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ESTIMATION OF DRIVERS ROUTE CHOICE USING

MULTI-PERIOD MULTINOMIAL CHOICE

MODELS

Stephen Clark and Dr Richard Batley

Institute for Transport StudiesUniversity of Leeds, U.K.

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Introduction

• Where ‘panel’ data is available on choices made by individuals, it is reasonable to assume that previous experiences somehow condition these choices

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Data set 1

• Number plate matching exercise conducted in the City of York, U.K.

• 100% survey• 08:00 to 09:00 • 27, 28 June; 7, 8, 9, 11, 13, 27

September; 18 October, 2000

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Repetition and contiguity

• Of the vehicles observed on 2 ‘adjacent’ survey days, over 50% used the same route on both days

• As the period between 2 survey days increased, this percentage dropped– e.g. for 2 survey days 14 working days

apart, the percentage was 35%-40%

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Repetition and O-D pairs• For a particular O-D movement on 4

‘consecutive’ days:– 3 vehicles travelled O-D on all 4 days– 8 vehicles travelled O-D on any 3

‘consecutive’ days– 28 vehicles travelled O-D on any 2

‘consecutive’ days

• Of these 39 repeat vehicles, only on 3 occasions out of the 53 possibilities did they follow a different route on a ‘consecutive’ day

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Habit• Suggests route choice data

contains a high degree of habitual information

• If habitual behaviour is explicitly modelled, then its strength can be estimated

• Failure to account for repetition and route experience may undermine the validity of any models

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Random effects probit

U t ilit y f r om alt er nat ive j at t ime t is given by:

jtjtjt xU TtJj ,...,1;,...,1

A ssume:

jjtjt uv ,

wher e v jt and u j ar e bot h N or mally dist r ibut ed wit h zer o means and ar e independent of each ot her

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2

1,corr

u

ujsjt

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Modelling problems

• LIMDEP failed to estimate a parameter in the range 1

• GAUSS code applying Chamberlain’s conditional maximum likelihood estimation detected lack of variability in explanatory variables unable to estimate model

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Multinomial multi-period probit

Autoregressive structure, correlations between alternatives and time periods, unobserved heterogeneity across individuals, differential variances across alternatives

Ut ility to person n f rom alternat ive j at t ime t is given by:

njtjnjtnjt xU TtJj ,...,1;,...,1

A ssume:

nJTTnnJnn ,...,,...,,..., 1111 ~ jk ,,0IIDN

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Geweke’s GAUSS code

• Multinomial multi-period probit• AR(1) errors for each choice• Individual-specific random effects

for each choice• Two estimation methods

1. Method of Simulated Moments2. Simulated Maximum Likelihood

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Modelling problems

• Both methods failed to estimate a model

• Presence of singular matrix• Again, suspected artefact of lack of

variability in explanatory variables

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Data set 2• Stated preference study of

route and departure time choice in City of York, U.K.– How do people respond to an increase

in travel time and/or travel time variability?

– 2-stage study, involving customisation

– 5 cards

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Stage 1

00:081 currentT

4currentD 30:082 currentT

35:083 currentT

For a typical working day, please could you give the time when you normally set out f rom home and the range of arrival times at work that result? Departure time f rom home: Earliest arrival time at work (if traffi c is very light): Latest arrival time at work (if traffi c is badly congested): Distance of this journey (in miles):

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Derived time variables• ‘get off earlier’ time (G)

• journey time (Q)

• journey time variability (S)

• late time (L)

11 TTG current

12 TTQ

23 TTS currentTTL 33

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Stage 2

Alternative

Departure Time

Distance Earliest arrival time

Latest arrival time

Ranking

1 9:45am 3 miles 10:30am 10:50am

2 9:40am 3 miles 10:15am 10:35am

3 9:20am 5 miles 9:55am 10:20am

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Field study• Members of staff at the York Health

Services Trust• Prize draw incentive• 165 usable first stage questionnaires• 56 usable second stage

questionnaires34% response rate for second stage

• Ranked data ‘exploded’ into binary choice data840 binary choice observations

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MNL Parameter Estimate t-statistic βD 0.3202E-01 0.6 βG -0.1983E-01 -3.5 βQ 0.1472 8.9 βS 0.1265 7.3 Mean LL -0.595124 Observations 840

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Random parameters logit

Utility to person n from alternative j at time t is specified:

njtnjtnnjtxU

where:

n ~ *f

njt ~ IID extreme value, independent of n and njtx

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Random parameters logit

D e c o m p o s e :

nn b

w h e r e :

b i s m e a n , n i s s t o c h a s t i c d e v i a t i o n

njtnjtnnjtnjt xxbU

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RPL 1 Parameter Estimate t-statistic βD 0.0631 1.026 βG -0.0408 -1.850

G 0.1549 6.462 βQ 0.2366 7.214

Q 0.1378 5.018 βS 0.1845 6.462

S 0.0934 2.807 Mean LL -0.500256 Observations 840

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RPL 2 Parameter Estimate t-statistic βD 0.0680 1.214

cG -4.6982 -5.683 sG 2.2337 5.383

βG -0.1104

G 1.3335 cQ -1.6738 -11.005 sQ 0.6600 4.377

βQ 0.2332

Q 0.1723 cS -1.8661 -12.827 sS 0.3094 1.230

βS 0.1623

S 0.0514 Mean LL -0.537409 Observations 840

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Summary• Where ‘panel’ data is available on

choices made by individuals, it is reasonable to assume that previous experiences somehow condition these choices

• Data set 1: RP route choice data– Random effects probit– Multi-period multinomial probit

• Data set 2: SP route and departure time choice– Pseudo-panel– Random parameters logit– Evidence of repeated observations effects