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Fishery Bulletin 1 12(4) 
els examine how anglers make choices about which 
fishing sites to visit on the basis of the costs of trav- 
el to a site and the qualities of a site. For models of 
recreational fishing, site quality is typically measured 
by the average harvest rate per angler at a site. The 
parameters of site-choice models are used to estimate 
economic values associated with recreational fishing. 
However, failure to account for the complex sampling 
design of the NMFS APAIS survey could result in bi- 
ased demand-model parameters. It is important to 
have unbiased model parameters to obtain accurate es- 
timates of benefits and costs and to ensure that policy 
recommendations are not misleading. 
The APAIS data are collected by using a stratified, 
multistage survey design with stratification that is 
based on intercept site, time of year, and other vari- 
ables. Therefore, the proportion of anglers interviewed 
at each intercept site may reflect sampling allocations 
and not necessarily reflect angler preferences or the 
demand for one site over another. This problem of de- 
mand estimation is commonly referred to as endogenous 
stratification. Another issue with demand estimation 
can arise when using APAIS data because more avid 
users tend to be overrepresented in intercept surveys. 
This problem, referred to as avidity bias, can cause de- 
mand-model parameters to be influenced more heavily 
by avid users. Hindsley et al. (2011), using simulated 
data sets, found evidence of both endogenous stratifica- 
tion and avidity bias. However, their analysis was per- 
formed before the new NMFS estimation methods were 
available. The sampling information made available 
through the updated estimation methods can be used 
to generate sampling weights to correct for endogenous 
stratification in recreational site-choice demand models 
developed with data from the APAIS. 
The goal of our analysis was to compare the esti- 
mates of parameters and economic value that result 
from the use of a typical NMFS recreational site-choice 
demand model with and without the newly available 
sampling weights designed to correct for endogenous 
stratification. We used a model of fishing site choices 
among private-boat anglers in the Gulf of Mexico who 
target groupers (Epinephelus spp., Hyporthodus spp., or 
Mycteroperca spp.) or red snapper (Lutjanus campecha- 
nus). Following Kuriyama et al. (2013), we focus on the 
correction for endogenous stratification and do not at- 
tempt to correct for potential avidity bias. More details 
on avidity bias and how to correct for it are given in 
Thomson (1991) and Hindsley et al. (2011). 
Materials and methods 
made (e.g., day). Following Whitehead and Habb (2000) 
and Gentner (2007), we limited the options available to 
each angler to trips at locations within a 300-mi (483 
km) round trip from an angler’s residence. We also as- 
sumed that the angler had already decided to fish from 
a private boat and had decided which species to target 
so that the primary choice was where to launch the 
boat. In our model, this choice is made by comparing 
the benefits or utility available from each potential 
launch site against the costs of getting to each site. 
The indirect utility, C/j, of going to site j for angler i 
can be written as 
^ji = a ji (<?j> m i ~ c ji) + £ji> If) 
where m x - income; and 
for angler i at site j: 
i>.. - the observable portion of utility; 
Cjj = the trip cost; 
gj = a vector of attributes that defines the qual- 
ity of fishing and other site features; and 
£jj = the error term that represents the unob- 
served (to the analyst) portion of utility. 
The observable portion of utility, such as travel costs 
and site characteristics (harvest rates for a site) or oth- 
er site amenities (such as those at a marina), is based 
on those attributes that can be observed and measured 
by the analyst. The unobserved portion includes infor- 
mation on characteristics of the site or angler that are 
unavailable to the analyst, for example, the presence 
of a tackle shop near a site or the number of years of 
experience an angler has at a given site. 
Under the assumptions of the random utility model 
(McFadden, 1974), an angler will choose the site that 
provides the greatest level of utility: 
Vij (Qj, m\ — c;j) + £;j > Uiglf/g, m{ — cj s ) + £; s V j i^s, (2) 
where V = the utility function; and 
j = a member of s recreation sites. 
Assuming that the observed portion of utility is linear, 
Vy (<7j, m[ - c;j) = PqQj + A; c ij> and the unobserved por- 
tions of utility, £., have a type-I extreme value distri- 
bution, the probability that angler i chooses site j can 
be estimated with a standard conditional logit model: 
Pa = P{yi=j) 
explffqgj + Axij) 
£ii e xp(/fy?j+AAj)’ 
(3) 
where y\ = the choice made by angler /; and 
and p c are parameters to be estimated. 
Model specification and estimation of angler willingness 
to pay 
The standard recreational discrete choice model that 
uses APAIS data has the angler choosing a preferred 
fishing site on any given occasion when a choice can be 
The parameters of the conditional logit model are typi- 
cally estimated through the use of maximum likelihood 
with the following log-likelihood expression: 
LUP) = Y" = i£f = Wijlog^, (4) 
where N - the number of anglers in a sample; and 
