1

9/25/2006

4

1920 1970 2000

(D. McFadden) (J. Heckman)

J.J. Louviere, D.A. Hensher, and J. Swait (2000) Stated Choice Methods,

Cambridge University Press.

K. Train (2003) Discrete Choice Methods with Simulation, Cambridge University

Press.

D.A. Hensher, J.M. Rose, and W.H. Greene (2005) Applied Choice Analysis,

Cambridge University Press.

( )

4.1 (RUT)

2

(Louviere et al.

2000 Ch.3 Train 2003 Ch.2 Hensher et al. 2005 Ch.3 )

(discrete choice)

(choice set)

(mutually exclusive)

(exhaustive)

(definite)

1

ADSL CATV

FTTH ADSL CATV FTTH1

(utility)

(random utility theory, RUT) 2

(representative utility)

(random component)

RUT n i

j i i j

n J n j

, 1...nj

U j J= n i i

j ( ,ni nj

U U i j> )

njx

ns

1 ADSL CATV

ADSL CATV

LANLAN

2 RUT Thurstone (1927) Marshack (1960)

3

( , )nj nj n

V V x s=nj

nj nj njU V= +

n=<

n1,...,

nJ> ( )nf

n i

Pr( )

Pr( )

Pr( )

( ) ( ) ,

ni ni nj

ni ni nj nj

nj ni ni nj

nj ni ni nj n n

P U U

V V

V V

I V V f d j i

= >

= + > +

= <

= <

(4.1)

(Train 2003 pp.18-19 ) ( )I i 1

0

RUT

1

K

nj j kj knjkV x

== + (4.2)

knjx jj kj

jk

(RUT)

4.1.1 RUT

RUT ADSL FTTH

(PRICE) (SPEED) ADSL FTTH

1 2

1 2

ADSL ADSL ADSL ADSL ADSL ADSL

FTTH FTTH FTTH FTTH FTTH FTTH

V PRICE SPEED

V PRICE SPEED

= + +

= + + (4.3)

FTTHFTTH FTTH ADSL ADSL

V V+ > +

4

Pr( )FTTH FTTH FTTH ADSL ADSL

P V V= + > + (4.4)

ADSLADSL

P

4.2 (CL)

(conditional logit,

CL) (Louviere et al. 2000 Ch.3 Train 2003 Ch.3 Hensher et al.

2005 Ch.10,11 )3

CL (independently and

identically distributed, IID) IID

IID

(independence of irrelevant alternative, IIA) 4

CLnj

IID (extreme value, EV)

nj

( )nj

nj e

njf e e= , ( )nje

njF e= (4.5)

EVnj ni

=

( ) /(1 )F e e= + (4.6)

CL ( CL )

( ) ( ) ,ni

nj

V

ni nj ni ni nj V

j

eP I V V f d j i

e= < = (4.7)

CL

1

1

,

K xj knjk kj

K xj knjk kj

ni

j

eP j i

e

+=

+=

= (4.8)

3 CL (multinomial logit MNL) 4 IIA Luce (1959) IIA RUT

Marshak (1960)Luce and Suppes (1965)

McFadden (1974)

5

(Train 2003 pp.38-40 )

(CL)

(CL) CL

IID

IID IIA

4.2.1( ) IIA

CL IIA

(Hausman and McFadden 1984 ) IIA

IIA

/

/

njnini

ni nk

nj nknk

VVV

j V Vni

V VVnk j

e eP ee

P ee e= = = (4.9)

i k i k

IIA

IIA (Hausman test)

IIA

CLu u

V

CLr r

V

1

[ ]'[ ] [ ]u r r u u r

V V

( 2 )

5% 2

2 IIA

IIA IID

4.2.2( ) CL

6

CL ( CL )

1% (%)

(Train 2003 pp.63-64 )

CL (own-elasticity) i

1% i i k

n ini

P

/(1 )

/ni

kni

P ni ni ni

x kni ni

kni kni kni

P P VE x P

x x x= = (4.10)

