Information Technology Reference
In-Depth Information
by ranking their preferences. The concept of a random utility model underlies this
approach. When a certain respondent
n
chooses item
i
, utility
U
ni
is denoted as
follows.
X
M
m¼
1
b
m
x
ni
þ e
ni
U
ni
¼
V
ni
þ e
ni
¼
(11.1)
V
ni
is an observable definite term, and
e
ni
is an unobservable error term for a
researcher.
x
ni
m
is the marginal utility of
the attribute, and this value is estimated as the sum of true marginal utility and the
product of the scale parameter proportional to the reciprocal of variance of an error
term. The scale parameter was normalized to 1.
2
The probability that a respondent
n
will choose
i
from a certain choice set
is an attribute that constitutes a choice.
b
C
¼
f
1
;
2
; ;
J
g
is denoted as
P
ni
. This behavior when a respondent
n
chooses
i
indicates that one choice's utility is higher than that of other choices
j
ð
j
2
C
;
i
6¼
j
Þ
; therefore,
P
ni
can be shown as follows.
P
ni
¼
Pr
½
U
ni
>
U
nj
;
i
;
j
2
C
;
i
6¼
j
¼
Pr
½
V
ni
V
nj
> e
nj
e
ni
;
i
;
j
2
C
;
i
6¼
j
(11.2)
e
nj
have the type I extreme value
distribution, then the difference between the error terms has the logistic distribu-
tion.
3
Therefore, the probability
P
ni
has the following conditional logit model: CL.
4
Here, if we assume that error terms
e
ni
and
2
This assumption indicates that the variance of an error term is constant.
3
Refer to McFadden (
1974
) and Train (
2009
).
4
The likelihood function of (
11.3
)is
Y
N
L
¼
P
ni
;
n
¼
1
and the log-likelihood function of this equation is
X
N
ln
L ¼
ln
P
ni
:
n
¼
1
i
n
is a dummy variable that assigns 1 when a respondent chooses
i
, and the parameter vector
d
b
can be derived as a solution of the following maximum problem.
X
X
i2C
d
N
i
n
ln
P
ni
ln
L
¼
n¼
1
