Multimodal Choice Modelling – Some Relevant Issues.

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Published paper

Ortuzar, J. de D. (1980)

Multimodal Choice Modelling – Some Relevant Issues.

Institute of Transport Studies, University of Leeds, Working Paper 138

ABSTRACT

ORTUZAR, J. de D. (1980) MultimodaL choice modelling

-

some r e l e v a n t i s s u e s . Leeds: University o f Leeds,

Inst.

Transp. Stud., WP 138. (unpublished)

This paper g i v e s an overview of t h e most r e l e v a n t

i s s u e s r e l a t i n g t o t h e a p p l i c a t i o n of multimodal choice

models ranging from d a t a c o n s i d e r a t i o n s , such a s a l t e r n a t i v e

sampling s t r a t e g i e s and measurement techniques, t o t h e h o t l y

debated aggregation i s s u e . P a r t i c u l a r emphasis i s placed on

t h e s p e c i f i c a t i o n and e s t i m a t i o n problems o f disaggregate

choice models.

D r . Ortuzar's address i s : Departamento de I n g e n i e r i a de Transporte Universidad C a t o l i c a de Chile

C a s i l l a

114-D

CONTENTS

Abstract

1. I n t r o d u c t i o n

2. The problem of aggregation

3. Data c o l l e c t i o n and measurement

3 . 1 Representation and measurement of t r a v e l a t t r i b u t e s 3.2 A l t e r n a t i v e sampling s t r a t e g i e s

4;

Model s p e c i f i c a t i o n

4 . 1

Model s e l e c t i o n

4.2 Choice s e t determination

4 . 3 Defining t h e form of t h e u t i l i t y function

4 . 4

Model s t r u c t u r e and v a r i a b l e s e l e c t i o n

5.

Model estimation

5.1 General statement of t h e problem

5.2

Maximum

l i k e l i h o o d estimation and a l l i e d s t a t i s t i c a l t e s t s

5.3 Model comparison through goodness-of-fit measures

5.4

Validation samples

5.5 Comparison of non-nested models

5.6

Estimation of models from choice-based samples

5.7

Estimation of h i e r a r c h i c a l l o g i t models Acknowledgements

Figures

M U L T I M O D A L C H O I C E M O D E L L I N G

-

SOME R E L E V A N T ISSUES

1. INTRODUCTION

The problems of mode choice modelling and f o r e c a s t i n g have been

approached i n many ways s i n c e t h e mid-50s, but f o r t h e most p a r t ,

research and a p p l i c a t i o n s have been concerned with choice between c a r

and public t r a n s p o r t which, it has been argued, i s t h e s i t u a t i o n faced by t h e m a j o r i t y of t r a v e l l e r s i n t h e journey-to-work. However, it i s obvious t h a t people do not n e c e s s a r i l y choose between two s p e c i f i c

a l t e r n a t i v e s only when making t h e i r choice, but i n s t e a d t h e y g e n e r a l l y

confront options such a s d r i v i n g a c a r , t r a v e l l i n g a s passengers i n a

c a r , bus o r t r a i n , r i d i n g a b i c y c l e o r a s c o o t e r o r simply walking. I n

a d d i t i o n , each t r i p might u t i l i s e a combination of modes, i . e . mixed-

mode t r i p s ( f o r example, park-and-ride), although it can be argued t h a t some mixed options a r e so u n l i k e l y t h a t t h e p r o b a b i l i t y of t h e i r

s e l e c t i o n can be considered a s zero. A s a consequence, it has often

been s u g g e s t e d t h a t i n d i v i d u a l s can be considered a s u s e r s of t h e i r

'main mode' (e.g. t h e procedure used i n t h e majority of t r a n s p o r t a t i o n

s t u d i e s i n t h e U.K. )

.

However, t h i s procedure i s c l e a r l y i n a c c u r a t e f o r many people who depend on another mode f o r access t o t h e major one.

Also, with t h e i n c r e a s i n g departure from t r a d i t i o n a l p o l i c i e s based on

a 'pure' mode context and t h e emphasis on an ' i n t e g r a t e d ' approach t o

urban t r a n s p o r t problems, t h e time i s r i p e f o r models which a r e more

o r i e n t e d towards a l t e r n a t i v e p o l i c i e s , such a s p r i c e penalty measures,

t r a f f i c r e s t r a i n t and exclusion schemes, bus p r i o r i t y measures,

i n c e n t i v e s t o park-and-ride and car-pooling, e t c . , and which must be

multimodal ( a s opposed t o b i n a r y ) i n n a t u r e .

During t h e l a s t decade, and p a r t i c u l a r l y over t h e l a s t f i v e y e a r s ,

s i g n i f i c a n t advances have been made i n t r a v e l demand f o r e c a s t i n g

methods. The most important and widely promoted new techniques have

been t h e so-called 'disaggregate' o r 'individual-choice' o r 'second

generation' models ( f o r a good review of t h e o r e t i c a l developments, see

Williams, 1979). These models have been u s u a l l y generated w i t h i n a

'random u t i l i t y ' t h e o r y framework(*) ( f o r a review, s e e Domencich and

-. .

( * ) Note t h a t t h e t h e o r y i s not constrained t o disaggregate models only;

McFadden, 1975). I n t h i s quanta1 choice theory, t h e decision-maker i s

assumed t o choose t h e option ( A . ) which possesses, a s f a r a s he i s

J

concerned, t h e g r e a t e s t u t i l i t y U . . I n order t o account f o r d i s p e r s i o n

J

-

t h e f a c t t h a t i n d i v i d u a l s with t h e same observable c h a r a c t e r i s t i c s do not n e c e s s a r i l y s e l e c t t h e same option

-

t h e modeller introduces

a random element e i n a d d i t i o n t o each measured i n d i v i d u a l ' s u t i l i t y

-

j

U..

I n t h i s way, t h e u t i l i t y of a l t e r n a t i v e A . i s a c t u a l l y represented

J J

as:

Ortuzar and Williams (1978) have described pedagogically, t h e

generation of random u t i l i t y models, ranging from t h e very convenient

but t h e o r e t i c a l l y r e s t r i c t i v e multinomial l o g i t (MNL) model, t o t h e

general and powerful but r a t h e r i n t r a c t a b l e multinomial p r o b i t ( M N P )

model.

I n t h i s paper we wish t o discuss b r i e f l y some i s s u e s r e l a t e d t o

t h e a p p l i c a t i o n o f such models (and i n some cases any model) t o t h e

problem of choice of mode f o r t h e journey-to-work. We w i l l consider questions of d a t a , such a s t y p e of data, a l t e r n a t i v e sampling s t r a t e g i e s

and problems of measurement, and modelling i s s u e s , such a s model

s p e c i f i c a t i o n and estimation. However, we

w i l l

f i r s t address t h e aggregation problem which l i e s a t t h e h e a r t of one of t o d a y ' s most

h o t l y contested debates

-

whether t o use aggregate o r disaggregate

models, and i n which circumstances.

We do not attempt t o be comprehensive on t h e s e i s s u e s , so we

r e f e r t h e reader t o good general discussions by McFadden (1976; 1979a);

Williams (1977; 1979); Hensher (1979a); Ben-Akiva e t a1 (1977; 1979);

Daganzo (1980) ; Daly (1979) ; Jansen e t a l (1979) ; Wnheim (1979) ;

Reid (1977) ; Spear (1977; 1979) ; and Williams and Ortuzar (1980b).

