Critical Issues in Estimating and Applying Nested Logit Mode Choice Models

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Critical Issues in Estimating and Applying Nested
Logit Mode Choice Models

• Ramachandran Balakrishna
• Srinivasan Sundaram
• Caliper Corporation
• 12th TRB National Transportation Planning
  Applications Conference, Houston, Texas
• 19th May, 2009

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Outline

• Introduction
• Motivation
• Non-uniqueness in model estimation
• Choice of utility scaling method
• Numerical example
• Conclusion
• References

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Introduction

• Nested Logit (NL) popular for mode choice
• Captures unobserved shared effects across modes
• Requires estimation from disaggregate data
• Unknowns
• Utility coefficients, nest thetas
• Software
• Biogeme, ALOGIT, TransCAD, etc.

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Motivation Highlight critical NL issues

• Estimates may not be unique
• Coefficients unique only for fixed thetas
• Daganzo and Kusnic (1992)
• Final estimates depend on starting thetas
• Koppelman Bhat (2006)
• Wide range of estimates possible
• Utilities must be scaled
• Parent thetas are built into the utilities
• Utilities need scaling before comparing across
  nests
• Estimation programs use different scaling methods
• Some are inconsistent with utility maximization
• Koppelman Wen (1998)

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Non-Uniqueness in Model Estimation (I)

• Example (from Koppelman Bhat, 2006)
• Three sets of starting theta values
• Results very sensitive to starting theta values
• Very similar or identical final LL likely
• Harder to select a good model
• Unrealistic estimates possible

Starting thetas Non-motorized 0.5 0.2 1.0
  Auto 0.5 0.7 1.0
Final thetas   Non-motorized Auto 0.579 9.00E-05 0.226 0.703 0.227 0.703
Constants Transit -1.34 -0.17 -0.169
  Shared Ride 2 -0.0001 -0.282 -0.282
ln(Persons per HH) Transit 0.545 0.899 0.9
  Shared Ride 2 0.0001 0.266 0.267
Travel time Motorized -9.00E-07 -0.0246 -0.0246
  Non-motorized -0.0762 -0.08 -0.08
Final log-likelihood (LL)   -4450.57 -4447.48 -4447.48
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Non-Uniqueness in Model Estimation (II)

• Model selection checks and guidelines
• Final log-likelihood need not be only criterion
• Coefficient magnitudes, signs
• Relevant ratios (e.g. value of time)
• Elasticities (within and across nests)
• Must re-estimate with various starting thetas
• Pick the best possible model
• Detailed multi-dimensional search
• One option grid search
• Implemented in TransCAD 5.0

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Utility Scaling

• Basic NL formulation
• q effects built into utilities
• Difficult to compare utilities across nests
• Counter-intuitive direct, cross elasticities
• Inconsistent with utility maximization
• Solution scale utilities to remove q effects
• Two scaling approaches

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Utility Scaling Methods (I)

• Scale by parent q
• Consistent with utility maximization
• Intuitive direct and cross elasticities
• Implemented in TransCAD 5.0

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Utility Scaling Methods (II)

• Scale by product of qs
• Requires dummy nests, constraints on qs
• Harder to apply and interpret
• ALOGIT

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Utility Scaling Methods (III)

• Choice of scaling method impacts mode shares
• Identical only for models with two levels of
  nests
• Estimation
• Utility maximization requires scaling by parent q
• Model application
• Critical to know how model was estimated!
• TransCAD 5.0
• Estimation options no scaling, scale by parent q
• Application options all three methods

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Numerical Example (I)

• TransCAD 5.0 (Caliper Corporation, 2008)
• Estimates and applies NL, MNL models
• Batch-enabled for efficient theta search
• Estimates select coefficients while fixing others
• Allows different scaling methods
• Has intuitive GUI
• Automatically combines different data sources
• Surveys, zonal tables, matrices, etc.
• Efficiently handles market segments

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Numerical Example (II)

• Travel survey (Southern California Assoc. of
  Govts., SCAG)
• 9885 survey records (home-based work trips)
• Modes Non-Motorized, Drive Alone, Carpool,
  Transit
• Utilities scaled by parent q
• 101 estimations of starting q in 0,1 , 0.01
  step size
• 52 valid runs with final q in 0,1
• Almost identical log-likelihood,

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Numerical Example (III)
Results Constants for DA, CP, NM
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Numerical Example (IV)
Results Coefficients of No_License Dummy, Walk
Time
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Numerical Example (V)
Results Estimated theta values
Theta_Auto (initial) Theta_Auto (estimated)
0.01 0.01207
0.02 -8.84438
0.59 0.012123
0.6 -8.91063
0.99 0.012115
0.9999 -8.84436
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Conclusion

• More care is required in estimating and applying
  Nested Logit mode choice models
• Good practice is to perform extensive estimation
  runs
• One should match the scaling used in estimation
  and application

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References
Caliper Corporation (2008) Travel Demand Modeling
with TransCAD, Version 5, Newton, MA. C. F.
Daganzo and M. Kusnic (1992) Another Look at the
Nested Logit Model, UC Berkeley report
UCB-ITS-RR-92-2. F. S. Koppelman and C. Bhat
(2006) A Self Instructing Course in Mode Choice
Modeling Multinomial and Nested Logit Models,
prepared for U.S. DOT, FTA. F. S. Koppelman and
C-H. Wen (1998) Alternative Nested Logit Models
Structure, Properties and Estimation.
Transportation Research 32B, No. 5, pp. 289-298.