26 
Fishery Bulletin 108(1 ) 
m 
Pi=0 
B u 2 = 0.5 
0i = 1 
C cr 2 = 0.1 
D <x 2 = 0.5 
0 
01 
ca 
"oT 
o 
A 
=Q. 
"ST 
0.0 0.5 1.0 1.5 2.0 0.0 0.5 
1.0 1.5 2.0 0.0 0.5 
00 
1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 
Figure 6 
Paired-tow fishing simulation results for log relative efficiency ( /3) of the test vessel compared 
to the control vessel. Simulations were based on the Atlantic cod ( Gadus morhua) scenario 
and fish-length-based data were generated for different assumed values of p(l) = p o + p l l and 
spatial heterogeneity (a 2 ) in fish densities encountered in each tow. Lengths were standard- 
ized, l sld = ( 1 - ^ 50 ^^ 75 -^ 25 ^’ where l a was the axl00% percentile of the lengths caught in all 
sets. Four models of spatial heterogeneity, described in Table 1, were used to estimate p (l), 
and four line patterns and shadings are used to show the results from each model at l std =0. 
Panel columns are for levels of a 2 and p x (i.e., cr 2 = 0 and 0j=O in A, E, I, and M, etc.) and 
the x-axis of each panel are for levels of p o . Bias (A-D) is the simulation median estimate 
of p minus 0 O . Cl indicates confidence interval, and P{0(Z sid )eCI} indicates the probability 
the Cl contains p(l std ), etc. References lines (solid) are shown in each panel, at zero (A-D), 
0.95 (E-H), and 0.025 (I-P). 
procedure. The advantage of the latter approach was 
its ability to accommodate more complicated types of 
random effects like those with autocorrelation. However, 
our simulations results indicated that estimates and 
CIs from the linearization method were less reliable 
than those from the marginal likelihood approach. We 
recommend the marginal approach to estimate GLMMs 
for comparative fishing data. 
We demonstrated that statistical inferences from 
GLMMs based on normal distribution random effects 
were equally as accurate when the random effects were 
actually the log of a ratio of two independent and iden- 
tically distributed gamma random variables, which we 
hypothesize is a real and important source of over- 
dispersion in vessel calibration studies. This is good 
because otherwise we could not recommend the stan- 