2. THE PROBLEM OF AGGREGATION

The aggregation i s s u e may be thought of i n very general terIUS a s

t h e path through which a d e t a i l e d d e s c r i p t i o n of an i n d i u i d u a l ' s

decision-making process, a s imputed by a modeller, i s transformed i n t o

a s e t of observable e n t i t i e s and f o r r e l a t i o n s which can be u s e f u l l y

employed by him. I n an econometric i n t e r p r e t a t i o n of ( t r a n s p o r t demand)

models, t h e aggregation ovsr

unobservabZe entities r e s u l t s i n

a

p r o b a b i l i s t i c d e c i s i o n ( c h o i c e ) micro model, and t h e aggregation over

aggregate o r macro r e l a t i o n s . I n t h i s sense, t h e d i f f i c u l t y of t h e

aggregation problem depends, t o a l a r g e e x t e n t , on how t h e components

of a system a r e described within t h e frame of r e f e r e n c e used by a

modeller, because it i s p r e c i s e l y t h i s framework which w i l l determine

(*I

t h e degree of v a r i a b i l i t y t o be accounted f o r i n a ' c a u s a l ' r e l a t i o n .

To give an example, if t h e frame of reference used by a modeller i s , say, t h a t provided by t h e entropy maximising approach, t h e explanation

of t h e s t a t i s t i c a l d i s p e r s i o n i n a given d a t a s e t w i l l be very d i f f e r e n t

t o t h a t provided by another observer using a random u t i l i t y maximising

approach, even i f t h e y both f i n i s h up with

identicaz model functions

( t h e e q u i - f i n a l i t y i s s u e , s e e , f o r example, Williams, 1979). The

i n t e r p r e t a t i o n of such a model, say t h e c l a s s i c i a l

MNL,

depends however

on t h e theory used t o generate i t , and t h i s i s p a r t i c u l a r l y important f o r i t s e l a s t i c i t y parameters. For t h e entropy maximising modeller,

t h e parameter corresponds t o a Lagrange m u l t i p l i e r a s s o c i a t e d

' I . . .

with the change i n ZikeZihood of observing a given

aZZocation (share) pattern

...

with respect t o incrementaZ

changes i n system

t r i p

cost measures".

(WiZZiams,

2 9 7 9 )

For t h e second modeller, t h e same parameter i s now i n v e r s e l y r e l a t e d

t o t h e standard d e v i a t i o n of t h e u t i l i t y d i s t r i b u t i o n s from which t h e

model i s generated (**) s e e ~ i l l i a m s (1.977).

I f we choose t o use a random u t i l i t y approach, t h e aggregation

problem w i l l reduce, t o o b t a i n from d a t a , a t t h e l e v e l of t h e i n d i v i d u a l , aggregate measures such a s market shares of d i f f e r e n t modes, flows on

l i n k s , e t c . , which a r e t y p i c a l f i n a l model outputs. There a r e two

obvious ways of proceeding, a s shown i n Figure l ( a ) , which a r e b a s i c a l l y

d i s t i n g u i s h e d by having t h e process of aggregating i n d i v i d u a l d a t a

before

o r

a f t e r

_{model e s t i m a t i o n . I f t h e data i s grouped p r i o r t o t h e}

estimation of t h e model, we w i l l have t h e c l a s s i c a l ' a g g r e g a t e b p p r o a c h

which has been h e a v i l y c r i t i c i s e d f o r being i n e f f i c i e n t i n t h e use of data (because data i s aggregated, each observation i s not used a s a data p o i n t and t h e r e f o r e more d a t a i s needed), f o r not accounting f o r

(*l

I am g r a t e f u l t o Huw Williams f o r having explained t h i s i n t e r p r e t a t i o n t o me.

(**I

Two comments a r e worthwhil e here: f i r s t l y t h e f u l l i n t e r p r e t a t i o n of model parameters is-not t r a n s f e r a b l e within t h e o r i e s ; and, secondly, while i n some cases t h e i n t e r p r e t a t i o n might not m a t t e r

( i . e . i f one i s i n t e r e s t e d on flows i n networks) i n o t h e r s it can be very c r u c i a l , f o r example, if we a r e seeking t o endow p r e d i c t e d

t h e full v a r i a b i l i t y i n t h e d a t a (e.g. within zone variance may be

<

higher than iner-zonal v a r i a n c e ) , and f o r r i s k i n g s t a t i s t i c a l

d i s t o r t i o n and b i a s (such a s t h e wgll-known e c o l o g i c a l f a l l a c y ) , e t c .

The 'disaggregate' approach, on t h e o t h e r hand, e s t i m a t e s t h e model a t

t h e l e v e l of t h e i n d i v i d u a l t h u s apparently answering, a t t h i s s t a g e ,

t h e c r i t i c i s m s mentioned above. The question t h a t remains, however,

i s how t o perform t h e aggregation operation over t h e micro r e l a t i o n s ?

As we w i l l see below, t h e answer i s

...

' r a t h e r simply',

if

we a r e i n t e r e s t e d i n short-term p r e d i c t i o n s of journey-to-work mode choice

models; however, f o r o t h e r modelling requirements, t h e answer ranges

from

...

' d i f f i c u l t ' , t o

...

'almost impossible', u n l e s s being self-defeating i n t h e sense of r e q u i r i n g h e r o i c assumptions ( a s bad a s

t h o s e c r i t i c i s e d i n t h e 'aggregate' approach) and/or enormous amounts

of e x t r a d a t a . I n f a c t , Reid (1977) i n t h e context of developing a

disaggregate model system has remarked t h a t

"

...

t h e r e a r e p r a c t i c a l and t h e o r e t i c a l l i m i t s t o t h e a p p l i c a t i o n of s t r i c t l y behavioural methods

...

it i s

d i f f i c u l t t o preserve a behavioural s t r u c t u r e and conform t o aggregate observations..."

Before b r i e f l y describing t h e main aggregation methods, l e t u s

note t h a t t h e approach followed i n B r i t i s h p r a c t i c e i s a hybrid o f t h e

two mentioned above a s shown i n Figure l ( b ) . For example, household

based ( r a t h e r t h a n zonal) category a n a l y s i s has been used a t t h e t r i p

generation s t a g e , while t h e SELNEC and subsequent s t u d i e s used

weighting c o e f f i c i e n t s obtained from a standard disaggregate study

(e.g. McIntosh and Quarmby, 1970), i n a g e n e r a l i s e d c o s t formulation.

However, t h e e l a s t i c i t y parameters (e.g. p and

A )

and o t h e r model constants have been determined from an aggregate c a l i b r a t i o n . This

' t r a n s f e r a b i l i t y ' of micro parameters ( * ) between d i f f e r e n t s t u d i e s

(e.g. d i f f e r e n t regions and d i f f e r e n t times) w i t h t h e p o s s i b i l i t y

of l o c a l ' t u n i n g ' (Goodwin, 1978) may be seen a s a pragmatic approach

t o t h e aggregation problem. This i s s u e i s discussed a t more l e n g t h

by Williams and Ortuzar (1980b).

('1

Which i n t e r e s t i n g l y bears c l o s e analogy t o t h e s t r a t e g y proposed by Ben-Akiva C19791 f o r t h e t r a n s f e r a b i l i t y of disaggregate models, although with d i f f e r e n t motivations.

Returning t o t h e general approaches shown i n Figure l a , much

research has been d i r e c t e d r e c e n t l y a t a comparative a s s e s ~ m e n t of

aggregation methods ( s e e , f o r example, Ben-Akiva and Atherton, 1977;

Ben-Akiva and Koppelman, 1974 ; Bouthelier and Daganzo, 1979 ; Daly

,

1976; Dehghani and T a l v i t i e , 1979 ; Hasan, 1977; Koppelman, 1974,

1976a, 1976b; Liou e t a l , 1975; McFadden and Reid, 1975; Meyburg

and Stopher, 1975; .Miller, 1974; Reid, 1978a, 19781,; Ruijgrok,

1979; Watanatada and Ben-Akiva, 1978). The various methods proposed

o f f e r d i f f e r e n t s t r a t e g i e s f o r computing t h e s m a t i o n / i n t e g r a t i o n

over micro r e l a t i o n s , and include, among o t h e r s : t h e ' n a i v e ' approach,

sample enumeration methods, and c l a s s i f i c a t i o n approaches.

