Cadigan and Dowden: Statistical inference about the relative efficiency of a new survey protocol 
27 
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P, =0 
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cr 2 = 0.5 
CJ 2 =0.1 
1 
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a 2 = 0.5 
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I 
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Figure 7 
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 length based data were generated for different assumed values of /3(Z) = /3 0 + /V and spatial 
heterogeneity (a 2 ) in fish densities encountered in each tow. Lengths were standardized, 
l std =(l ~ ^ 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 /3 ( 7 ) , and 
four line patterns and shadings are used to show the results from each model at l std =1. 
Panel columns are for levels of a 2 and /3 X (i.e. , ct 2 = 0 and /3 X = 0 in A, E, I, and M, etc.) and 
the x-axis of each panel are for levels of /3 0 . Bias (A-D) is the simulation median estimate of 
/3 minus P 0 +P 1 - Cl indicates confidence interval, and P{|3(Z s((i )£rCI| 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). 
dard GLMM approach. However, this does not mean 
that GLMMs are always robust to mis-specifications of 
random effects (e.g., Heagerty and Kurland, 2001). We 
demonstrated this in our length-based simulations. 
We demonstrated that the random intercept model 
gave inaccurate statistical inferences (bias and CIs) if 
there was between-set random variations in length ef- 
fects. This is a type of model mis-specification. However, 
we did not fully examine the other side of this result, 
which is bias caused by assuming between-set random 
variation in length effects when in fact none exists. 
Results from simulations with a 2 =0 for both vessel and 
length effects showed that the random intercept and 
slope model (i.e., VLM is ) provided reliable statistical 
