Cadigan and Dowden: Statistical inference about the relative efficiency of a new survey protocol 
23 
Table 4 
The size of a vessel effect (i.e., change in relative efficiency, p-1, in %) that can be detected with power= 
for values of o 2 (i.e., the random effect variance) and rows are for species simulation scenarios. 
0.8 or 0.95 
Columns are 
Species 
Power = 
= 0.8 /o 2 
Power=0.95 /o 2 
0.0 
0.1 
0.5 
0.9 
0.0 
0.1 
0.5 
0.9 
American plaice ( Hippoglossoides platessoides) 
5 
13 
23 
32 
9 
24 
44 
64 
Atlantic cod ( Gadus morhua) 
10 
18 
33 
42 
17 
33 
68 
92 
deepwater redfish ( Sebastes mentella) 
5 
15 
30 
43 
7 
27 
60 
99 
Greenland halibut ( Reinhardtius hippoglossoides) 
16 
23 
39 
54 
28 
44 
86 
134 
thorny skate ( Raja radiata) 
13 
20 
34 
45 
23 
38 
71 
101 
witch flounder ( Glyptocephalus cynoglossus) 
8 
17 
34 
49 
13 
31 
72 
113 
yellowtail flounder (Limanda ferruginea) 
8 
25 
62 
101 
13 
50 
164 
372 
was 0.055 when /3 0 = 2, ^=0, ct 2 = 0.9, and 
l std - 0 for Atlantic cod. In 95% of the simu- 
lations for all species the absolute error for 
the lower Cl was less than 0.013, and for 
the upper interval it was less than 0.016. 
This demonstrates that CIs from the VLM is 
model were almost always very accurate. 
Discussion 
Our simulation results demonstrated that 
the commonly used over-dispersed bino- 
mial logistic regression model did not 
provide accurate statistical inferences for 
paired-trawl calibration data when there 
was spatial variation in stock densities. 
In practice, such variations will occur and 
therefore this approach is not recommended. 
Fortunately, our simulations showed that 
a binomial logistic regression model that 
included random site effects in addition 
to fixed vessel effects did provide accurate 
inferences for a wide range of spatial varia- 
tions in stock densities. This conclusion also 
applied to pooled or length-based analyses. 
We recommend this binomial generalized 
linear mixed-effects model (GLMM) for 
analyzing comparative fishing data. When 
assessing for length effects, we recommend 
using a binomial GLMM with between-site 
random variation in both the vessel and 
length effects. 
Between-set variability in catchability 
is commonly observed in covered-codend 
experiments (e.g., Fryer 1991, Millar et. al. 
2004) that directly measure catchability. 
This will also produce between-site vari- 
ability in p. Trenkel and Skaug (2005) assumed that 
the Poisson density for fish abundance was spatially 
constant on a small scale (~1000 km 2 ), and that be- 
0.6 - 
Standardized length (l sld ) 
Figure 3 
95% confidence intervals for the relative efficiency of the test vessel 
compared to the control vessel for catches (in numbers) of witch 
flounder (Glyptocephalus cynoglossus). Relative efficiency was modeled 
as a function of length l, p(Z) = exp(j3 0 +/3 1 Z), and length was standard- 
ized, l std =( 1 - Z 50 y^ 7 s~^ 25 ^’ where l a was the axl00% percentile of the 
lengths caught in all sets. The five models indicated by different 
line patterns and shading are described in Table 1. Two lines of 
the same pattern and shading are plotted for the lower and upper 
confidence interval endpoints. The thin horizontal line represents 
equal catchability, p(l) = 1. 
tween-haul variation in catchability caused all addi- 
tional Poisson over-dispersion in bottom-trawl survey 
catches. Cadigan et al. 2 demonstrated that this type of 
