Lecture 6 - Mode & Destination Choice Models

CIVE 461/861: Urban Transportation Planning

Outline

  1. Utility function variables
  2. Direct & cross-elasticity
  3. Forecasting & aggregation
  4. Limitations
  5. Extension to other choices

Trip-End Models

  • Trip end mode split (choice) models apply before trip distribution & split trip ends estimated in trip generation among ends (destinations)
  • Basically mode-specific trip generation models (e.g., regression or cross-classification)
  • Trip-end mode split is a function of socio-economic variables such as income & auto ownership
  • Cannot include modal level-of-service attributes (travel time, cost, etc.) since do not yet have O-D flows
  • Works better for short-term & when there is no modal competition & traffic congestion – small urban & rural areas where transit is a social service

Trip End Model Example

Trip Interchange Model

  • Trip interchange mode split (choice) models apply after trip distribution & split trip interchanges estimated in trip distribution
  • Since O-D flows are known, can compute travel times, costs, etc. for competing modes
  • Trip interchange models generally applied in medium to large urban areas where alternative modes are competitive & traffic congestion is a factor
  • Can assess broad range of policies:
    • Improved transit service (e.g., headways, coverage, travel time)
    • Road pricing, gasoline taxes, etc.
    • Transit fare policy
    • Parking supply & cost
    • HOV policies

Explanatory Variables in Mode Choice Models

Alternative Specific Variables

  • Travel time
    • In-vehicle
    • Out-of-vehicle
    • Walk (access & egress)
    • Wait (initial & transfer)
  • Out-of-pocket travel costs
    • Transit fare or “in-vehicle” auto cost
    • Parking cost
  • Other factors? Reliability, safety, comfort, convenience, etc.

Explanatory Variables in Mode Choice Models

Tripmaker Specific Variables

  • Income
  • Vehicle availability
  • No. of vehicles in household
  • Driver’s license? (0/1)
  • Age
  • Gender
  • Occupation
  • Household composition

Modeled Alternatives: The Choice Set

The number & definition of modeled modes depends on

  • Problem application
  • Available data
  • Network modeling capabilities
  • At a minimum, requires some representation of competition between auto & transit

Auto Mode Representation

  • Common to distinguish between drivers & passengers:
    • Auto driver mode: trip-maker drives a vehicle from origin to destination
    • Auto passenger mode: trip-maker is a passenger in car from origin to destination
  • Alternatively, we can distinguish between drive alone & shared trips
    • Drive alone mode: trip-maker is sole occupant of vehicle from origin to destination (single occupancy vehicle (SOV) trip)
    • Shared-ride mode: trip-maker is one of several vehicle occupants from origin to destination
      • Car driver for shared ride
      • Car passenger for shared ride with household member
      • Car pooling: driver or passenger in vehicle with non-household members

Transit Mode Representation

  • Possible ways to categorize transit include
    • Local (e.g., StarTran or Metro Transit) vs. regional (e.g., OMALiNK or N-E Ride)
    • Surface shared right-of-way (bus, streetcar) vs. dedicated ROW (subway, LRT, busway)
    • Bus vs. rail
    • Regular service vs. express vs. other premium service

Mixed Modes

  • Combined auto-transit modes exist, in which auto is used to access transit system
    • Park & Ride: trip-maker drives to a transit station & parks their vehicle at station
    • Kiss & Ride: trip-maker is driven as a passenger to a transit station & is dropped off there
  • Auto access greatly expands catchment area of transit services

Other Modes

There has been an explosion of modes in the last decade

  • Transportation network companies (TNCs): Uber, Lyft
    • Single ride
    • Pooled rides & van pools
  • Regular taxis
  • Motorcycles
  • Jitneys
  • Ferries, water taxis
  • Non-motorized modes
    • Walking
    • Bicycling
    • E-bikes
    • E-Scooters

Decision Structure

  • Mode choice can be represented as decision tree
  • Each node of tree represents an alternative & relationships among choices indicated via hierarchical tree structure (often called nesting structure)

