37
P
U U
j i
j C
V
V
V V
i
i
j
i
i
j
j
i
j
j
i
=
>
∀ ≠
∀ ∈
=
+ > +
=
− > −
Pr
,
Pr
Pr
ε
ε
ε ε
(3.2)
The probability of choosing alternative i is able to be written the following equation if each ε i is assumed to distribute with a type I extreme value distribution,
P
V
V
i
i
j C
j
=
( )
( )
∈
∑
exp
exp
(3.3)
While we estimated the results using both a conditional logit (CL) and a random
parameter logit (RPL) models, in the present study, the results of only the RPL
models were represented. That was why the results of the RPL models were superior to those of the CL as followers. First, RPL models do not require fulfilling the
independence of irrelevant alternatives (IIA) condition, which is required by the
conditional logit model. In addition, previous studies showed that tourists had preference heterogeneity (Kubo et al. 2019; Mejía and Brandt 2015) for nature-based
tours, which is accommodated by RPL models.
According to Hensher et al. (2015), in RPL models, V nit on the Eq. 3.3 is showed
the following form using the individual n, choosing alternative i and period t:
V
x
Z
n
n
n
n
nit
n it
= ′
= +
+
β
β β
ν
∆
Γ
(3.4)
where β indicates the population mean of the coefficient of random parameters; ΔZ n
indicate observed preference heterogeneity; on the other hand, unobserved preference heterogeneity is showed in Γν n ; x nit is the attributes in choice set which respondents are asked. This model can incorporate unobserved and observed preference
heterogeneity through the random terms in the distributions of parameters (Hensher
et al. 2015). We are able to calculate the expected probability using multivariate
probability density function of β:
E
P
f
d
x
x
f
n
n
n
n
j C
=
⋅ ( ) =
′
(
)
′
(
)
⋅ ( )
∫
∑ ∈
( )
exp
exp
β
β
β
β
β
β
|
nit
nit
Ω
∫
dβ
(3.5)
The parameter is estimated by simulated maximum likelihood techniques that
maximize the log-likelihood function, because the integral of estimating this model
does not have a closed form (McFadden and Train 2000; Train 2009).
In present study, we used Carp Removal option, Pick-up option, Tour Time and
Tour Time squared (Tour Time
2
), Tour Fee, and an alternative-specific constant
(ASC) as explanatory variables: x nit , and as observed preference heterogeneity, we
incorporate the dummy variable of information provision that is if respondents were
3 How to Engage Tourists in Invasive Carp Removal: Application of a Discrete Choice…
P
U U
j i
j C
V
V
V V
i
i
j
i
i
j
j
i
j
j
i
=
>
∀ ≠
∀ ∈
=
+ > +
=
− > −
Pr
,
Pr
Pr
ε
ε
ε ε
(3.2)
The probability of choosing alternative i is able to be written the following equation if each ε i is assumed to distribute with a type I extreme value distribution,
P
V
V
i
i
j C
j
=
( )
( )
∈
∑
exp
exp
(3.3)
While we estimated the results using both a conditional logit (CL) and a random
parameter logit (RPL) models, in the present study, the results of only the RPL
models were represented. That was why the results of the RPL models were superior to those of the CL as followers. First, RPL models do not require fulfilling the
independence of irrelevant alternatives (IIA) condition, which is required by the
conditional logit model. In addition, previous studies showed that tourists had preference heterogeneity (Kubo et al. 2019; Mejía and Brandt 2015) for nature-based
tours, which is accommodated by RPL models.
According to Hensher et al. (2015), in RPL models, V nit on the Eq. 3.3 is showed
the following form using the individual n, choosing alternative i and period t:
V
x
Z
n
n
n
n
nit
n it
= ′
= +
+
β
β β
ν
∆
Γ
(3.4)
where β indicates the population mean of the coefficient of random parameters; ΔZ n
indicate observed preference heterogeneity; on the other hand, unobserved preference heterogeneity is showed in Γν n ; x nit is the attributes in choice set which respondents are asked. This model can incorporate unobserved and observed preference
heterogeneity through the random terms in the distributions of parameters (Hensher
et al. 2015). We are able to calculate the expected probability using multivariate
probability density function of β:
E
P
f
d
x
x
f
n
n
n
n
j C
=
⋅ ( ) =
′
(
)
′
(
)
⋅ ( )
∫
∑ ∈
( )
exp
exp
β
β
β
β
β
β
|
nit
nit
Ω
∫
dβ
(3.5)
The parameter is estimated by simulated maximum likelihood techniques that
maximize the log-likelihood function, because the integral of estimating this model
does not have a closed form (McFadden and Train 2000; Train 2009).
In present study, we used Carp Removal option, Pick-up option, Tour Time and
Tour Time squared (Tour Time
2
), Tour Fee, and an alternative-specific constant
(ASC) as explanatory variables: x nit , and as observed preference heterogeneity, we
incorporate the dummy variable of information provision that is if respondents were
3 How to Engage Tourists in Invasive Carp Removal: Application of a Discrete Choice…