the impacts of
a broad range of transportation policies:
– improved transit service (headway, coverage, travel
times, etc.)
– road pricing, gasoline taxes, etc.
– transit fare policy
– parking supply/cost
– HOV policies
– etc.

7
Explanatory Variables

• Variables characterizing each mode available to the

trip-maker:
– Travel time:
• in-vehicle
• out-of-vehicle
– walk (access, egress)
– wait (initial, transfer)
– Out-of-pocket travel cost:
• transit fare or “in-vehicle” auto cost
• parking cost
– other (reliability, safety, comfort, convenience, …)

8
Explanatory Variables - ii

• Variables characterizing the trip-maker:

– Income
– Auto availability
• no. of cars in household
• driver’s license?
– age
– sex
– occupation
– household composition
– ….

9
Modes Modeled

• The number and definition of modes modeled

depends on the problem application, available data,
network modeling capabilities, etc.
• At a minimum, some representation of the
competition between auto and transit is usually
required
• Distinguish between drivers and passengers in
AUTO mode:
– Auto Drive Mode: trip-maker drives a car from origin to
destination
– Auto Passenger Mode: trip-maker is a passenger in a car
from origin to destination
10
Auto Mode Modeling

• Alternatively, we can distinguish between drive-

alone and shared-ride:
– Drive-Alone Mode: trip-maker is the driver and sole
occupant of a car from origin to destination (also referred
to as a single-occupancy vehicle (SOV) trip)
– Shared-Ride Mode: trip-maker is one of several
occupants (driver or passenger) of a car from origin to
destination (also referred to as a high-occupancy vehicle
(HOV) trip)

11
Shared Ride Mode

• The shared-ride mode is sometimes further broken

down by number of occupants, e.g.:
– 2 persons
– 3 or more
• Shared rides can occur among household members
(e.g., parent drives child to school) or people from
different households (e.g., co-workers carpool to
work)

12
Transit Mode Representation

• Possible ways of categorizing transit include:

– Local Transit vs. Regional Transit
– Surface, shared right-of-way (bus, streetcar) vs.
Dedicated ROW (subway, LRT, bus ways)
– Bus vs. Rail
– Regular service vs. Express or other “premium” service

13
Mixed Modes

• Combined auto-transit modes exist, in which auto is

used to access the transit system:
– Park & Ride: trip-makers drives to a transit station and
parks the car at the station
– Kiss & Ride: trip-maker is driven as a passenger to a
transit station and is dropped off there
– Auto access greatly extends the “catchment area” of the
transit service

14
Mixed Mode Example: Commuter Rail and Buses

Access Sta. 1
Access Sta. 2

Origin
Zone
Egress Station
auto or local transit
access trip link local transit or walk
egress trip link

Rail line-haul
Access Sta. 4 trip link Dest’n
(chosen station Zone
Access Sta. 3
for this trip)

15
Alternative Modes

• Other motorized modes of interest in some cities

might include:
– jitneys
– ferries, water taxis
– taxis
– van pools
– motorcycles
– ridesharing
– micromobility
• Non-motorized modes also generally of importance:
– walking
– bicycles
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Decision Structures

• Given the set of modes to be included in the model,

one can always represent the mode choice decision
for a given trip as a decision tree.
– In a decision tree, each node of the tree represents an
alternative and relationships among choices can be
indicated through the hierarchical arrangement of the tree

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Mode Definition & Choice Structures

Auto Auto Transit Subway, Commuter Rail, Commuter Rail Walk

Drive Passenger Allway Auto Access Auto Access Tran. Access Allway

Access Access Access Access

Sta. 1 ... Sta. n Sta. 1 ... Sta. n

Access Access
Sta. 1 ... Sta. n

18
Alternative Choice Structures

Auto Local Commuter Non-

Transit Rail Motorized

Auto Auto Transit Subway, Commuter Rail, Commuter Rail Walk Bicycle
Drive Passenger Allway Auto Access Auto Access Tran. Access Allway