(1 )ki kni nix P= (

1

K

ni ki knikV x

== )

CL (cross-elasticity) j 1%

i j k n i

niP

/

/

ni

knj

njP ni nix knj nj

knj knj knj

VP PE x P

x x x= = (4.11)

kj knj njx P= (1

K

nj kj knjkV x

== )

CL j i

j CL j i

CL IID IIA

4.2.3( ) (MLE)

CL (maximum likelihood estimation, MLE)

MLE

(Louviere et al. 2000 p.43 )

RUT n j j U

nj

i U

ni

7

CL j U

nji

U

ni

MLE n j ( ) njI

j njP

1nj

I = n j 1 0

N j (likelihood function)

( ) ( ) , 1... , 1...njI

n j njL P n N j J= = = (4.12)

(log-likelihood function)

( ) ln , 1... , 1...n j nj nj

LL I P n N j J= = = (4.13)

( ) / 0dLL d = (4.14)

(Train 2003 pp.64-65 )

4.2.4( ) ( )

( R2 )

MLE

( )LL (0)LL

( )1

(0)

LL

LL= (4.15)

0-1

0.25

5 MLE 2

R

8

4.2.5 CL

CL

ADSL CATV FTTH

4.1(a)

IIA

ADSL CATV FTTH 3 1 1 CATV

ADSL FTTH 3 1

75% 25%

4.1

4.1(b) ( )LL (0)LL

=0.33 2R

0.6 t

ADSL FTTH

MLE t

t t

t 1.96 5%

t ADSL

FTTH 6

4.1(c)

ADSL -0.96 CATV

-2.56 FTTH -3.2

1 ADSL

CATV FTTH

[ 0.1, 0.2, 0.3, 0.4, 0.5]= 2R [0.3, 0.5, 0.6, 0.8, 0.9]

(Domenich and McFadden 1975 ) 6 (willingness to pay, WTP)

9

ADSL CATV FTTH

1.44 CL IID

WTP 4.1(d)

1Mbps

1Mbps WTP 0.02/0.0008=25

4.2.6 CL

CL IID IIA

IID

CL

(taste variation) CL

(substitution pattern) CL

(serial correlation) CL

CL IID

(Train 2003 p.46 )

4.3 (NL)

CL (nested logit,

NL) (Louviere et al. 2000 Ch.6 Train 2003 Ch.4 Hensher et al.

2005 Ch.13,14 )7

7 CL IID (generalized extreme value,

GEV) GEV EV

NL GEV

10

8 NL

NL IID

IID CL

NL IIA

NL

(independence of irrelevant nests, IIN) NL

(inclusive value, IV)

ISDN ADSL CATV

FTTH FTTH

( ) FTTH ADSL

( )

ISDN ADSL

CATV FTTH

ADSL CATV FTTH

NL9

NL 10 j K

1, ,

KB B NL

1,...,

nj n nJ=< >

/

( )

( ) , 1...nj k k

k j Bke

njF e k K= = (4.16)

kk ,nj nm kB

8 NL

9 (Cameron 1982 )

NL (1)

(2)IV (3)

(Louviere et al. 2000 ) 10 NL Daly and Zachary (1978) McFadden (1978) Williams

(1977)

11

nj nm k

IV11 1

NL (RU) 2 (Louviere et

al. 2000 pp.165-167 )

1(RU1)

2(RU2)

RU1 RU2 RU2

RUT RU2

(Hund 1998 )

NL ( NL )

// 1

/

1

( )

( )

nj kni k k

k

nj k l

l

VV

j B

ni VK

l j B

e eP

e=

= (4.17)

(Train 2003 pp.83-84 )

NL CL

2 4

(full information maximum likelihood FIML)12

(NL)

CL IID (NL)

NL

IID

4.3.1( ) NL

NL (4.17) NL

11 RUT IV 0-1 12

12

nk

B j

nkW

njY

,nj nk nj nj kU W Y j B= + + (4.18)

NL

|k k

ni ni B nBP P P= (4.19)

