Cadigan and Dowden: Statistical inference about the relative efficiency of a new survey protocol 
25 
Figure 5 
Paired-tow comparative fishing simulation results for log relative efficiency (fi) of the test 
vessel compared to the control vessel. Simulations were based on the thorny skate ( Raja 
radiata) scenario and data were generated for different assumed values of p (i.e., P 0 ) and 
spatial heterogeneity (a 2 ) in fish densities encountered in each tow. Three models of spatial 
heterogeneity, described in Table 1, were used to estimate /3, and three line patterns are 
used to show the results from each model. Panel columns are for levels of o 2 (i.e., ct 2 = 0 
in A, E, I, and M, etc.) and the x-axis of each panel are for levels of f3. Bias (A-D) is the 
simulation median estimate of p minus p 0 . Cl indicates confidence interval, and P (p GrCI) 
indicates the probability the Cl contains p, etc. References lines (solid) are shown in each 
panel, at zero (A-D), 0.95 (E-H), and 0.025 (I-P). 
and 50% would be important in stock assessment, and 
our simulation results indicated that more sets would 
be necessary to detect such changes in a comparison 
of paired-tow fishing data when the amount of spatial 
heterogeneity is similar to the levels in Cadigan et al. 3 . 
If spatial heterogeneity could somehow be removed or 
kept low, then 50% changes in catchability could be 
detected with high power. 
Another common approach to analyze comparative 
fishing data is to log transform catches and use normal 
linear models for analysis; however, this approach does 
not often adequately account for the stochastic nature 
of the data (e.g., counts) and involves arbitrary choices 
to deal with zero catches. However, the lognormal ap- 
proach may be reasonable and appropriate in some 
situations, or when the focus is on catch weights (e.g., 
Kingsley et al., 2008). 
We studied two methods to estimate GLMMs. One 
was based on maximizing the marginal likelihood, in- 
tegrated over the random effects. The other approach 
was penalized quasi-likelihood estimation based on a 
linearization of the model and a double optimization 
