Poster presented at TRB 2015. www.trb.org/AnnualMeeting2015/annualmeeting2015.aspx www.its.leeds.ac.uk/people/t.dekker

1. Indirect Inference for the application of Random Regret-Minimisation to large
scale travel demand
Thijs Dekker, Stephane Hess and Sander van Cranenburgh
University of Leeds, Delft University of Technology
Objective
Reducing the computational burden of estimating
large-scale Random Regret Minimisation models.
Introduction
• Estimating large-scale RRM-based discrete choice
models is time consuming.
• The computational burden increases exponentially
with the number of alternatives in the choice set.
• This paper applies Indirect Inference to
significantly reduce estimation time without
losing too much accuracy.
Random Regret Minimization
• Random Regret Minimization: individuals select
alternatives based on the notion of least regret
(Chorus, 2010).
• Regret arises when an alternative performs
worse than other activities on a particular
attribute.
• Alternative decision rule accounting for context
effects and semi-compensatory choice behaviour
• In RRM relative attribute level performance is
more important that absolute attribute level
performance.
• Regret R is defined by:
Rnti =
K
k=1 j=i
ln(1 + exp(βk(xntjk − xntik))) (1)
• n is the individual, t the choice task
• i and j represent alternatives
• k denotes attributes such as travel time and cost
• β and x are the coefficients and attribute levels
Indirect Inference
1 Indirect Inference (Gourieroux et al. (1993))
avoids estimation of a complex true model.
2 True model only used for simulating M datasets
with different β.
3 A simpler auxiliary model is used in estimation.
4 Simulation datasets are used to understand the
relationship between the simulated parameters for
the true models, and the estimated parameters
for the auxiliary model. The relationship is
captured by the binding function.
5 Finally, the true parameters (including standard
errors) are estimated on the true data using the
binding function and the auxiliary model.
Applications of Indirect Inference for discrete choice
modelling are discussed in Keane and Smith (2003)
and Wang et al. (2013).
II for RRM
• The true model is the RRM model
• Requires (J-1) pairwise comparisons for each alternative
on each attribute
• The auxiliary model is the standard
linear-in-parameters RUM model
• No binary comparisons required
• Linear binding function applied, polynomial
approximations will be explored in future research.
Model specification
• Station choice model is of MNL form, NL
explored in future research.
• In total the model comprises 20 parameters, 12
RUM (constants), 8 RRM (TT + # connections)
• Non-II estimation of RRM model takes > 8 days.
Important Results
• ‘Station choice’ model important input for the ‘mode choice’ model in the Dutch National Model.
• The II method reduces the computational burden of an RRM-based station choice model by > 75%.
• We show that estimation of RRM-based large-scale travel demand models becomes more feasible.
• Appropriate selection of the binding function and domain for simulation is challenging in II.
Dutch National Model - Station choice
• Selection of departure and arrival train stations and related access and egress modes of 791 commuters.
• 36 station pairs and 19 possible access-egress combinations, i.e. 684 alternatives.
• Revealed preference data from MON2004 household surveys.
• RUM and RRM model both have similar model fit, implications for model prediction yet unclear.
• Two rounds of II applied to update the domain of the parameters, both use M = 150.
• Bias wrt true RRM parameters reduces significantly in the second round due to selection of more
appropriate domain in the simulation stage (see Table). They also fall within two standard deviations
of the true model parameters suggesting the II method works.
Results II
True RRM II Round 2 Bias
Est SE Est SE
CdAcc -2.83 0.25 -2.87 0.29 -0.04
CpAcc -4.13 0.41 -4.28 0.79 -0.15
BtAcc -2.80 0.31 -2.82 0.36 -0.02
CyAcc -0.20 0.17 -0.21 0.17 -0.01
CpEgr -5.67 0.47 -5.75 0.82 -0.08
BtEgr -3.83 0.24 -3.97 0.22 -0.14
CyEgr -2.46 0.17 -2.48 0.19 -0.02
AccTCd* -0.10 0.01 -0.10 0.02 0.00
AccTBt* -0.08 0.01 -0.08 0.02 0.00
AccTCy* -0.22 0.01 -0.22 0.01 0.00
AccTWk* -0.18 0.01 -0.18 0.01 0.00
EgrTBt* -0.04 0.01 -0.04 0.02 0.00
EgrTCy* -0.21 0.02 -0.21 0.03 0.01
EgrTWk* -0.17 0.01 -0.17 0.01 0.00
AETCp* -0.20 0.03 -0.19 0.03 0.01
Conxstat* 3.79 0.33 4.84 0.34 1.05
BtAccUrb4 1.01 0.27 1.02 0.35 0.01
BtAccUrb5 1.21 0.30 1.21 0.33 0.00
BtEgrUrb4 0.07 0.30 0.11 0.33 0.04
BtEgrUrb5 1.22 0.23 1.30 0.26 0.08
References
Chorus, C. (2010) ‘A new model of random regret
minimization’ EJTIR, 10(2).
Gourieroux, C., Montfort, A. and E. Renault
(1993) ‘Indirect Inference’, Journal of applied
econometrics,8(1),85-118.
Keane, M. and A. Smith (2003) ‘Generalized indi-
rect inference for discrete choice models’ Yale.
Wang, Q., A. Karlstrom and M. Sundberg (2013)
‘Bias correction via indirect inference for mixed
logit specifications under sampling of alternatives.
hEART conference 2013, Stockholm
Contact Information
Dr. Thijs Dekker
t.dekker@leeds.ac.uk