Access Access Access Access

Sta. 1 ... Sta. n Sta. 1 ... Sta. n

Access Access
Sta. 1 ... Sta. n

19
General procedure for model application

Individual & Travel Data Predict Exogenous

Explanatory & Policy
Variables
Choice
Model
Formulation Estimate Aggregate
Apply
Disaggregat (TAZ)
Prediction
e Choice Travel
Model(s) Procedure
Prediction

Insert Predicted
Proportions for Each
Mode in the Four
Step Sequence
20
Discrete Choice

– In the transportation literature, Discrete choice

model has been referred to as Binary Logit,
Multinomial Logit, Conditional model, etc.

– The main differences between these approaches

are in number of alternatives and inclusion of
attributes of the choices and characteristics of
the individuals in the utility of the alternatives.

– In the case of mode choice, the utility of mode j

is explained by the attributes of the alternatives
and the characteristics of the trip maker i.
21
Logit Mode Choice Models

• Current state of practice in modeling trip-

interchange mode split is to use the Discrete Choice
models
• This model is derived from basic principles of
random utility theory developed in economics and
psychology
– Daniel McFadden, a Berkley economist, received Nobel
Prize in 2000 for his research in Discrete Choice Models

22
 Theory from microeconomics
• Brief theoretical description of principles and
theorems
• Emphasize practical aspects
• Note: Dan McFadden is Professor of Economics
and Nobel Laureate in Economics
http://emlab.berkeley.edu/users/mcfadden/
• A site that contains a very good bibliography on
Random Utility Models

23
Dependent Variable:
Discrete: Nominal scale

Independent Variables:
Discrete or Continuous

Example:
Commuters had a choice of three alternate
routes; a four-lane arterial (speed limit = 60
km/h, 2 lanes each direction), a two-lane
highway (speed limit = 60 km/h, 1 lane each
direction) and a limited access four-lane freeway
(speed limit = 90 km/h, 2 lanes each direction).
24
Example:
Pipes carrying various commodities (oil, gas,
water, etc.) experience failures. Can the type of
pipe be predicted as a function of commodity,
location, age of pipe, ambient temperature,
etc.?

Example:
Can accident type (rear-end, rollover, run off
road, etc.) be predicted by roadway functional
class, VMT, time of day, age of driver, speed
limit, etc.?
25
 Basic Assumptions (1)
• Suppose a trip maker i faces J options (choices
or alternatives) with index j=1,2,3…J.
• Assume that each trip maker associates with
each choice j=1,2,...,J a function called
UTILITY representing the "convenience" of
choosing mode j.
• j=1,2,..., J is called the choice set. This is the
set from which a decision maker chooses an
option.
• Note: Let’s assume that choice and consideration sets are the same.

26
 Basic Assumptions Example
– A person, i, needs to go to work from home
to the downtown area.
– Suppose this person has three possible modes
to choose from: Car (j=1), Bus (j=2), and her
Bike (j=3). Total number of options (J=3).
– One possible form of the person ’ s
convenience function (called utility) is:

Ucar=F (car attributes, person characteristics, trip attributes)

Ubus=F (bus attributes, person characteristics, trip attributes)
Ubike=F (bike attributes, person characteristics, trip attributes)
27
Random Utility Theory

• Define the following terms:

Ci = Set of feasible alternatives available to trip-maker i
Uij = “Utility” of alternative j for trip-maker i
• It is assumed that people are “rational” and so will chose the
alternative j* which maximizes their utility for the given trip
• i.e., a trip-maker’s decision rule is:
– Chose alternative j Î Ci
– if Uij ³ Uik for all k ¹ j [1]
• We do not observe person t’s utility Uij. The best that we
can say is that:
Uij = Vij + eij [2]
Vij = “Systematic” or “observable” utility
eij = Random utility
i.e., utility is random, and so we cannot say with certainty which
alternative will be chosen
28
Systematic Utility Function