The naive approach c o n s i s t s of t h e d i r e c t s u b s t i t u t i o n of

aggregate o r average values o f t h e explanatory v a r i a b l e s i n t o t y p i c a l l y

non-linear, micro r e l a t i o n s , and it has been found t h a t t h e aggregation

b i a s may be severe i n t h i s case. I n t h e sample enumeration approach,

t h e impact of a given p o l i c y on each i n d i v i d u a l , i n a r e p r e s e n t a t i v e

sample, i s determined from t h e disaggregate model and population

f o r e c a s t s a r e t h e n computed by straightforward sumnation of t h e e f f e c t

over i n d i v i d u a l s according t o t h e sampling s t r a t e g y . This method i s

considered t o be p a r t i c u l a r l y u s e f u l f o r estimating impacts f o r

short-term p o l i c i e s ( s e e Ben-Akiva and Atherton, 1977). but must be modified when t h e c h a r a c t e r i s t i c s of t h e population change over t h e

f o r e c a s t i n g period ( s i n c e it cannot be assumed t h a t t h e d i s t r i b u t i o n of observable a t t r i b u t e s remains c o n s t a n t ] .

I n t h e c l a s s i f i c a t i o n approach, t h e t o t a l population i s p a r t i t i o n e d

i n t o r e l a t i v e l y homogeneous groups and then average (group) values of

t h e explanatory v a r i a b l e s a r e i n s e r t e d i n t o t h e disaggregate model t o

( * )

determine demand i n each group according t o t h e naive approach

.

The accuracy and e f f i c i e n c y of t h e method depends on t h e c l a s s i f i c a t i o n

involved, e.g. t h e t y p e and number of groups and t h e c h a r a c t e r i s t i c s

of t h e v a r i a b l e s included.

[*I

I n terms of i t s aggregation c h a r a c t e r i s t i c s , t h e p r a c t i c e i n B r i t i s h s t u d i e s w i t h use of market segment d i f f e r e n t i a t e d models, may perhaps b e s t be seen a s a v a r i a t i o n of t h i s c l a s s i f i c a t i o n

For

mode

choice s t u d i e s where only s h o r t term e l a s t i c i t i e s a r e required, t h e r e i s a consensus t h a t aggregating micro-relations, i . e .

' t h e 'disaggregate' approach, i s both f e a s i b l e , e f f i c i e n t and hence

d e s i r a b l e . However, i n longer term contexts where l o c a t i o n

( d i s t r i b u t i o n ) models need t o be considered and/or when network flows

a r e required t h e problem becomes much more involved. Very few s t u d i e s

have attempted t h e aggregation of micro-models i n t h e s e contexts so

it i s premature t o make d e f i n i t i v e judgements. One which did, t h e

SIGMO study ( P r o j e c t Bureau I n t e g r a l T r a f f i c and Transportation S t u d i e s ,

1977) encountered severe problems i n attempting t o r e c o n c i l e micro

d e s t i n a t i o n choice models with aggregate t r i p p a t t e r n s and abandoned

t h e disaggregate approach i n favour of an e x i s t i n g d i s t r i b u t i o n model

based on g e n e r a l i s e d c o s t s . More g e n e r a l l y , Reid (1977) has noted t h a t

while i n p r i n c i p l e a disaggregate model has a b e t t e r chance of

capturing t h e e s s e n t i a l c a u s a l i t y i n t h e d a t a , i n p r a c t i c e

"...

if t h e behavioural theory i s weak o r t h e models u n t e s t e d a g a i n s t experience, such a s with current i n d i v i d u a l l o c a t i o n models, t h e y may f a i l t o include some important f a c t o r s which a r e embodied i n aggregate o r summary v a r i a b l e s which merely show a c o r r e l a t i o n t o demand. These a r e more l i k e l y t o pick up unknown e f f e c t s

. . .

(and)

. . .

i f adequate disaggregate d a t a

w i l l not be a v a i l a b l e f o r f o r e c a s t i n g , models c a l i b r a t e d on aggregate d a t a w i l l be more accurate."

In t h e e a r l y 1970's t h e process of aggregation was u s u a l l y viewed

a s t h e r a t h e r s t r a i g h t f o r w a r d s o l u t i o n of a numerical problem which was

well understood i n p r i n c i p l e . I n p r a c t i c e , however, it has shown i t s e l f t o be a highly n o n - t r i v i a l process which embraces not only

considerations of numerical e f f i c i e n c y , but a l s o questions r e l a t i n g t o

t h e a v a i l a b i l i t y of f o r e c a s t s f o r i n d i v i d u a l explanatory v a r i a b l e s and

t h e s t a b i l i t y of t h e d i s t r i b u t i o n of explanatory v a r i a b l e s over time.

Furthermore, t h e r e i s a l s o concern about t h e r e l a t i o n of p r e d i c t i o n s t o

estimation and d a t a designs; t h e r e f o r e , any comparison of 'aggregatet

and 'disaggregatet models must involve, i m p l i c i t l y o r e x p l i c i t l y , a

3 . DATA COLLECTION AND MEASUREMENT

3.1 Representation and measurement of t r a v e l a t t r i b u t e s

I n any p a r t i c u l a r study, out of t h e l a r g e v a r i e t y of p o t e n t i a l l y

a v a i l a b l e f o r e c a s t i n g methods ( e .g. cross-sectional a n a l y s i s ; panel

data methods; aggregate time s e r i e s approaches) and estimation

techniques, data considerations alone w i l l normally r e s t r i c t t h e choice

t o one s i n g l e method. H i s t o r i c a l l y , t h e c r o s s - s e c t i o n a l approach has

c l e a r l y dominated, t y p i c a l l y i n conjunction with revealed preference

methods, although a l t e r n a t i v e approaches based, f o r example, on s t a t e d

p r e f e r e n c e s / i n t e n t i o n s , have been p r e f e r r e d on s e v e r a l occasions ( s e e

Ortuzar, 1980a). However, t h e general problem of discounting f o r t h e

over-enthusiasm o f respondents ( t h e 'yeah' b i a s ) has not y e t been

solved, and it has r e c e n t l y been suggested t h a t s t a t e d and revealed

preference methods may perhaps be b e t t e r used i n a complementary fashion,

where i n s i g h t s can be obtained which would not a r i s e i f e i t h e r approach

were used alone Csee, f o r example, Hensher and Louviere, 1979; Gensch,

1980). We have argued elsewhere, ( ~ i l l i a m s and Ortuzar, 1980a), t h a t it

i s not p o s s i b l e a t t h e cross-section t o discriminate between a l a r g e

v a r i e t y of p o s s i b l e sources of dispersion i n d a t a p a t t e r n s (such a s

preference d i s p e r s i o n , c o n s t r a i n t s , h a b i t e f f e c t s , e t c . ) . Panel d a t a

o r more simply, before-and-after information, may o f f e r some means t o

d i r e c t l y t e s t and perhaps r e j e c t hypotheses r e l a t i n g t o response, ( s e e

an i n t e r e s t i n g example i n Johnson and Hensher, 1980). On t h e o t h e r hand

models b u i l t on ' l o n g i t u d i n a l ' ( a s opposed t o cross-sectional d a t a )

have t e c h n i c a l problems of t h e i r own (e.g. how b e s t t o 'pool' t h e

information), b u t a discussion of t h e i r m e r i t s i s beyond t h e scope of

t h i s paper.

A r e l a t e d a r e a of concern has t o do with t h e problem o f measurement.