Alternative Decision Structures

Example: Work Trip Mode Choice Model

A regional morning peak-period work trip mode choice model is a three-mode logit model as follows

d = auto-drive

p = auto passenger

t = transit

Example: Work Trip Mode Choice Model

\(V_m\) = utility for mode m

\(COST_m\) = out-of-pocket travel cost ($) for mode m

\(IVTT_m\) = in-vehicle travel time (min.) for mode m

\(OVTT_m\) = out-of-vehicle travel time (min.) for mode m

NVEH = avg. no. of vehicles per household in home zone

TWY = 1 if employment zone is located within the catchment area of a transitway station outside the CBD = 0 otherwise

REGION = 1 if home zone is located in a specific area = 0 otherwise

Example: Work Trip Mode Choice Model

Systematic utility functions

\[𝑉_𝑑=−0.55−0.57×𝐶𝑂𝑆𝑇_𝑑−0.20×𝐼𝑉𝑇𝑇_𝑑+0.75×𝑁𝑉𝐸𝐻\]

\[𝑉_𝑝=−2.28−0.57×𝐶𝑂𝑆𝑇_𝑝−0.20×𝐼𝑉𝑇𝑇_𝑝−0.30×𝑂𝑉𝑇𝑇_𝑡 +0.45×𝑁𝑉𝐸𝐻\]

\[𝑉_𝑡=−0.57×𝐶𝑂𝑆𝑇_𝑡−0.20×𝐼𝑉𝑇𝑇_𝑡−0.30×𝑂𝑉𝑇𝑇_𝑡+1.07×𝑇𝑊𝑌 −0.98×𝑅𝐸𝐺𝐼𝑂𝑁\]

Example: Work Trip Mode Choice Model

Important Notes on Mode Choice Example

  • Cost, IVTT, & OVTT are generic variables
    • Enter all utility with same parameter values (no OVTT for driver)
  • NVEH is an alternative specific variable
    • Enters two utility functions with different parameter values
  • There are alternative specific constants for drive & passenger modes but not transit
    • If there are M alternatives, we can statically identify M-1 alternative specific constants (ASC)
    • ASC account for unobserved but non-random variation – ASC will match market share for multinomial logit model

Important Notes on Mode Choice Example

  • Socio-economic variables do not vary between alternatives
    • If included in model, must enter as alternative specific variables
    • If included in model as generic variables, would add same utility to all alternatives & have no impact on choice probability
    • Can interact socio-economic variables with level of service (LOS) variables
      • E.g., travel cost / household income

Calculating Value of Travel Time (VTT) from Utility Function

  • We can calculate an implied VTT from model coefficients
  • From our previous example

\[−0.57×𝐶𝑂𝑆𝑇($)=−0.20×𝐼𝑉𝑇𝑇(𝑚𝑖𝑛)\]

  • How many $ would one pay to reduce their travel time by one hour?

\[𝑉𝑇𝑇=𝛽_{𝑡𝑖𝑚𝑒}/𝛽_{𝑐𝑜𝑠𝑡} =(−0.20)/(−0.57)=$21/ℎ𝑜𝑢𝑟\]

  • Similarly, VTT for OVTT = $31.6/hour
  • Question: How do you think VTT for IVTT compares for auto vs. transit modes?

Direct & Cross Elasticity

  • Direct elasticity: direct effect of changing a variable value related to a good on demand for the same good
    • E.g., elasticity of transit demand wrt transit fare, transit travel time, or transit headway
  • Cross elasticity: effect of changing a variable value related to a good on demand for a different good
  • E.g., elasticity of transit demand wrt auto travel time

Logit - Direct Elasticity

  • Direct elasticity of the probability of an individual \(n\) choosing alternative \(i\) wrt a change in an attribute/independent variable \(X_{ik}\) with coefficient \(\beta_k\) (ignoring \(n\) subscripts for simplicity)

\[e_{direct} = \frac{\partial P_i}{\partial X_{ik}}\frac{X_{ik}}{P_i} = (1-P_i)X_{ik}\beta_k\]

Logit - Cross Elasticity

  • Cross elasticity of the probability of an individual \(n\) choosing alternative \(i\) wrt a change in an attribute/independent variable \(X_{jk}\) with coefficient \(\beta_k\) for a different alternative

\[e_{cross}=-P_j X_{jk} \beta_k\]