• Generally assume:
Vij = b’Xij [5.1]
= b0 + b1Xij1 + b2Xij2 + … + bmXijm [5.2]
b = Vector of parameters (utility function weights)
Xijm = Vector of explanatory variables

29
 Utility components
n Variables describing the individual --> this is an attempt to
represent "taste variation" from person to person. In our
example if young persons have systematically differing
preferences from the older individuals, then, age would be one
of the variables.

n Variables describing the choice characteristics (called choice

attributes) in the choice set. For example, some travel modes
are less expensive than others. Cost of the trip for each
available mode would be another variable in the utility. Travel
time is another key variable.

n Variables describing the context such as the trip type, time of

day, budget constraints.

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 Key Assumption (maximum utility)
• Travelers (decision makers) formulate for each
option a utility and they calculate its value.
• Then, they choose the option with the most
advantageous utility (maximum utility).
• Example: U(car,bus,bike)=-0.5*cost-2*waiting time
• Cost by bus=$1, Waiting time=5 minutes
• Cost by car=$2.5, Waiting time=1 minute
• Cost by bike=$0.2, Waiting time=0 minutes

Which mode is the most desirable, second less desirable, etc?

Utility is actually an Indirect Conditional Utility
31
 Uncertainty in utility (1)
• We (analysts) do not know all the factors that influence
choice behavior
• Travelers (decision makers) do not always make choices
consistently
• We are not interested in including all possible variables that
affect behavior in our models
• We are interested in policy variables (taxes, fares, gasoline
costs, waiting times) that we can “manipulate” to find
travelers reaction
• We are also interested in social, demographic, and
economic traveler characteristics because these variables
allow us to link models to TAZs

32
 Incorporating uncertainty and
traveler/trip characteristics
• The example becomes: U(bus,car,bike)=-
0.5*cost-2*waiting time + SOMETHING ELSE

• The “something else” is an indicator of

“general mode attractiveness” AND a
random component

• Let’s look at the details:

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 Utility elements

nUij = aj-0.5*costj-
2*waiting timej
+ bj * agei + eij

Utility of person i for mode j

34
Utility elements

A constant for each mode j.

Captures desirability of j
for unknown reasons

nUij = aj-0.5*costj-2*waiting
timej + bj * agei + eij
35
 Utility elements
Cost is different for each mode j

nUij = aj-0.5*costj-
2*waiting timej + bj*agei +eij

Waiting time is different for each mode j

36
Utility elements

nUij = aj-0.5*costj-2*waiting
timej + bj * agei + eij

The effect of the age variable is different

for each alternate mode
(Class: Let’s talk about behavioral
meaning - bikes?) 37
Utility elements

nUij = aj-0.5*costj-2*waiting
timej + bj * agei + eij

The key indicator of uncertainty =

our ignorance &
traveler variability for unknown reasons 38
 Utility elements
nIn a similar way as for age we can
include other traveler and trip
characteristics (explanatory)

nUij = aj-0.5*costj-2*waiting timej + bj * agei + eij

In applications: These are parameters we

estimate from data
39
 Utility elements
nUij = aj-0.5*costj-2*waiting timej
+ bj * agei + eij
nCan write as: Uij = Vjj + eij

Random
Systematic & measurable part
40
 Numerical example
(trip from home to work/school)
nUicar = - 0.5*cost - 2*waiting time + eicar
nUibus = 5 - 0.5*cost - 2*waiting time +
0.25 * agei + eibus
nUibike = 12 - 0.5*cost - 2*waiting time -
0.3 * agei + eibike

41
Note: Different age coefficients - why?
Compare systematic part (V)
• Compute for each person the systematic
part of utility for each mode
• Plot all V (syst. utilities) for all persons
• Horizontal = age
• Vertical = V the systematic part of utility
of each mode