/

| /

ni k

k nj k

k

Y

ni B Y

j B

eP

e= ,

1

nk k nk

k nl l nl

W IV

nB W IVK

l

eP

e

+

+

=

= , /

lnnj k

k

Y

nk j BIV e=

(Train 2003 pp.85-87 )ni

P

|k

ni BP n

kB i

knB

P n

kB

k nkIV n

kB

nkIV

kIV

4.3.2( ) NL

NL ( NL ) NL

CL

NL

|

1[(1 ) ( 1)(1 )] ,ni

ni i k

P

x n ni B ni k

k

E P P x i B= + (4.20)

|

1[ ( 1) ] , ,ni

nj j k

P

x n nj B nj k

k

E P P x i j B= + (4.21)

1k

CL NL

13

131

k= CL NL

4.3.3 NL

NL

ADSL CATV FTTH

NL IIA

CL ADSL CATV FTTH

3 1 1 CATV IIA

ADSL FTTH 3 1

CATV ADSL ADSL FTTH

4 1 ADSL CATV

FTTH CATV

CL 2 2

5% 5.99 IIA14

IIA CL

ADSL CATV FTTH

ADSL CATV NL

4.2(b) NL 4.1(b) CL

0.40

CL t

IV IV 0-1 t

4.2(c) NL

(ADSL CATV )

(FTTH) 15

13

14

2 15 FTTH ADSL CATV

IIN

14

4.2

4.3.4( ) HEV

GEV (heteroscedastic

extreme value, HEV) HEV16 HEV

NL IIN HEV IIA

HEV

( ) / / /[ ] ( / )

V Vni nj ni j ni ini ie e

ni j i ni iP e e e d+

= (4.22)

(Train 2003 p.96 ) (closed form)

HEV

4.4 (ML)

CL (mixed logit, ML)

(Louviere et al. 2000 Ch.6 Train 2003 Ch.5,6 Hensher et al. 2005

Ch.15,16 ) ML

ML (random parameter)17

ML ( )f ( )f18 n

i

16 Allenby and Ginter (1995) Bhat (1995) Hensher (1997a, 1998a, b)

17 ML Train et al. (1987a) Ben-Akiva et al. (1993)

ML

Bhat (1998a) Brownstone and Train (1999) Erden (1996)

Revelt and Train (1998) Bhat (2000) 18

15

( )

( )

1

( )ni

nj

V

ni J V

j

eL

e=

= (4.23)

ML

( ML ) ( )f ( )ni

L

ML

( ) ( )ni niP L f d= (4.24)

(Train 2003 p.138 )

1 0 ML

NL EV

1'

K

n nj nk jkkx dμ μ

== 1jkd = k 1

0nk

μ (0, )k

N

k

jkd

(Ben-Akiva et al. 2001 )

ML ( ML ) ( )f

j k 1% i

( )( )[ ] ( )

knj

ni nix k nj

ni

LE L f d

P= (4.25)

(Train 2003 p.145 ) ML

ML

(Revelt and Train 2000

) n yn

h( | yn ) =P(yn | ) f ( )

P(yn | ) f ( )d (4.26)

(ML)

16

CL (ML) ML

IID

4.4.1( )

ML ML

( | )f ML

(Train 2003 p.148 )

( | )f R ( , 1...r

r R= )

r ( )

niL

( )ni

L1

1ˆ ( )R r

ni nirP L

R=

=

ˆni

P ML R

(simulated log likelihood,

SLL)1 1

ˆlnN J

nj nin jd P

= =n j

1njd = 0 (maximum simulated

likelihood, MSL) SLL

(random draw)

(Train 2003 p.208 )

5 10 1000

100 (Louviere et al. 2000 )

(Train 2003 p.224

17

) 3 0-1 1/3 2/3

1/9 4/9 7/9 2/9 5/9 8/9

100 MSL 1000

MSL (Bhat 2001 )19

4.4.2 ML

ML

ADSL CATV FTTH

ML

MSL

ADSL CATV

ADSL CATV NL

WTP20

4.3(b)

