Lovell and Carter: Sampling weights in regression models of recreational fishing-site choice 
251 
Table 4 
The mean willingness to pay (in dollars) per angler for an additional fish caught and 
kept (with standard errors) estimated for groupers ( Epinephelus spp., Hyporthodus 
spp., or Mycteroperca spp.) and red snapper ( Lutjanus campechanus ) and based on a 
conditional logit model of angler preferences for fishing sites in the Gulf of Mexico 
in 2009. The lower limit and upper limit of the 95% confidence intervals of mean 
willingness to pay also are shown. Four versions of the model were used to estimate 
willingness to pay. The first version did not account for survey weights (unweighted). 
The other versions of the model were adjusted with weights on the basis of the ratio 
of the proportion of total angler trips to sample proportions and with a weighted ex- 
ogenous sampling maximum likelihood function (WESML). In the second version, the 
total population proportion of trips was evaluated at the mean, in the third version 
it was evaluated at the lower limit of the 95% confidence interval, and in the fourth 
version, it was evaluated at the upper limit of the 95% confidence interval. 
Model 
Mean 
Standard 
error 
Lower 
limit 
Upper 
limit 
Groupers 
Unweighted 
$13.01 
2.95 
$7.22 
$18.80 
WESML (mean) 
$14.67 
2.91 
$8.96 
$20.39 
WESML (lower limit) 
$8.07 
3.95 
$0.33 
$15.81 
WESML (upper limit) 
$15.32 
2.89 
$9.65 
$20.98 
Red snapper 
Unweighted 
$7.81 
1.61 
$4.66 
$10.97 
WESML (mean) 
$10.81 
1.59 
$7.68 
$13.93 
WESML (lower limit) 
$4.51 
1.84 
$0.90 
$8.11 
WESML (upper limit) 
$13.81 
1.60 
$10.67 
$16.95 
in parameter estimates translated into different WTP 
amounts for an additional fish caught and kept. How- 
ever, the differences in angler WTP estimated between 
the weighted and unweighted versions of the model 
were not statistically different. This finding indicates 
that, although sampling weights can be used to correct 
for issues of endogenous stratification in on-site sam- 
pling and to reduce bias in parameter estimates, the 
bias in the related angler WTP measures may not be 
severe in the APAIS data used in our study. Whether 
this holds for other APAIS samples is an open question. 
For researchers who estimate recreational site-choice 
models with APAIS data, it is advisable to compare re- 
sults produced with and without the APAIS sampling 
weights developed by NMFS. We have shown how to 
incorporate APAIS sampling weights into site-choice 
models using data from a popular recreational fishery 
in the Gulf of Mexico. The question of whether weight- 
ed or unweighted results should be used in future ap- 
plications will have to be determined on a case-by-case 
basis. 
Acknowledgments 
We wish to acknowledge the expertise and advice pro- 
vided by J. Foster of the NMFS Office of Science and 
Technology with regard to our understanding of the 
APAIS weights and survey sampling designs. We also 
would like to thank S. Steinback of the Northeast Fish- 
eries Science Center, J. Hilger of the Southwest Fisher- 
ies Science Center, and C. Liese of the Southeast Fish- 
eries Science Center for numerous helpful discussions 
and advice on this research. 
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