42
 Modal Utilities
20

10
Utility Value

Vbus
0
Vbike
0 20 40 60 80 100
-10

-20
Age

43
 Probability of Choice
• We need to convert utilities to an estimate
of the chance to choose a mode
• The specific equation to use depends on
the probability distribution of the random
component (e) in the utility function
(U=V+e)
• Ease of calculations should be considered
in selecting a probability function

44
Random Utility Theory - ii

Pij = Probability that person i will choose alt. j

= Probability that j is the max. utility alt. for i
= P(Uij ³ Uik for all k ¹ j ; k,j Î Ci) [3]
– The mathematical expression for Pij depends upon the
distribution of the random “error” term, eij
• The most common assumption is that the error
terms are identically and independently distributed
(iid) with the Type 1 Extreme Value (Gumbel)
distribution
– This assumption generates the logit model:
Vij [4]
e
Pij =
åk
eVik
45
 LOGIT Model

• Assume the random components (ei) of

the utility are independent identically
Gumbel distributed random variables
then:
exp(Vicar )
Pi ( car ) = bus ,bike
å exp(Vij )
j = car 46
 exp(Vibus )
Pi (bus ) = bus ,bike
å exp(Vij )
j = car

exp(Vibike )
Pi (bike) = bus ,bike

å exp(V
j = car
ij )

47
 Probability

1.2
Probability to choose a

0.8
Pcar
mode

0.6 Pbus
Pbike
0.4

0.2

0
0 20 40 60 80 100
Age of Traveler
48
 Applications
• Modal split (type of mode)
• Route choice (link by link or entire path)
• Car ownership (type of car)
• Destination choice (shopping place)
• Activity types (type of activity)
• Residential unit (size and type of home)

49
Example: Binomial Logit

• Data consist of morning peak-period (6:00-8:59 a.m. start

times) work trips from origins within an urban area to
employment locations within the Central Business District
(CBD).
• All trips selected used auto-drive or transit as their travel
mode.
Origin Origin traffic zone
Dest. Destination traffic zone
Age Age of worker
Female = 1 if the worker is female; = 0 otherwise
Aivtt Origin-destination travel time by auto mode (min.)
Acost Origin-destination travel cost by auto mode (1996$)
Tivtt Origin-destination in-vehicle travel time by transit (min.)
Twalk Origin-destination walk to/from transit (min.)
Twait Total wait + transfer time for transit trip (min.)
ParkCost Daily parking cost at destination zone (1996$)
Tfare Origin-destination transit fare (1996$) (note: = $1.71 for all trips)
Mode = 1 if auto-drive mode chosen; = 2 if transit chosen 50
Data for Binomial Logit
Origin Dest. Age Female Aivtt Acost Tivtt Twait Twalk ParkCost Tfare Mode
148 205 32 1 11.8 0.28 13.34 8.99 2.5 4.83 1.71 1
362 229 55 1 18.87 0.57 26.47 8.76 4.5 15.8 1.71 1
22 219 32 0 28.44 0.94 34 8.72 4.25 21.5 1.71 1
6 242 28 0 25.92 1.03 58.5 12.56 8.55 5.4 1.71 1
454 154 26 0 38.96 1.71 61 16.84 8.57 1.32 1.71 1
274 249 29 1 13.43 0.47 29 8.28 3.22 1.37 1.71 1
31 194 32 1 28.87 1.1 39.51 11.96 3.08 11.3 1.71 1
170 243 24 1 19.2 0.68 34.97 11.76 4.53 6.39 1.71 1
369 222 38 0 14.13 0.51 29.54 9.33 3.81 15 1.71 1
145 222 57 1 19.18 0.55 23.12 15 2.59 15 1.71 1
372 212 35 1 35.77
… 1.51 53.68 12.8 3.27 6.89 1.71 1