We wish t o d i s c u s s b r i e f l y h e r e t h e implications f o r parameter estimates

of using d i f f e r e n t measurement techniques and/or philosophies. For a

deeper i n s i g h t i n t o t h e problem we r e f e r t h e reader t o t h e e x c e l l e n t

discussions by Daly (1978) and Bruzelius (1979). The problems involved

i n obtaining measures of explanatory v a r i a b l e s (e.g. c o s t and time

requirements by a l t e r n a t i v e modes) a r e shown schematically i n Figure 2.

I d e a l l y we would l i k e t o o b t a i n information on t h e s e v a r i a b l e s a s

perceived by t h e commuter when t a k i n g h i s d e c i s i o n , e s p e c i a l l y i f we

about a f u t u r e s i t u a t i o n ? ) , but perhaps i n obtaining 'values of t i m e ' .

The f i g u r e r e f l e c t s t h e state-of-the-art i n t h e understanding o f t h e

r e l a t i o n s h i p s between ' a c t u a l ' , 'perceived', 'reported' and 'measured'

values. The t r o u b l e i s t h a t none of t h e arrows and boxes i n t h e f i g u r e

have y e t been q u a n t i f i e d . Knowledge i n t h i s a r e a , i s , l i t e r a l l y , sketchy!

The a n a l y s t i s t h e r e f o r e made t o choose between reported and measured ( o r

'engineering' o r ' s y n t h e s i s e d ' ) d a t a , and while models estimated on each

type of d a t a may prove reasonable i n themselves

"...

it i s very d i f f i c u l t t o p o s t u l a t e r e l a t i o n s h i p s t h a t

w i l l allow models c a l i b r a t e d on reported d a t a t o be applied t o synthesised data o r v i c e versa." ( ~ a l y , 1978)

Most probably t h e s a f e s t way out i s t o c o l l e c t information on both

reported and engineering values and t o make comparisons i n o r d e r t o gain

i n s i g h t from t h e two approaches. This i s , of course, more c o s t l y and

time consuming and, a s Hensher ( 1 9 7 9 ~ ) and o t h e r s have remarked, it i s seldom t h e case t h a t t h e a n d y s t f i n d s himself with t h e luxury ( o r

embarassment) of a l t e r n a t i v e data/methods a t hand.

We mentioned above t h a t one p o s s i b l e and a l t e r n a t i v e use f o r a model,

i n s t e a d of f o r e c a s t i n g , i s t o employ it f o r e s t i m a t i n g , f o r example, values of time ( ~ r u z e l i u s , 1979; Daly, 1978; Hensher, 1972; McFadden,

1978b; Prashker, 1979; Quarmby, 1967; Train, 1977; Gunn, Mackie and

Ortuzar, 1980; and some of t h e references c i t e d t h e r e i n ) . An o l d i s s u e

i n t h i s context i s t h e 'trader/non-trader' question, e.g. should t h o s e

i n d i v i d u a l s who appear t o be faced with a dominant(*) o p t i o n be excluded

from t h e sample? As Daly (1978) has c l e a r l y pointed o u t , t h e answer i s

d e f i n i t e l y no! The main d i f f i c u l t y has a c t u a l l y been due t o a

misunderstanding: t h a t only

observable,

and hence measured ( o r measurable)

a t t r i b u t e s should m a t t e r when defining whether an option i s dominant,

leaving out t h e c r u c i a l unobservables and/or unmeasured c h a r a c t e r i s t i c s .

I n t h i s sense, t h e l a r g e r t h e number of measured a t t r i b u t e s incorporated

i n t h e model, t h e smaller w i l l be t h e number of apparent 'non-traders' and,

b e t t e r s t i l l , t h e l e s s t h e i n f l u e n c e of unmeasured f a c t o r s (simply because

more of t h o s e a r e i n c o r p o r a t e d . )

( * ) An option which,

to the modeller,

looks b e t t e r i n every r e s p e c t

than t h e o t h e r s and happens t o be t h e chosen one ( i f it i s not t h e chosen one t h e i n d i v i d u a l i s deemed i r r a t i o n a l ! ) . Notice

t h a t t h i s i s not t o be confused with t h e i s s u e of

captive t r a v e l l e r s

(e.g. a person who needs'the c a r during t h e day) who should be

This brings us n a t u r a l l y i n t o the question o r using

a t t i t u d i n a l varia'bles feg. comfort, convenience, r e l i a b i l i t y ) t o

improve our models. (For a more complete discussion see,

Foerster, 19'(9b, Johnson, 1975; Spear, 1976; Stopher

e t

~1.1974; and Wemuth, 1978). I n terms of t h e influence of a t t i t u d i n a l

measures on t h e value of other parameters and on the general

performance of a model, there

i s

conflicting evidence i n t h e l i t e r a t u r e . McFadden (1976)

,

f o r example, concluded t h a t choice

was explained, t o a g r e a t extent, by t h e typical level-of-service

variables used i n conventional studies and t h a t a t t i t u a n a l

(t)

measures added very l i t t l e explanatory power t o the models

.

More recently, however, Prashker (19'(9) has found t h a t including

measures of r e l i a b i l i t y (eg. r e l i a b i l i t y of finding a parking

space; r e l i a b i l i t y of bus a r r i v a l s )

,

both s u b s t a n t i a l l y increased

t h e explanatory power of the models ( f o r example, it produced mode-

specific constants which were not statistically d i f f e r e n t from zero),

1

and change s i g n i f i c m t l y the values of some p a r m e t e r s ( i n p a r t i -

cular the value of in-vehscle time). Once more, the s a f e s t recom-

mendation seems t o be t o examine the p o s s i b i l i t y of measuring some

'unconventional' f a c t o r s (eg. r e l i a b i l i t y , c o w o r t , convenience,

etc.) and t o t e s t f o r t h e i r e f f e c t s on t h e other parameter estimates

and model explanatory power. Again, however, t h i s would n a t u r a l l y

imply higher data collection and analysis c o s t s .

("1t

i s

f a i r t o say, though, t h a t t h e models discussed by McFadden

3.2 Alternative sampling s t r a t e g i e s

The development and implementation of t r a v e l demand models

have t r a d i t i o n a l l y been associated with l a r g e data c o l l e c t i o n

e f f o r t s , involving, p r i n c i p a l l y , very expensive home interview

surveys. Because conventional aggregate models used data a t t h e

zonal l e v e l f a i r l y l a r g e random samples wererequired f o r c a l i b r a -

t i o n purposes, and it i s ~ e l l - ~ a m t h a t on many occasions t h e

c o s t and time consumed i n t h e c o l l e c t i o n and a n a l y s i s of the data

prevented t h e a n a l y s t s from examining a s u f f i c i e n t range of

a l t e r n a t i v e p o l i c i e s .

One of t h e advantages t r a d i t i o n a l l y c i t e d f o r disaggregate

models i s t h e e f f i c i e n c y with which they can make use of a v a i l a b l e

data and t h e p o t e n t i a l f o r reducing t h e time and e f f o r t expended

on data collection. A s we saw above, t h i s claim (together with

-

o t h e r s ) has not been universally achieved, but

it i s

t r u e t o s a y t h a t i n c e r t a i n s i t u a t i o n s t h e f a c t that disaggregate choice models

use observations of individual decision makers, r a t h e r than

geographically defined groups, can s u b s t a n t i a l l y reduce data col-

l e c t i o n costs. The r e s t o f t h i s s e c t i o n s u m a r i s e s two e x c e l l e n t

papers by Lerman and Manski (3.~76; 1979) Which c o n s t i t u t e t h e

state-of-the-art i n t h i s area.

