Cadigan and Dowden: Statistical inference about the relative efficiency of a new survey protocol 
21 
paired-tows (R[). However, there was 
an additional simulation factor for the 
slope of the length effect. We standard- 
ized lengths in the data from Cadigan 
et al. 3 : 
l-l 
l std 
50 
^75 ^25 
( 10 ) 
where l a = the ath percentile of the 
lengths from all sets, 
weighted by total catch, for 
each species. 
This standardization allowed us to use 
the same slopes in simulations for dif- 
ferent species; we considered l\=0, 0.5, 
1.0 to represent no, medium, and large 
length effects. This scale increased the 
number of simulations three-fold. The 
length-based models were also slower to 
estimate because of the larger size of the 
data sets (see n in Table 2), and to save 
time we reduced the number of simula- 
tions to 1000. 
We simulated data from Equation 7. 
We set a| = a| = o 2 and used the same 
values as before, o 2 - 0, 0.1, 0.5, and 0.9. 
However, we fitted both Equation 6 and 
Equation 7 to the simulated data. This 
procedure allowed us to examine the ac- 
curacy of statistical inferences from the 
random intercept model, which is a com- 
mon mixed effects model, when slopes 
were random as well. We summarized 
the simulations for P(l st d^ = Po + l\htd 
three points, l st(1 = 0, 0.5, and 1.0, which 
reflects relative efficiency at median to 
large lengths. 
Results 
0 2 4 6 8 10 12 14 
Test vessel (number per tow) 
Figure 2 
Comparative fishing survey results for witch flounder (Glyptocephalus 
cynoglossus). (A) Catches from the test and control vessels with 57 
paired-tows. Thick line segments connect the offset adjustments for 
differences in tow duration and subsampling of catches (see text for 
further detail) and indicate equal catchability (i.e., p = l); that is, if 
p=l, the scatter of points should be centered around the offset adjust- 
ments. Solid circles indicate paired-sets with substantially different 
catches. (B) Total catch per 1-cm length classes over all sets, for the 
test vessel, the test vessel adjusted for tow duration and subsampling, 
and the control vessel. 
Case study 
We illustrate methods using data for witch flounder 
from Cadigan et al. 3 . There is some evidence that the 
catchability of the control vessel was less than the test 
vessel. For example, there were five sets (solid circles 
in Fig. 2 where the test vessel caught more than 100 
fish but the control vessel caught fewer than 100 fish. 
Rarely were catches by the control vessel much larger 
than the test vessel. However, in most paired-tows the 
catches by both vessels, when adjusted for tow distance 
and subsampling, were similar. The length distribu- 
tions over all sets (Fig. 2, bottom panel) did not indicate 
that potential differences in catchabilities were length 
dependent because catch differences were approximately 
equally distributed over a broad range of sizes. 
The GLIM estimate of ft=\og(p) (Table 3; VO model) 
was significantly less than zero indicating that the con- 
trol vessel had a catchability that was significantly less 
than the test vessel. However, both GLMM estimates 
(VM, VP) were somewhat larger and not significant, in- 
dicating that the test and control vessels catchabilities 
were not significantly different. The VM and VP esti- 
mates of p and o 2 were very similar. The PQL software 
(PROC GLIMMIX) we used did not provide standard 
errors for the estimate of o 2 , but the marginal MLE 
software (PROC NLMIXED) did. 
The length-based models provided similar results, 
with the GLIM model (VLO) producing significant dif- 
ferences whereas the mixed models did not. Note that 
the length-based estimates are very different from those 
in Cadigan et al. 3 because we standardized lengths (i.e., 