275 222 35 0 21.87 0.7 29.69 8.84 6.32 15 1.71 2

275 211 30 0 21.17 0.78 31.55 8.28 11.59 9.38 1.71 2
259 195 30 1 7.2 0.2 6.99 10.76 1.32 9.33 1.71 2
127 222 39 1 24.05 0.87 33.36 12.6 4.59 15 1.71 2
313 215 34 1 32.83 1.13 34.61 8.41 5.78 11.4 1.71 2
122 233 27 1 13.6 0.42 20.32 9.07 3.08 5.67 1.71 2
233 193 33 0 2.63 0.12 4.76 6.8 1.27 7.8 1.71 2
459 228 51 1 39.73 1.59 53.92 8.76 5.65 11.67 1.71 2
107 239 62 1 27.1 1.02 34.73 8.12 3.18 9.73 1.71 2
345 215 45 0 26.2 1.04 39.14 8.86 4.47 11.4 1.71 2
142 220 23 1 14.89 0.47 15.9 10.68 2.59 19.4 1.71 2
288 154 35 1 16.37 0.6 25.89 12.57 4.87 1.32 1.71 2
129 212 38 1 22.63 0.82 35.15 11.76 6.04 6.89 1.71 2

51
Binary Logit Results
Beta Value Std. Error t value
(Intercept) 0.00759 1 0.0076 0.3995 0.0190
FEMALE -1.14253 0 0.0000 0.1336 -8.5505
AGE25 -0.58257 1 -0.5826 0.3257 -1.7884
AIVTT -0.01582 22 -0.3480 0.0179 -0.8823
TIVTT 0.02410 45 1.0843 0.0117 2.0595
ACTOT -0.07608 4 -0.3043 0.0158 -4.8299
TOVTT 0.04229 5 0.2114 0.0258 1.6394

P(auto) 51.71%
P(transit) 48.29%

Beta Value Std. Error t value

(Intercept) 0.00759 1 0.0076 0.3995 0.0190
FEMALE -1.14253 1 -1.1425 0.1336 -8.5505
AGE25 -0.58257 1 -0.5826 0.3257 -1.7884
AIVTT -0.01582 22 -0.3480 0.0179 -0.8823
TIVTT 0.02410 45 1.0843 0.0117 2.0595
ACTOT -0.07608 4 -0.3043 0.0158 -4.8299
TOVTT 0.04229 5 0.2114 0.0258 1.6394

P(auto) 25.46%
P(transit) 74.54%
52
Example: Work Trip Mode Choice

• The example is from Ottawa-Carleton (O-C)

Regional morning peak-period work trip mode
choice
• The model is a three-mode logit model.
– Modes modeled:
• d Þ auto drive, all way
• p Þ auto passenger, all way
• t Þ transit all way

53
Example: Work Trip Mode Choice - ii
• Variable definitions:
– Vm= utility for mode m (m = d, drive; p, passenger; t,
transit)
– COSTm= out-of-pocket travel cost ($), mode m
– IVTTm = in-vehicle travel time for mode m (min.)
– OVTTm= out-of-vehicle travel time for mode m (min.)
– NVEH = avg. no. of vehicles per household in home
zone
– TWY = 1 if emp. zone is located within the catchment
area of a Transit-way station outside the CBD;
= 0 otherwise
– REGION =1 if the home zone is located in the Outaouais;
= 0 otherwise
54
Example: Work Trip Mode Choice - iii

• Systematic utility functions:

– Vd = -0.5472 - 0.5691*COSTd - 0.0161*IVTTd +
0.7520*NVEH [6.1]
– Vp = -2.282 - 0.5691*COSTp - 0.0161*IVTTp -
0.0261*OVTTp + 0.4529*NVEH [6.2]
– Vt = - 0.5691*COSTt - 0.0161*IVTTt - 0.0261*OVTTt +
1.0746*TWY- 0.9784*REGION [6.3] V
e ij

Pij =
åe
k
Vik

Mode COST IVTT OVTT NVEH TWY REG Vm exp(Vm) Pm

Drive 2.6 15 1.4 -1.2156 0.297 42.57%
Pass 0.8 15 5 1.4 -2.4752 0.084 12.08%
Tran 1 20 10 0 0 -1.1521 0.316 45.36%
0.697 100.0%
55
Logit Parameter Estimation

• Commercial software exists to estimate model

parameters using the method of maximum
likelihood estimation. Examples include:
– ALOGIT
– NLOGIT (LIMDEP)
– Biogeme
– TransCAD
– SAS
– R
• Results are interpreted very similarly to regression
(t-statistics, goodness-of-fit measures, etc.)