  • Above is same regardless of alternative \(i\). I.e., all modes have the same cross-elasticity wrt an attribute \(k\) of mode alternative \(j\)
    • Above results from independence of irrelevant alternatives (IIA) property of basis logit model

Forecasting Mode Choice (Model Application)

  • Mode choice models generate choice probability predictions for individuals
  • For planning purposes, we are interested in total number of people in a zone or study area likely to choose each mode
  • Must aggregate individual choices
    • Total enumeration/microsimulation
    • Sample enumeration
    • Naïve aggregation
    • Classify with naïve aggregation

Total Enumeration

  • Simplest method but often not practical
  • Enumerate all individuals in study area
  • Calculate mode choice probabilities
  • Sum probabilities over all individuals
  • Problem: extremely expensive to survey all individuals & difficult to simulate them
  • Microsimulation models can be used to simulate individuals

Sample Enumeration

  • Second best to total enumeration
  • Requires representative sample of population
  • Calculate mode choice probabilities for sample
  • Sample prediction of mode shares can be substituted for population prediction
  • Problem: How to synthesize a sample for a future year?

Naive Aggregation

  • Treat individual choice model as an aggregate model
  • Use zonal averages for variables as inputs to compute “average” zonal probability
  • Problem: Choice probabilities are non-linear functions of variables so aggregation bias
  • Avoid this method!

Classification with Naive Aggregation

  • Classify population into relatively homogenous groups
  • E.g., by vehicle ownership & transit availability
  • Determine variable averages for each classification group
  • Use group averages to compute average mode shares
  • Sum mode shares
  • Most common method used in practice

Classification with Naïve Aggregation Example

A work trip mode split logit model includes the no. of hh. vehicles (NVEH) and whether a worker has a driver’s license (DLIC) as variables. The aggregation/forecasting procedure used is to:

  • Divide workers into “n” NVEH & DLIC categories
  • Estimate percentage of workers in each category by O-D pair
  • Compute mode choice probabilities for each category
  • Compute weighted average mode splits for each O-D pair

Aggregation Bias

  • Consider a zone in which people are identical except for their income, and that the probability of a person using transit depends only on the person’s income.

Aggregation Bias

  • Bias becomes worse for more heterogenous populations

Forecasting Example

\[𝑉_𝑎=\beta_1+\beta_2 𝐼𝑉𝑇𝑇_a+\beta_4 𝑂𝑉𝑇𝑇_𝑎+\beta_5 ((𝑂𝑃𝑇𝐶_a)/𝐼𝑁𝐶)+\beta_6 𝐴𝑂\]

\[𝑉_𝑡=\beta_3 𝐼𝑉𝑇𝑇_𝑡+\beta_4 𝑂𝑉𝑇𝑇_𝑡+\beta_5 ((𝑂𝑃𝑇𝐶_𝑡)/𝐼𝑁𝐶)\]

  • IVTT = in-vehicle travel time
  • OVTT = out-of-vehicle travel time
  • OPTC = out-of-pocket travel cost
  • INC = household income
  • AO = auto ownership level

Forecasting Example - Full Enumeration & Naive Aggregation

In this example, naive aggregation results in 3% overprediction of auto

Forecasting Example - Full Enumeration & Classification with Naive Aggregation

In this example, classification with naive aggregation results in <1% overprediction of auto

Destination Choice

  • Like mode choice, we can consider the trip distribution process using disaggregate choice models
  • Destination choice models attempt to represent the decision-process by individuals when deciding where to make a trip

Destination Choice

  • Unfortunately, destination choice is more complex than mode choice due to choice set explosion
  • We can address challenge by making use of logit properties to draw a random sample of alternatives

Joint Mode-Destination Choice

Often mode-destination choice a joint process: choosing to walk will affect destination choice & choosing a close destination will affect mode choice

Other Choices

  • Home location choice (multinomial logit) – similar to destination choice
  • Vehicle ownership choice? 1, 2, 3, 4, etc. vehicles (ordered logit)
  • Departure time choice? 8AM, 9AM, 10AM, etc. (ordered logit)
  • Party size choice? 1, 2, 3, 4, 5, etc. persons (ordered logit)
  • Choice set formation
    • What destinations do I consider? Do I consider only destinations within my neighborhood? Do I consider only destinations within a certain distance or travel time?