The majority of a p p l i c a t i o n s of disaggregate cholce models

have r e l i e d on randomly sampled data, eg. s l i g h t v a r i a t i o n s on t h e

t y p i c a l home interview survey. A few s t u d i e s have used strati-

f i e d sampling, where t h e population of i n t e r e s t i s b v i d e d i n t o

groups according t o some c h a r a c t e r i s t i c s such a s c a r ownership

(which must be known i n advance) and each subpopulation is sampled

very expensive indeed

i n

cases wheee an option of i n t e r e s t has a

very low p r o b a b i l i t y of s e l e c t i o n ; because t o achieve a-reasonable

representation of' t h e option i n question

it

i s necessary t o c o l l e c t a very l a r g e sample. A choice-based sample t t h a t i s , one where

observations a r e drawn based on t h e outcome of t h e decision-aaking

process under study1 designed s o t h a t t h e number o f users o f t h e

low option i s

redetermined

o f f e r s one way t o solve t h i s problem.

Choice-based samples a r e not uncommon i n t r a n s p o r t studies.

Typical examples a r e on-board t r a i n and bus surveys, and roadside

interviews i n t h e case of mode ehoice modelling. They can fre-

quently be obtained f a i r l y inexpensively, but (because o f t h e way

t h e parameters of ( d i s a g ~ e ~ a t e ) models a r e generally c a l i b r a t e d )

have seldom been used f o r c a l i b r a t i n g models ( s e e C o s s l e t t , 1980).

A s we w i l l see below each sampling s t r a t e g y r e s u l t s i n a d i f f e r e n t

d i s t r i b u t i o n of observed choices and c h a r a c t e r i s t i c s i n t h e sample

t h a t i n c e r t a i n s i t u a t i o n s t h e f a c t t h a t disaggreeate choice models

m e observations of individual decision makers, r a t h e r than

geographically defined groups. can s u b s t a n t i a l l y reduce data col-

l e c t i o n costs. The r e s t of t h i s section summarises two e x c e l l e n t

papera by Lerman nnd Manski (1976; 1979) which c o n s t i t u t e t h e state-.of-the-art i n t h i s area.

The majority of applications of disaggregate choice models

have r e l i e d on randomly sampled data, eg. s l i g h t v a r i a t i o n s on t h e

t y p i c a l home interview survey. A few studies have used s t r a t i -

f j e d sampling, where t h e population of i n t e r e s t i s chvided i n t o

groups according t o some c h a r a c t e r i s t i c s such a s c a r ownership

(which must be known i n advance) and each subpopulation i s sampled

-

very expensive indeed i n cases where an option of i n t e r e s t has a

very lor? p r o b a b i l i t y Of s e l e c t i o n ; because t o achieve a reasonable

representation of t h e option i n question

i t

i.s necessary t o c o l l e c t a very l a r g e sanple. A choice-based sample (that i s , one where

observations a r e drawn based on t h e outcome of t h e decision-making

process under study) designed s o t h a t t h e number of users of t h e

low option i s predetermined o f f e r s one way t o solve t h i s problem.

Choice-based samples a r e not uncommon i n t r a n s p o r t s t u d i e s .

Yypical examples a r e on-board t r a i n and bus surveys, and roadside

interviews in t h e case of mode choice modelling. They can f r e -

quently be obtained f a i r l y inexpensively, hut (because of t h e way

t h e p a r m e t e r s of (disagyregate) models a r e generaU y c a l i b r a t e d )

have ackdom been used f o r c a l i b r a t i n g models ( s e e Cossleti;, 1900).

A s we w i l l see below each sampling s t r a t e g y r e s u l t s i n a d i f f e r e n t

d i s t r i b u t i o n of observed choices and c h a r a c t e r i s t i c s i n t h e sample

and hence each has a s s o c i a t e d

a

d i f f e r e n t c a l i b r a t i o n f h c t i o n (such a s l i k e l i h o o d l . Although t h e f i r s t two sanpling methods

present no problems t o e x i s t i n g software, t h e choice-based

u.pproach needs some modirications (Lermm, hhnski and Atherton,

1976; Lerman and t.fansk~, 1976) o r e x i s t i n g programs w i l l

(*J produce biased paxameters

.

Given t h e existence of a p r a c t i c a l estimation procedure f o r

choice-based samples, t h e question i s what sampling s t r a t e g y

should be preferred. Leman and Fanski (1976; 1979) have argued

t h a t unfortunately, t h e anawer i s extremely s i t u a t i o n - s p e c i f l c

and depends on

...

...

...

.

. .

. . . . . . . . .

_-.

...

...

...

. .

.

...

-

the c o s t o f various sampling methods

-

t h e choice being modelled

-

t h e c h a r a c t e r i s t i c s of t h e population under study

-

t h e s o c i a l c o s t o f estimation e r r o r s i n terms of

a p p l i c a t i o n s of misguided p o l i c i e s

(T)

Random samples o f t e n r e q u i r e a major expenditure of time and -

money t o c o l l e c t .

.

Normally they should be based on homes

-

i f done anywhere e l s e they would be choice-based because t h e respon-

dent has already made a t r i p choice

-

wjth a l l t h e p r o b l e m associated with home interview surveys. However t h e r e i s scope

f o r longer and more in-depth interviewing.

A fbrther problem of' random sarnples

i s

t h a t they o f f e r no opportunity t o i n c r e a s e t h e amount of information given a f i x e d

sumple s i z e . Variation

i n

the

d a t a ( * ) cannot be c o n t r o l l e d i n t h i s c a s e , being r a t h e r a random outcome of t h e sao?.plin& process.

S t r a t i f i e d samples on t h e o t h e r hand should help i n t h i s sense,

because even if t h e c h ~ s a c t e r i s t i c s of t h e population vary l i t t l e ,

t h e s m p l e i t ~ t e l f can have a h i & variance, i e , c e r t a i n s t r a t a

can be sampled a t d i f f e r e n t r a t e s from others. However, s , t r a t i -

f i e d samples a r e often more expensive than random ones b e c ~ u s e ,

i n order t o s q l e a t random f r m a subpopulation, one m u s t f i r s t

be able t o i s o l a t e the subpopulation; i n p r a c t i c e t h i s nay be

d i f f i c u l t (and expensive) t o achieve

C**).

. . .

...

...

_{. . . . . . . . . ...}

..*

...

.

.

. . . .

.

. .

(*)SeeGensch

(1900)

f o r an i n t e r e s t i n g example about t h e p o s s i b l e magnitude mf such c o s t s .

(*)The more v a r i a t i o n i n t h e h t a , t h e more re1labl.e a r e t n e para-

meter estimates.

-.

**

( _{iTor exnmple one may need t o begin an interview t o f i n d o u t t h e}

In general choice-based samples a r e t h e l e a s t expensive but

they r e q u i r e p r i o r ktiowledge of t h e r a t i o of t h e share.of t h e

e n t i r e populetion chooslng each a l t e r n a t i v e t o t h e sample shere.

Fortunntely, t h e former i s an aggregate s t a t i s t i c which might he

obtained from s e v e r a l sources (Lerman and Manski, 19.16). _Another

problem of t h i s sampling s t r a t e g y i s t h a t of b i a s (*), o r a l t e r -

native]-y, how t o ensure t h a t t h e sample, given t h e u s e r s o f an

option, i o readam.. Lerman and Manski (1979) mention a s an

example 'the problem, i n an on-.bus survey, of allowing f o r t h e f a c t

t h a t sane routes may have a higher percentage of e l d e r l y users

while others may a t t r a c t primarily workers. Another c a s e i s t h a t

associated with high r e j e c t i o n r a t e s of mail-back questionnaires

where it

i s

u n l i k e l y t h a t t h e

distribution

of c h a r a c t e r i s t i c s of those who choose t o respond w i l l be t h e same a s t h a t o f t h e

population a s a whole.

Bearing all t h e above i s s u e s i n mind, Lenaen and Manski

(1976) concluded i n t h e i r paper

"...