56
 Practical issues
• Choice set - consideration set
• Variables to include in utility
• Measurement of mode attributes (e.g.,in-
vehicle-travel-time)
• Need survey data and mode by mode
attributes!

57
Individual & Travel Data Predict Exogenous
Explanatory & Policy
Variables
Choice
Model
Formulation
Estimate Aggregate
Apply
Disaggregate (TAZ) Travel
Prediction
Choice Prediction
Procedure
Model(s)

Insert in the
Four Step
Sequence

58
 For the four step modal split
• We need aggregate TAZ proportions by
each mode (% of trips by car, % trips
by bus, % trips by bike)
• We have a disaggregate (individual)
model which tells us the likelihood
(chance) of a person to choose each
mode
• We need a procedure to go from
disaggregate predictions of chance to
aggregate predictions of proportions
59
Taking Average TAZ Characteristics
Does Not Work
• (Pa+Pb)/2 is not the same as
P([Va+Vb]/2) - a and b are value points
for V
• When the two are equated we have the
Naïve method of aggregation
• Bias depends on how close the probability
function is to a linear function
• Following is an example from Probability
to choose bus as an option
60
 Pbus

1.2 a TAZ with two persons with V=2 &V=12

Consider
Proability of Choice

0.8
P(V=12)=0.679
0.6 Pbus
0.4
0.2
P(V=2)=0.034
0 V=2 V=12
-5 0 5 10 15 20
Systematic Utility of Bus (Vbus)
61
 What is the correct TAZ Proportion of
Choosing the Bus?

• (P(V=2)+P(V=12))/2
• or
• P((2+12)/2)=P(V=7)

62
 Pbus
The correct value is: [P(V=2)+P(V=12)]/2=0.357
1.2
Proability of Choice

0.8
P(V=12)=0.679
0.6 Pbus
0.4
P(V=7)=0.223
0.2
P(V=2)=0.034
0
V=2 V=7 V=12
-5 0 5 10 15 20
Systematic Utility of Bus (Vbus)
63
 Pbus

1.2
Proability of Choice

0.8
0.6 Pbus
[P(V=2)+P(V=12)]/2=0.357
0.4
P(V=7)=0.223
0.2 Bias

0
V=2 V=7 V=12
-5 0 5 10 15 20
Systematic Utility of Bus (Vbus)
64
 Naïve Aggregation
• For each TAZ take the average value of
explanatory variables
• Compute average value for each utility
function for each mode
• Compute the corresponding probability
and use it as the TAZ proportion choosing
each mode

65
 Market Segmenation
• Divide the residents in each TAZ into
relatively homogeneous segments
• Apply Naïve aggregation to each segment
and get proportions for each mode
• Compute the TAZ proportion either as
average segment-specific proportion or
weighted segment-specific proportion

66
 Complete Enumeration
• Compute for each person and for each
mode the probability to choose a mode
• Compute the proportion for each mode as
an average of the individual probabilities
• Stochastic microsimulation is a method
derived from this - see Chapter 12 of
Goulias, 2003 (Transportation Systems
Planning: Methods and Application)