ADSL CATV 1

0.7 8% 92%

0.02

0.015 5% 95%21

19 (anomaly)

( Train 2003 ) 20 WTP

21

18

ML 4.3(c) ML

ADSL CATV

ADSL CATV

4.3

4.4.3( )

ML CL

(multinomial probit, MNP) 22

1, ,

n n nj=< > J

11

'2

/ 2 1/ 2

1( )

(2 ) | |

n n

n Je= (4.27)

MNP ( MNP )

( ) ( )ni ni ni nj nj n nP I V V d= + > + (4.28)

(Train 2003 pp.101-102 ) MNP (J-1)

MNP

ML

(Louviere et al. 2000 pp.199-204

)23

4.5 RP SP

2

(Louviere et al. 2000 Ch.8,9 Train 2003 Ch.7

22 Thurstone (1927)

MNP Hausman and Wise (1978) Daganzo (1979)Ben-Akiva and Bolduc (1996) Revelt and Train (1998) Bhat

(1997a) McFadden and Train (1996) Brownstone, Bunch and Train (1998)

23 ML (Cholesky)L A A=LL’

19

Hensher et al. 2005 Ch.4.6 ) (revealed preference, RP)

(stated

preference, SP)

RP RP

RUT RP

RP

RP

RP

RP (Louviere et al. 2000 pp.23-24 )

RP

RP

RP

RP

RP

RP

RP RP

RP

RP

SP RP

SP SP

SP (Louviere et al. 2000 pp.23-24 )

SP

SP

20

SP (label)

SP

SP

SP

RP SP

RP SP

RP

SP RP

SP

RP SP

RP SP

RP

SP

4.5.1( ) RP SP

RP SP RP

SP

RP SP24

RP SP

RP SP

(Louviere et al. 2000 pp.244 )

RP SP CL

LL(RP) LL(SP)

RP SP CL 24 Morikawa (1989) Ben-Akiva and Morikawa (1990)Ben-Akiva, Morikawa and Shiroishi (1991)

21

LL(RP+SP)

RP SP

(RP SP

= ) 2[( ( ) ( )) ( )]LL RP LL SP LL RP SP+ +

2

4.1 RP CL LL(RP) -1000

SP CL

LL(SP)=-900 RP SP

CL LL(RP+SP) -1896

8 4 2

5% 9.49 RP SP

RP SP

4.6

SP SP

(conjoint) (Louviere et al. 2000 Ch.4,5,7

Hensher et al. 2005 Ch.4,5,6 )

(experimental design)

(profile)

(Hensher

et al. 2005 Figure 5.1 )

1. (problem refinements)

2. (stimuli refinements)

(alternative identification)

(attributes identification)

(attributes level identification)

3. (experimental design consideration)

(types of design)

(model specification)

(reducing experimental size)

4. (generate experimental design)

5. (allocate attributes to design columns)

(main effects vs. interactive effects)

6. (generate choice sets)

22

7. (randomize choice sets)

8. (construct survey instrument)

3

(full factorial design)

2

(L) (M) (H) 3

[ , ] 9

[L,L] [L,M] [L,H] [M,L] [M,M] [M,H] [H,L] [H,M] [H,H]

(code)

2

(design code) L=0 M=1 H=2

(orthogonal code) L=-1

M=0 H=1

4.4

4.4

1 2

ADSL FTTH

4.5

4.5

(main effects) ( )

(interaction effects)

( )

70-90%

(Dawes

and Corrigan 1974 )

23

SP

4.6.1( )

32

(Carson et al. 1994 )

L M A

LMA LA

2 2

3 32*2=81

32=9

(orthogonality)

(orthogonal factorial design)

(Hensher et

al. 2005 pp.112-116 )

4.6.2( )

2 2

( ) 4

5

MA+1 A+1

4.7

24

CL CL

CL IID

IIA

IID NL NL

NL

IID ML ML

ML

RP SP RP

SP

RP SP

SP

25

(0)LL

( )LL

26

( )LL

(0)LL

27

( )LL

(0)LL

28

29