20 
Fishery Bulletin 108(1 ) 
Table 2 
Paired-tow fishing simulation parameters based on the species in Cadigan et al. 3 n is the total number of paired-sets, n* is the 
total number of sets and length classes, R=R t +R c is the total catch by the test (t) and control (c) vessels, and R t /R c is the ratio of 
catches from each vessel. The mean, median and coefficient of variation (CV) are for total catch (R). R25 and R75 are the lower 
and upper 25th percentiles of R. See Table 1 for definitions of notations. 
Species 
n 
n* 
R 
RJR C 
mean 
median 
R25 
R75 
CV 
American plaice 
( Hippoglossoides platessoides) 
105 
2035 
11,494 
1.051 
109.5 
40.0 
9 
169 
126 
Atlantic cod 
( Gadus morhua) 
91 
1132 
3926 
1.067 
43.1 
4.0 
2 
31 
217 
Deepwater redfish 
( Sebastes mentella ) 
63 
1030 
12,069 
1.207 
191.6 
88.0 
14 
379 
104 
Greenland halibut 
(. Reinhardtius hippoglossoides ) 
56 
585 
1359 
1.243 
24.3 
13.5 
4 
36 
120 
Thorny skate 
( Raja radiata) 
79 
990 
2394 
1.124 
30.3 
9.0 
3 
20 
226 
Witch flounder 
( Glyptocephalus cynoglossus ) 
57 
970 
5046 
1.334 
88.5 
52.0 
6 
151 
108 
Yellowtail flounder 
(Limanda ferruginea) 
24 
536 
5795 
1.250 
241.5 
159.0 
5 
503 
102 
the simulation based on American plaice ( Hippoglos - 
soides platessoides), data were generated for 105 paired- 
tows with an average R of 109.5. Twenty-five percent 
of the sets had R< 9, and 25% of sets had i?>169. The 
number of paired-tows in the seven sets of simulations 
varied from 25 to 105 which is a practical range con- 
sistent with many comparative fishing studies (e.g., 
Table 2 in Pelletier, 1998). The catches ranged from low 
(Atlantic cod, Gadus morhua ) to high (yellowtail floun- 
der, Limanda ferruginea). Some of the stocks had very 
skewed catches; for example, Atlantic cod and thorny 
skate ( Raja radiata) had mean catches that exceeded 
their 75th percentiles. 
The simulations were similar to a parametric boot- 
strap procedure; however we varied f) and o 2 to examine 
how the accuracy of statistical inferences varied with 
changes in these parameters. The values of (3 ranged 
from 0 to 2 by increments of 0.25, with 13=0, or p=l, 
representing no vessel effect, and (3= 2, or p=7.4 , repre- 
senting a test vessel catchability that was 14% of the 
control vessel. Note that this range in /3 is much larger 
than the results in Cadigan et al. (Table 7 in Cadigan 
et al. 3 ). Their largest absolute estimate was 0.08; how- 
ever, these simulations were designed to examine the 
accuracy of statistical inferences for small and large 
vessel effects. The levels of o 2 = 0, 0.1, 0.5, and 0.9 rep- 
resented no to high spatial heterogeneity and broadly 
reflected the range of estimates in Cadigan et al. (Table 
7 in Cadigan et al. 3 ). The lowest estimate of o 2 in Cadi- 
gan et al. 3 was 0.10 for Greenland halibut (Reinhardtius 
hippoglossoides), and the highest estimate was 0.99 for 
Atlantic cod. 
Simulated catches for the control vessel (R c ) were 
generated as binomial random numbers; the number of 
trials was equal to the observed R in Cadigan et al. 3 
and probability was based on Equation 5. The 5s were 
generated randomly from a normal distribution with 
mean zero and variance o 2 . The simulated test vessel 
catch was R t =R-R c . Note that the total catches for each 
paired-tow, R, ... , R n , were the same in each simula- 
tion; hence, our simulation results were conditioned on 
these values. 
We examined the robustness of the GLMM results to 
the assumption of a normal distribution for the random 
effects, 5, when in fact 5 was the log of a ratio of two 
independent and identically distributed gamma random 
variables with Var(5) = o 2 . 
Estimates and 95% CIs for were obtained from 
2000 simulations. We approximated the estimation bias 
as the median (3 from the simulations minus the true 
simulation value. Bias results based on means were 
very similar. The coverage accuracy of the CIs was 
measured as the proportion of simulations in which the 
Cl contained the true value of /3. If the 95% CIs are ac- 
curate, then the simulation proportion should be close to 
0.95. We also computed the proportion of simulations in 
which /3 was less than the lower Cl, and the proportion 
in which /3 was greater than the upper CL If the CIs 
are two-sided accurate, then these proportions should 
both equal 0.025. 
We performed other simulations using a much finer 
scale for /3 to examine the power of detecting a vessel 
effect based on the proportion of simulations whose CIs 
did not cover zero when the true /3 was greater than 
zero. 
Vessel and fish-length effects These simulations were 
similar to those described in the last section. We simu- 
lated data for the seven species and with the same 
number of tows and total catches-at-length for both 