I n a l l p r o b a b i l i t y t h e question o f sample deslgn

w i l l remain a judgemental problem."

and we s e e no reason why we should challenge t h i s view.

4.

Model Specif ?cat ion

Having a v a i l a b l e , o r having decided t o c o l l e c t dJtta i n a

c e r t a i n way and o f a given type

-

t y p i c a l l y

a

random sample of cross-sectional information on revealed preferences, where values

of a t t r i b u t e s a r e e i t h e r measured o r synthesised

-

t h e a n a l y s t

s t i l l has some o p t i o n s open i n terms o f t h e model s t r u c t u r e , _{I .}

...

...

...

... . . .

-.

...

. . .

. .

.

...

...

...

...

s p e c i f i c a t i o n and estimation method t o use. I n s e c t i o n

5

we w i l l present a f a i r l y comprehensive review of t h e most widely recommended

method of estimating d i s c r e t e choice models

-

Maximum Likelihood

(ML) estimation

-

with p a r t i c u l a r emphasis on disaggregate data.

(Elsewhere, ( H a r t l e y and Ortuzar, 19801, we have discussed t h e method

a s applied t o t h e c a l i b r a t i o n of aggregate h i e r a r c h i c a l l o g i t modal

s p l i t models and compared it w i t h a l t e r n a t i v e procedures. ) F i r s t l y though, we wish t o b r i e f l y comment h e r e on t h e r e l a t e d problem o f

model s e l e c t i o n i n g e n e r a l .

4 . 1

Model s e l e c t i o n

I n general, t h e s t r u c t u r e of a model, t h e v a r i a b l e s e n t e r i n g

it and t h e i r form, t h e form of t h e utility functions thenselves,

and so on, are matters f o r t e s t i n g and experimentation ( s e e

t h e e x c e l l e n t book by Learnel-, 19781, and a r e q u i t e o f t e n a s t r o n g

function of context and data a v a i l a b i l i t y . Aggregate models

have often been c r i t i c a l l y vi.ewed a s p o l i c y insensi.tivc, e i t h e r

because a key v a r i a b l e has been completely l e f t out of t h e model;

o r from some component(s) of t h e model thought t o be s e n s i t i v e t o

i t

(eg. i n e l a s t i c t r i p g e n e r a t i o n ) ; or because severe d i s t o r t i o n s could be introduced from s p e c i f i c a t i o n o r aggregation b i a s e r r o r s .

I n t h i s sense t h e Amerlcan WPS system was p a r t i c u l a r l y weak

(Ben-Akiva

et

aZ.

,

1977).

I n B r i t i s h p r a c t i c e , however; t h e concept o f g e n e r a l i s e d

c o s t s , together with network modifications, have been used t o t e s t

l

a very wide range of p o l i c i e s (eg. from road investments t o parking

I

r e s t r a i n t and park-and-ride systems), although t h e s e have only been I

i n t e r p r e t e d on t e ~ s of t h e v a r i a b l e s ( * ) : in-vehicle-time, out-of-

.

. .

...

.

. .

.

.

. ...

_...

_...

_{... .}

_{. .}

_{. . .}

_.

_{. .}

_{. .}

_.

(*) Although disaggregate models include many more explanatory v a r i a b l e s , including socio-economic,-level-of-service and even a t t i t u d i n a l v a r i a b l e s , we mentioned i n s e c t i o n

3

t h a t most o f t h e s t a t i s t i c a l explanatory power of t h e models (excepting t h e l a r g e amount explained by mode-specific constants, T a l v i t i e and Kirshner, _{1978) r e s t s i n r e l a t i v e l y few of} t h e s e a t t r i b u t e s , including t h e usual level-of-service v a r i a b l e s

v e h i c l e time and out-of-pocket c o s t s ( s u i t a b l e s c a l e d by t h e generalised

c o s t c o e f f i c i e n t ) . Also a l a r g e v a r i e t y of model s t r u c t u r e s have been

employed ( s e e t h e d i s c u s s i o n by W i l l i a m s , 1979) including both simultaneous

and s e q u e n t i a l model forms, and t h e p o l i c y responsiveness of models has

been found t o be c r i t i c a l l y dependent on model s p e c i f i c a t i o n , t o t h e extent

t h a t c e r t a i n models s i n c e have been recognised a s ' p a t h o l o g i c a l 1

G . e . implied e l a s t i c i t i e s of t h e wrong s i g n ) because t h e i r s t r u c t u r e s

were not p r o p e r l y diagnosed f o r s p e c i f i c a t i o n e r r o r s ( s e e Senior and

Williams, 1977; and Williams and Senior, 1977).

The c o n s i d e r a t i o n of a v a i l a b l e a l t e r n a t i v e s (which could a l s o be

discussed a s an aggregation i s s u e ) i s another p a r t of t h e s p e c i f i c a t i o n process with s t r o n g i m p l i c a t i o n s f o r policy s e n s i t i v i t y . I n t h e v a s t

m a j o r i t y of aggregate s t u d i e s only b i n a r y choice between c a r and public

t r a n s p o r t has been considered, w i t h t h e consequence t h a t t h e multimodal

problem h a s not been t r e a t e d very s e r i o u s l y . I n t h e b e s t c a s e s t h e

consideration of a l t e r n a t i v e public t r a n s p o r t options has been r e l e g a t e d

t o t h e assignment s t a g e , employing 'all-or-nothing' o r 'multipathl a l l o c a t i o n

of t r i p s t o sub-modal network l i n k s . We have given elsewhere, ( H a r t l y and

Ortuzar, 1980), a p r a c t i c a l example of f i t t i n g a r a t h e r more general

s t r u c t u r e than t h e simple 1DtL t o aggregate modal s p l i t d a t a f o r t h r e e

modes ( c a r , bus and t r a i n ) and show how a p r i o r i notions which l e d u s

t o p o s t u l a t e such s t r u c t u r e were confirmed by a p p r o p r i a t e s t r u c t v a l

diagnosis t e s t s . Here we w i l l concentrate on disaggregate models both because t h e f u l l range of i s s u e s i n t h e i r s p e c i f i c a t i o n a r e more apparent

and because t h e y have been more thoroughly a i r e d and discussed.

We mentioned above t h a t t h e f i n a l s p e c i f i c a t i o n of a model t e n d s t o he a s t r o n g f u n c t i o n of context and d a t a a v a i l a b i l i t y . A p r i o r i

notions and t h e o r e t i c a l i n s i g h t a l s o provide valuable h e l p while another

important pragmatic f a c t o r i s t h e a v a i l a b i l i t y of s p e c i a l i s e d software.

In f a c t , one reason why linear-in-the-parameters l o g i t (and simple b i n a r y p r o b i t ) models have been so popular i s t h a t t h e y can e a s i l y be estimated

using a v a i l a b l e software [for w e l l documented examples, s e e Boyce, Desfor,

e t al., 1974; Domencich and McFadden, 1975; Ben-Akiva and Atherton, 1977;

Hensher, 1 9 7 9 ~ ; and T a l v i t i e and Kirshner, 1978) w h i l s t o t h e r more general

forms normally present enormous d i f f i c u l t i e s ( s e e t h e d i s c u s s i o n on

On t h e o t h e r hand, t h e l i m i t a t i o n s of 'simple scaleable choice models1 t y p i f i e d by t h e

MNL

s t r u c t u r e have been one o f t h e prime motivations behind t h e i n t e r e s t i n a l t e r n a t i v e models of t h e decision process; although we have argued elsewhere ( ~ i l l i a m s and Ortuzar,1980a) t h a t , in a c e r t a i n sense, t h e development of more general random

u t i l i t y s t r u c t u r e s (such a s t h e M N P ) has removed some of t h e o r i g i n a l j u s t i f i c a t i o n s f o r building such models. However, t h i s does not mean t h a t t h e more conventional models a r e n e c e s s a r i l y appropriate; indeed,

it i s often u s e f u l and d e s i r a b l e t o examine competing frameworks. One I

1

cause f o r concern, though, i s t h a t d i f f e r e n t model s t r u c t u r e s and forms tend t o produce d i f f e r e n t parameter estimates and response e l a s t i c i t i e s , whilst we do not have means t o discriminate between them a t t h e cross- s e c t i o n (see TTilliams and Ortuzar, 1980a).