67
 Example
(TAZ with four persons)
Age Vcar Vbus Vbike
Segment 1 45 7.500 5.750 -1.600
Segment 2 21 3.900 -0.250 5.600
Segment 2 20 3.750 -0.500 5.900
Segment 3 79 12.600 14.250 -11.800
Average 41.25 6.938 4.813 -0.475
Exp (U) 1030.192 123.039 0.622
Naïve Prob 0.893 0.107 0.001
Vicar = - 0.5*cost - 2*waiting time + 0.15 * agei
Vibus = 5 - 0.5*cost - 2*waiting time + 0.25 * agei
Vibike = 12 - 0.5*cost - 2*waiting time - 0.3 * agei
68
 Compare values of the three
methods
Pcar Pbus Pbike
Average of Segments 0.372 0.329 0.298
Weigthed Average
of Segments 0.305 0.247 0.447

Naïve Aggregation 0.893 0.107 0.001

Complete Enumeration 0.318 0.248 0.434

69
Forecasting

• In forecasting, aggregate, zone-to-zone flows are

the required output
– Must aggregate (“sum up”) over individual trip makers
(either explicitly or implicitly) to generate required
aggregate results
– Most common practical method is so-called
“segmentation (classification) with naive aggregation”

70
Forecasting Example

• A work-trip mode split logit model developed for a

large metropolitan area includes the number of
household vehicles (NVEH) and whether a worker
has a driver’s license (DLIC) as variables.
• The aggregation/forecasting procedure used is to:
– Divide workers into 5 different NVEH, DLIC categories
– Estimate the percentage of workers in each category for
each O-D pair
– Compute mode choice probabilities for each category for
each O-D pair
– Compute weighted average mode splits for each O-D pair

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Forecasting Example - ii

• Define:
Tijm = Predicted trips from i to j by mode m
Tij = Total trips from i to j
wijk = Fraction of workers living in i, working in j who
belong in NVEH-DLIC category k
Pijkm = Logit probability of a worker of type k, living in i,
working in j, using mode m
Then:
Tijm = Tij *{Sk wijk* Pijkm} [7]

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Theoretical issues

• Gumbel IID convenient but is it realistic?

• IID components imply unrelated options in the
unobserved components - new models account for
relations
• Trips are related
– IIA problem
– Use different formulations

73
Independence of Irrelevant Alternatives (IIA)

• Note that for two modes in the choice set, say m and
n:
Pim eVim
= Vin = eVim -Vin [8]
Pin e
– i.e., relative probability of choosing mode m versus mode
n depends only on the utilities of m and n, independent of
what other alternatives are in the choice set
• Problems with this?
• Blue Bus - Red Bus

74
IIA - ii

• If the IIA assumption is not valid, we can return to

Eqn. [3] and make another distributional
assumptions about the error term, which will
generate a new model with different characteristics
• The two most common alternatives to the logit
model are:
– Nested logit (can handle complex decision structures)
– Probit (normal error terms; very general model, but
difficult to work with).

75
Elasticity-based models

• The elasticity of demand with respect to (wrt) a

variable such as price, will measure the impact of
change in price on the quantity demanded. This is
referred to as the price elasticity of demand.
– Elasticity is defined as the rate of change in travel
demand wrt a variable, normalized by the current levels
of demand and the variable in question.
– If D0 is the current demand level, and x0 is the current
value of the system variable of interest, the elasticity of
demand wrt x is represented as follows
¶ D / ¶ x ¶ D / D0
– eDx = = [9]
D0 / x0 ¶ x / x0
76
Point estimate of elasticity

• Where ¶ D / ¶ x is the partial derivative of D wrt x

• Elasticity as a point estimate
– Equation [9] expresses elasticity as a point estimate for
the “operating point” (D0,x0). The derivative at the
operating point to measure the rate of change.
– Elasticity changes from one point to another thus
representing the sensitivity of demand to changes in
system
– To differentiate demand function D wrt x requires the
demand function expressed as function of x
– If demand functions are not available, we use Arc
Elasticity

77
Arc elasticity

• If we know how demand changed in response to a

specific change in the system, arc elasticity is used.
– Arc elasticity is therefore the percentage change in
demand given a percentage change in an explanatory
variable
– DD / D0 DD / Dx [10]
eDx = =
Dx / x0 D0 / x0
• DD is the change in demand level from the original
value, DD = (D1-D0)
• Dx is the change in system variable from the original
value, Dx = (x1-x0)
– The point elasticity of demand and arc elasticity of
demand are same only when D is represented as a linear
function of x 78
Elasticity definitions

