Critical Issues in Estimating and Applying Nested Logit Mode

Choice Models

Ramachandran BalakrishnaSrinivasan Sundaram

Caliper Corporation

12th TRB National Transportation Planning Applications Conference, Houston, Texas

19th May, 2009

Outline

• Introduction• Motivation• Non-uniqueness in model

estimation• Choice of utility scaling method• Numerical example• Conclusion• References

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.

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)

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

0.5799.00E-05

0.2260.703

0.2270.703

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

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

Utility Scaling

• Basic NL formulation

– effects built into utilities– Difficult to compare utilities across nests– Counter-intuitive direct, cross elasticities– Inconsistent with utility maximization

– Solution: scale utilities to remove effects• Two scaling approaches

)ln(

)| (

CPDA

CPDA

DA

VV

VV

V

eeLogsumAuto

ee

eAutoAloneDriveP

Utility Scaling Methods (I)

• Scale by parent

− Consistent with utility maximization− Intuitive direct and cross elasticities− Implemented in TransCAD 5.0

AutoCPAutoDA

AutoCPAutoDA

AutoDA

VV

VV

V

eeLogsumAuto

ee

eAutoAloneDriveP

//

//

/

ln

)| (

Utility Scaling Methods (II)

• Scale by product of ’s− Requires dummy nests, constraints on ‘s− Harder to apply and interpret− ALOGIT

Auto

VV

VV

V

CPDA

CPDA

DA

eeLogsumAuto

ee

eAutoAloneDriveP

Motorized

//

//

/

where

ln

)| (

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

• Model application– Critical to know how model was estimated!

• TransCAD 5.0– Estimation options: no scaling, scale by parent – Application options: all three methods

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

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 • 101 estimations of starting in [0,1] , 0.01

step size• 52 valid runs with final in [0,1]

− Almost identical log-likelihood,

Numerical Example (III)Results: Constants for DA, CP, NM

Numerical Example (IV)

Results: Coefficients of No_License Dummy, Walk Time

Numerical Example (V)

Results: Estimated theta values

Theta_Auto (initial)

Theta_Auto (estimated)

0.01 0.012070.02 -8.844380.59 0.0121230.6 -8.910630.99 0.012115

0.9999 -8.84436

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

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.