Now more than two choices, e.g.:
Go swimming, go shopping, stay home, go to movies, ...
Many possible times-to-depart (discretized into 5-min bins).
See Fig. 29.4.
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Concentrate on option ``1''.
![]() |
(29.23) |
![]() |
(29.24) |
Alternatively:
As in binary choice, a Gaussian distribution will lead to use of the error function. This will not be discussed any further here.
A Gumbel distribution will lead to the use of the logistic distribution.
multinomial choice with Gumbel-distributed randomness.
We had:
![]() |
(29.26) |
Two steps:
Gumbel-distributed
also Gumbel-distributed.
and
Gumbel-distributed
logistically distributed.
Only problem is to keep track of the transformations of the two
parameters and
.
Result of second step is (remember: similar to binary logit)
Either via normalization or via really computing as the new
of the Gumbel distribution one obtains