4.2

Choice s e t determination

One of t h e f i r s t problems an analyst has t o solve, given a t y p i c a l ( i . e . as defined above) data s e t i s t h a t of deciding which a l t e r n a t i v e s

a r e a v a i l a b l e t o each individual i n t h e sample. As Hensher ( 1 9 7 9 ~ ) has

1

noted

". . .

Choice s e t determination

.

.

.

i s t h e mast d i f f i c u l t ' o f all t h e i s s u e s t o resolve. It r e f l e c t s

...

t h e

dilemma which a modeller has t o t a c k l e m a r r i v i n g at, a s u i t a b l e trade-off between modelling relevance and modelling complexity. Usually, however,

data

maiZab;iZitg

acts

as a

~ardstick."

(our emphasis)

It

i s

extremely d i f f i c u l t t o decide on an i n d i v i d u a l ' s choice s e t unless one asks him; t h e r e f o r e t h e problem i s c l o s e l y oonnec-

t e d with t h e already discussed dilemma of whether t o use reported

or measured data. Yhe obvious procedures o f ( a ) Caking i n t o

account only those a l t e r n a t i v e s which a r e e f f e c t i v e l y chosen i n

t h e sample; o r

(b)

t o assume t h a t everybody has

a l l

a l t e r n a t i v e s a v a i l a b l e (and hence Let t h e model decide t h a t t h e choice proba-

b i l i t i e s of t h e u n r e a l i s t i c a l t e r n a t i v e s a r e low o r zero) have

a l s o obvious disadvsntages.- For example, i n t h e former case it

(due t o the s p e c i f i c sanple o r s a p l i n g tecnnique). I n t h e

l a t t e r case, t k h c l u s i o n of too many a l t e r n a t i v e s may a f f e c t the

discriminatory c a p a c i t i e s of t h e model, i n t h e sense t h a t a model

capable of dealing with u n r e a l i s t i c a l t e r n a t i v e s may not be a b l e

t o describe adequately t h e choices among r e a l i s t i c options ( s e e ,

Huijgrok, 1979). Fortunately, i n t h e context t h a t i n t e r e s t us

here

-

mode choice modelling

-

t h e number of a l t e r n a t i v e s i s usually small and t h e problem should not be severe.

By

c o n t r a s t , i n destination choice modelling ( l e . t r i p

d i s t r i b u t i o n ) t h e i d e n t i f i c a t i o n of a l t e r n a t i v e s i n t h e choice s e t

i s a c r u c i a l matter, and not simply because t h e t o t a l number of

a l t e r n a t i v e s i s usually very high(*).

-

To i l l u s t r a t e t h i s , con-

s i d e r t h e case of modelling t h e behaviour of a group of individuals

who vary a great deal i n terms of t h e i r knowledge of p o t e n t i a l

destinations (owing perhaps t o varying lengths of residence i n t h e

d e s c r ~ b e t h e r e l a t i o n s h i p between predicted

utilities

and observed choices, may be influenced a s much by v a r i a t i o n i n choice s e t s

among individuals (which a r e

not

f u l l y accounted f o r i n t h e model)

,

a s by v a r i a t i o n s i n a c t u a l preferences (which a r e accounted I'Or).

Because changes i n t h e nature O f destinations may a f f e c t both

choice s e t a d preferences t o d i f f e r e n t degrees, t h i s confusion

may be l i k e l y t o plqf havoc with t h e use of t h e models i n fore-

c a s t i n g o r i n tne p o s s i b i l i t y of t r a a s f e r r i n g t h e i r s p e c i f i c a t i o n

over space. I t i s i n t e r e s t i n g t o note i n t h i s context t h a t

McFadden (1978a) has shown t h a t f o r a

MNL,

t h e model parameters

can be estimated without b i a s by sampling a l t e r n a t i v e s a t random

from t h e F u l l s e t of options, with appropriate adjustments i n the

e s t h a t i o n mechanisms. This

-.

i s

,however, not possible f o r t h e

KMP, f o r example, p r e c i s e l y due t o i t s improved s p e c i f i c a t i o n which

allows f o r i n t e r a c t i o n between all a l t e r n a t i v e s .

4.3 Defining t h e form of t h e u t i l i t y function

Another a r e a of concern i n ' s p e c i f i c a t i o n searches' r e l a t e s t o t h e

form of t h e u t i . l i t y functions. Although t h e r e i s broad agreement among

e x p e r t s t h a t f o r mode choice modelling t h e

convenient

a s s w p t i o n of

' r e p r e s e n t a t i v e

'

u t i l i t i e s w i t h linear-in-the-parameters (LTP) forms

should present l i t t l e d i f f i c u l t y , i n o t h e r contexts such as d e s t i n a t i o n

choice modelling'*' t h e general agreement i s t h a t LTP u t i l i t y f u n c t i o n s

a r e not v a l i d ( s e e , f o r example, F o e r s t e r , 1979a; Daly, 1979; Louviere

and Meyer, 1979). The problem t h i s time i s p a r t l y t h e l a c k of a p p r o p r i a t e estimation software, and p a r t l y theoretical(**! Three

general approaches have been proposed t o deal with t h i s problem:

-

t h e use of f u n c t i o n a l measurement/conjoint a n a l y s i s techniques w i t h experimental design d a t a ( ~ e r m a n and

Louviere, 1978; Hensher, 1979a, 1979b; Hensher and

Louviere, 1979

1.

-

t h e use of 'form searches' by means o f s t a t i s t i c a l

transformations (e.g. t h e Box-Cox method) a s i n t h e

work o f Gaudry and Wills (1977).

-

t h e c o n s t r u c t i v e use of t h e economic theory i t s e l f f o r t h e d e r i v a t i o n of form (Train and McFadden, 1978;

Hensher and Johnson, 1980).

Exploring t h i s i s s u e f u r t h e r would be o u t s i d e t h e scope o f t h i s paper

but we wish t o mention not o n l y t h a t non-linear u t i l i t y forms imply

d i f f e r e n t trade-off mechanisms than t h o s e u s u a l l y a s s o c i a t e d with a

concept l i k e t h e 'value-of-time'; but a l s o , and more importantly,

t h a t model e l a s t i c i t i e s and f o r e c a s t i n g power have been shown t o

vary d r a m a t i c a l l y w i t h f u n c t i o n a l form ( s e e , Dagenais, Gaudry and

Liem, 1980). Thus t h e i s s u e has important i m p l i c a t i o n s f o r model

design and hypothesis t e s t i n g .

.

.

.

... .

.

.

... . . . ...

...

...

. . . .

.

.

.

.

.

...

(*) A f u r t h e r major challenge i n d e s t i n a t i o n choice modelling (and i n a d d i t i o n i n mode choice modelling f o r non-work journeys such a s shopping t r i p s ) i s

how t o measure and/or r e p r e s e n t t h e a t t r a c t i v e n e s s of d e s t i n a t i o n s . For t h e case of mode choice f o r t h e journey-to-eork t h i s i s not a problem because i n t h e s h o r t term it c m b e s a f e l y assumed t h a t d e s t i n a t i o n s a r e f i x e d ; t h e r e f o r e , t h e i r a t t r a c t i o n s a r e common t o a l l competing modes and t h u s cancel o u t . When t h i s assumption does not hold ( a s i s t h e case with shopping trips) we f a c e a problem which h a s , so f a r a s we a r e aware, no s a t i s f a c t o r y answers.

