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Fishery Bulletin 108(1) 
inferences when no random effects exist, and we specu- 
late that the same result will hold when only random 
intercept effects exist. Hence, we recommend the VLM is 
approach when there is either within-pair variation in 
the density of fish or in their length compositions. 
A type of model we did not consider involves large- 
scale within-pair random variations in the densities 
of fish encountered by both vessels, and smaller-scale 
length-specific random variations in length composi- 
tions. When plotted like Figure 1, log density ratios 
would appear as a scatter of points about horizontal 
lines. The intercepts of the horizontal lines would de- 
pend on the large-scale random variation in the fish 
densities, and the variation in the scatter about these 
horizontal lines would depend on the smaller-scale 
length-specific random variations in length composi- 
tions. These types of effects can be modeled with hier- 
archical random effects (i.e., set, and length within set). 
This procedure would be fairly straightforward with a 
PQL approach but more difficult with marginal MLE. 
The reliability of estimates (relative efficiency and vari- 
ance parameters) is uncertain. Even more complicated 
hierarchical random-effect models for both vessel and 
catch length-composition effects could be considered. 
This was beyond our scope but important to understand 
for reliable statistical inference. In reality, random ef- 
fects in log density ratios may also have non-normal 
and skewed distributions, and it would be helpful to 
understand the robustness of VLM 1S to these types of 
model mis-specifications. 
Another sensible simulation procedure is to specify 
the stock densities fished by both vessels from site to 
site, and generate random catches for both vessels. The 
stock densities could be specified by using a variety of 
spatial models, as long as the within-pair and between- 
pair variations in densities are reasonably consistent 
with what one might expect in practice. However, this 
would not be a conditional simulation because the total 
catches by both vessels (and for all sets) would vary 
from simulation to simulation. It would still be use- 
ful to examine if the conditional CIs are accurate in 
this more general setting. However, the results from 
our conditional simulations were very similar for each 
of the seven species scenarios we considered and we 
anticipate they would also be accurate in the more 
general setting. 
Cadigan et al. (2006) used a random effect for <5=<5(Z) 
that was autocorrelated in length l, corr{<5(Z),<5(f)}=y lz_n . 
This is a strategy to model smooth functions (e.g., 
Brown and de Jong, 2001). We used a simpler approach 
based on the assumption that 5 (l) varied linearly with l. 
A GLMM in which 5(1) is autocorrelated can be fitted by 
using PQL software, but is time consuming to simulate 
and therefore we decided to focus on Equation 7 which 
is much easier to estimate. 
Another approach to estimate relative efficiency (i.e., 
Pelletier, 1998) is maximum likelihood based on the 
negative binomial (NB) distribution. We have pursued 
this approach; however, there are complications in esti- 
mating the NB over-dispersion parameter based on the 
joint likelihood of both trawl catches and this problem 
affects the accuracy of CIs. The conditional approach is 
also more complicated for the NB distribution. We will 
report on this elsewhere. 
Fryer et al. (2003) showed how to use spline methods 
for smooth, but otherwise nonparametric, estimates of 
relative efficiency. This is a useful estimation approach, 
especially to check the adequacy of a parametric model. 
The simple logistic-linear model we considered may be 
sufficient to test whether there is a significant length- 
dependent vessel effect but the logistic-linear model 
may not be sufficiently flexible for reliable estimation 
of relative efficiency over all lengths. 
Lewy et. al. (2004) advocated paired-trawls along the 
same trawl track-line to avoid complications due to spa- 
tial variations in stock densities. However, such trawling 
introduces a different complication which involves dis- 
turbance of the fish densities encountered by the second 
vessel because of the fishing activity of the first vessel. 
Another potential advantage of GLMMs is less sensi- 
tivity to outliers. Figures 14 and 15 of Cadigan et al. 2 
indicated that GLMM estimates of /3 were less sensitive 
to outliers than GLIM estimates. This lack of sensi- 
tivity is a considerable advantage because identifying 
outliers is time consuming in practice when conversion 
factors are estimated for many species. In addition, 
standard errors may be too small when observations 
are incorrectly deemed to be outliers and removed from 
the analysis. Atlantic cod and thorny skate had mean 
total catches (for both vessels) that exceeded the 75th 
percentile (Table 2), indicating that there were a few 
large catches that may have undue influence on esti- 
mates. The GLMMs seem better suited for this type of 
data. It would be useful to test these methods through 
simulation to assess robustness to outliers. The random- 
ization approach used by Benoit 1 is another appropriate 
and robust procedure (e.g., Cox and Hinkley, 1974, p. 
180-181) to test for the statistical significance of vessel 
effects, and we recommend this approach in addition to 
the use of GLMMs. However, it does not provide robust 
estimates of vessel effects and the approach cannot 
replace a GLMM. 
Acknowledgments 
The authors are grateful for the expertise, assistance, 
and many discussions with S. Walsh and B. Brodie, of 
the Northwest Atlantic Fisheries Center, Fisheries and 
Oceans Canada (DFO). M. Koen-Alonso of DFO also 
provided comments on earlier draft. 
Literature cited 
Benoit, H.P., and D. P. Swain. 
2003. Accounting for length- and depth-dependent diel 
variation in catchability of fish and invertebrates in 
an annual bottom-trawl survey. ICES J. Mar. Sci. 
60:1298-1317. 