• Elastic demand
– When the absolute value of elasticity is greater than 1,
i.e., a percentage change in x is accompanied by a greater
than one percentage change in demand, the demand is
said to be elastic wrt x
• Inelastic demand
– When the absolute value of elasticity is less than 1, i.e., a
percentage change in x is accompanied by a less than one
percentage change in demand, the demand is said to be
inelastic wrt x
• Unit elasticity
– When the absolute value of eDx is exactly 1
79
Direct and Cross elasticities

• Direct demand elasticity

– When elasticity measures the change in demand for a
good or service wrt a variable that is directly related to
that good or service.
• For example, measuring the elasticity of transit
demand wrt transit fare
• Cross demand elasticity
– When elasticity measures the change in demand for a
good or service wrt a variable that is related to a
comparable good or service.
• For example, measuring the elasticity of transit
demand wrt automobile travel cost

80
Direct Elasticity Formulae
Direct Elasticity of the individual selecting alternative i with
respect to a change in some attributes of the alternative i.

%age_Change_in_P dt 8.5%
Arc _ Elasticity = = = -0.85
%age_Change_in_Cost dt - 10%

Direct Elasticity of Pautod wrt COSTd

Weight of attribute (Bdt) -0.5691

Amount of attribute (Xdt) 2.6
Probability of mode (Pdt) 42.57%
Direct Elasticity= Bdt * Xdt * (1-Pdt) -0.85

81
Direct Elasticity :Auto Choice & Trip Costs
Direct Elasticity and Change in Auto Mode Choice

%-d_Pautod Elasticity

100.0% 0.00

80.0% -0.10
Percentage Change in Auto mode-splits
Percentage in Auto Mode Choice

-0.20
60.0%
-0.30
40.0%

Elasticity Values
Elasticity Values
-0.40
20.0%
-0.50
0.0%
-0.60
-90%
-80%
-70%
-60%
-50%
-40%
-30%
-20%
-10%

10%
20%
30%
40%
50%
60%
70%
80%
90%
-100%

100%
0%
-20.0%
-0.70
-40.0%
-0.80

-60.0% -0.90

-80.0% -1.00
Percentage Change in Auto Trip Cost

82
Cross Elasticity Formulae
Cross Elasticity of the individual selecting alternative i with respect
to a change in some attributes of the alternative j.

%age_Change_in_P dt - 2.6%
Cross _ Elasticity = = = 0.26
%age_Change_in_Cost tt - 10%

X-elasticity of Pautod wrt COSTt

Weight of attribute (Btt) -0.5691

Amount of attribute (Xtt) 1
Probability of mode (Ptt) 45.36%
Cross Elasticity= Btt * Xtt * (-Ptt) 0.26

83
Cross Elasticities: Auto Choice & Transit Fare

%-d_Pautod
Percentage Change in Auto Driver Mode Choice

30.0%

20.0%

10.0%

0.0%

-10.0%

-20.0%

-30.0%
-100% -50% 0% 50% 100%

Percentage Change in Transit Fare

84
 Additional sources
• Ortuzar Willumsen - Chapters 8 and 9
• http://www.bts.gov/ntl/DOCS/SICM.html
(Spear’s report on how to apply models)
• http://www.bts.gov/ntl/DOCS/UT.html
(self-instructional overview with examples)
• http://www.tfhrc.gov/safety/pedbike/vol2/
sec2.5.htm (simple description of most of
the key issues)

85
 Summary
• Rational economic behavior
• Utility linear in systematic and random
components
• Choice probability is function of utilities
– non linear function!
• Application by enumeration is best -
weighted average by market segments
may be good - depends on application!
• Aggregate models are also available –
approximate!
• Surveys must be used for this step
86