( * * ) S p e c i f i c a l l y t h e problem i s t h a t f o r non-linear u t i l i t y expressions t h e r e

4.4

Model s t r u c t u r e and v a r i a b l e s e l e c t i o n

Raving solved o r simply avoided ( a s i n our case) t h e

aforementioned problems we have t o deal with tm f u r t h e r

obstacles:

-

what model form land s t r u c t u r e ) t o use, eg. l o g i t

-

given t h e s t r u c t u r e ,

what

v a r i a b l e s shouLd e n t e r t h e u t i l i t y f'unctions and i n what

f o m

We t h i n k

it

i s f a i r t o say t h a t t h e question o f model s t r u c t u r e can only be resolved by examining t h e p a r t i c u l a r s i t u a t i o n under study.

If we have reasons t o b e l i e v e t h a t a l t e r n a t i v e s a r e independent and

t h a t v a r i a t i o n s in t a s t e among i n d i v i d u a l s i n t h e population a r e not important (.e.g. we can speak of a s i n g l e value, r a t h e r t h a n a

d i s t r i b u t i o n , f o r t h e c o e f f i c i e n t s multiplying t h e a t t r i b u t e s e n t e r i n g

t h e u t i l i t y f u n c t i o n s ) , t h e n we may c o n f i d e n t l y choose t h e MNL model.

I f , on t h e o t h e r hand, t h e above conditions a r e not met o r if we a r e not c e r t a i n , t h e n we

shouZd t e s t a l t e r n a t i v e (more complex) model

s t r u c t u r e s a g a i n s t t h e convenient MNL. For example, i f we suspect t h a t

c o r r e l a t i o n between a l t e r n a t i v e s may be a s e r i o u s problem, we can

e i t h e r t e s t i f t h e 'independence from i r r e l e v a n t a l t e r n a t i e s ' condition

i s s a t i s f i e d [McFadden, Tye and T r a i n , 1976) o r , b e t t e r s t i l l , e s t i m a t e

a h i e r a r c h i c a l l o g i t model which includes b u i l t - i n s t r u c t u r a l diagnosis

t e s t s ( s o b e l , 1980; Ortuzar, 1980b; Ortuzar 1 9 8 0 ~ ) . On t h e o t h e r hand,

if we have reasons t o b e l i e v e t h a t t h e r e a r e s t r o n g t a s t e v a r i a t i o n s e f f e c t s , we might have t o t r y and f i t a 'random c o e f f i c i e n t s ' model.

The simplest one

i s

t h e CRA Hedonics model (Cardell and Reddy, 1977) which s t i l l has t h e r e s t r i c t i o n of assuming non-correlated a l t e r n a t i v e s

a s t h e MNL. The most g e n e r a l model s t r u c t u r e p o s s i b l e , and sadly t h e

more complex t o e s t i m a t e c * ) , i s t h e MNP model which allows f o r t h e e x i s t e n c e of both c o r r e l a t i o n and t a s t e v a r i a t i o n s i n t h e d a t a .

It i s important t o r e a l i s e t h a t use of an inadequate model, such a s

t h e MNL, can l e a d t o s e r i o u s e r r o r s (~ausman and Wise, 1978; Horowitz,

1978, 1979a, l979b, 19801 and s t u d i e s on t h e comparison of a l t e r n a t i v e

... . . . . . . . . .

...

_-

. . . ... . . .

... ... . . . . . .

model s t r u c t u r e s using simulated data, such a s those described i n Ortuzar (1978, 1979, 1980a) and ~ i l l i a m s and Ortuzar (1980a) among o t h e r s , have tended t o confirm t h i s view.

Even i f the analyst i s convinced ( o r has no choice but t o

be convinced) t h a t a given model s t r u c t u r e (say a MNL model) i s adeg,uate and t h a t linear-in-the-parmeters u t i l i t y Functions pose

no d i f f i c u l t i e s , he has

s t i l l

t o decide what variables should e n t e r t h e u t i l i t y expressions, and i n what form. This question

i s p a r t i c u l a r l y relevant i n t h e case of socio-economic variables.

I n disaggregate modelling work t h e most common approach u n t i l t h e

mid-1970's was t o add these variables a s additional l i n e a r terms;

t h i s

i s

consistent with t h e hypothesis t h a t any trade-off mecha- nisms involving say, time and c o s t s , a r e the same f o r a l l

individuals.

Two

a l t e r n a t i v e approaches allow d i f f e r e n t trade-off functions for groups of people with d i f f e r e n t characteristics. The f i r s t ,

which

i s

f'uJ.1~ consistent with t h e requirement of observing groups of individuals with t h e sane choices and c o n s t r a i n t s ,

i s

t o s t r a t i * the sample on t h e basis of t h e individual charac-

t e r i s t i c s and t o c a l i b r a t e

a

model f o r each market segment. I n t h i s w a y t h e model. coefficients a r e allowed to vary f o r t h e

d i f f e r e n t market segments, thus r e s u l t i n g i n p o t e n t i a l l y d i f f e r e n t

trade-off mechanisms(*). The problem i s , a s usual, one of data:

t h e l a r g e r the number of market segnents, the smaller t h e number

of observations on each f o r a given s m p l e size. The second one,

which can be used i n conjlulction with t h e first, i s t o express

c e r t a i n coefficients (eg. of t h e time o r cost v a r i a b l e s ) a s a

function of an individual descriptor, usually income (see the

discussion by Train and McFadden, 19'18). I n a value-of-time

context t h i s would, f o r example, r e s u l t i n time being valued a s

a percentage of t h e wage r a t e I~cFadden, 197b).

The decision about what variables enter t h e u t i l i t y function

and i n what form (eg. level-of-service v a r i a b l e s being generic o r

mode-specific, etc.1

i s

usual% approached i n a stepwise fashion by t e s t i n g

if

t h e e x t r a v a r i a b l e o r form adds e x t r a explanatory power t o the model. This i s r e l a t e d t o questions of model

c r e d i b i l i t y and policy s e n s i t i v i t y i n the following sense; it may

often occur t h a t

a

v a r i a b l e which

i s

considered t o be important, e i t h e r on strong a p r i o r i grounds o r because

it

i s a key one i n t h e policy-model i n t e r f a c e leg. a c o s t v a r i a b l e i n a study of p r i c i n g

mechanisms), would be l e f t o u t a s s t a t i s t i c a l l y insigtlificant by a

s t e m s e selection procedure. I n such a case, t h e tendency has

been t o override t h e 'automatic' s e l e c t i o n procedure ( s e e Gunn

and Bates, 1980). The stepwise s e l e c t i o n of v a r i a b l e s is usually done a s p a r t of t k e model estimation phase; s o we

will

postpone a discussion on methods t o do t h i s u n t i l section

5.2.

5.

MODEL ESTIMATION

5.1

General statement o f t h e problem ("

I n t r a v e l demand modelling ( a s i n most modelling exercises)

.

i n t e r e s t centres on finding a cau8aZ r e l a t i o n s h i p between one

variable, o r s e t of v a r i a b l e s , held t o be dependent on another

variable, o r s e t of variables. The purpose of t h e exeraise i s

t o p r e d i c t what value t h e dependent variable

w i l l

take given p a r t i c u l a r known o r bypothesised ( f o r e c a s t ) values of t h e

...

.

. . .

. . .

. . .

.

.

_...

_...

_...

_{. . .}

_...

_...

_{. .}

_.

(*) I w i l l draw heavily here on unpublished seminar n o t e s by Hugh Gunn, with whom I _{have a l s o benefited g r e a t l y from discussions i n a l l}