22 
Fishery Bulletin 108(1) 
Table 3 
Parameter estimates, standard errors (SE), and lower 
and upper 95% confidence interval limits from various 
models for paired-tow comparative fishing data. See Table 
1 for definitions of model acronyms and parameters. The v 
and / parameter subscripts indicate a vessel or fish-length 
effect. 
Model Parameter 
Estimate 
SE 
Lower 
Upper 
VO 
ft, 
-0.153 
0.069 
-0.290 
-0.018 
<P 
5.888 
— 
— 
— 
VP 
ft, 
-0.094 
0.093 
-0.279 
0.091 
V 2 
0.301 
0.088 
— 
— 
VM 
ft, 
-0.097 
0.093 
-0.283 
0.089 
V, 2 
0.302 
0.089 
0.124 
0.480 
VLO 
ft, 
-0.166 
0.037 
-0.239 
-0.094 
ft 
-0.053 
0.052 
-0.154 
0.048 
<P 
1.628 
— 
— 
— 
VLP, 
ft, 
-0.102 
0.092 
-0.286 
0.082 
ft 
0.058 
0.052 
-0.045 
0.160 
°v 
0.296 
0.086 
— 
— 
VLM, 
ft, 
-0.105 
0.092 
-0.290 
0.079 
ft 
0.058 
0.052 
-0.047 
0.164 
% 2 
0.295 
0.086 
0.121 
0.468 
VLP 1S 
ft, 
-0.099 
0.094 
-0.288 
0.090 
ft 
0.059 
0.080 
-0.098 
0.215 
0.299 
0.088 
— 
— 
°l 2 
0.119 
0.061 
— 
— 
VLM is 
ft, 
-0.103 
0.095 
-0.294 
0.088 
ft 
0.061 
0.081 
-0.101 
0.224 
0.303 
0.091 
0.121 
0.484 
o, 2 
0.122 
0.065 
-0.008 
0.252 
Eq. 10) but Cadigan et al. 3 did not. The 25th, 50th, and 
75th length percentiles were 22, 29, and 34 cm. CIs for 
p(l) based on Equation 9 were derived for l std =0, ... , 2 
(Fig. 3). The VLO model suggested p(l ) decreased with l 
and was significantly different from one over the range 
of lengths. The four mixed models all indicated a slight 
increase in p(l) with l but were not significantly differ- 
ent from one for any length. The CIs for the random 
intercept model (Eq. 6) were shorter than those for the 
random intercept and slope models, especially when 
l std > 1. The marginal MLE CIs (VLM,, VLM 1S ) were 
slightly wider than PQLE CIs (VLPj, VLP is ). 
Simulations 
Vessel effect Simulation results were very similar for 
the seven species. We present the best and worst cases 
in Figures 4 and 5. The VO model performed poorly 
even when there was small spatial heterogeneity in 
stock densities (i.e., o 2 = 0.1). The likelihood ratio CIs 
had poor coverage properties and the probability that 
they contained the true value of the vessel effect (/3) was 
much less than the 95% nominal value. When o 2 and /3 
were large this method produced biased estimates of /3 
and very inaccurate CIs. Note that to facilitate compari- 
son of the methods the y-axis was fixed to be less than 
the range of some of the GLIM results, particularly in 
Figure 5. The VP CIs were more accurate, except when 
cP> 0.5 for the thorny skate simulation (Fig. 5). For larger 
values of /3 the CIs from this method covered less than 
95%, about 80% for o 2 = 0.9 and /3 =2. The bias was nega- 
tive which meant that the lower and upper bounds were 
too small. The VM CIs were quite reliable across the 
range of values for a 2 and /3, and for all seven simulation 
scenarios (i.e., species). The log gamma ratio simulation 
results were almost identical to the normal simulations 
results and are not presented. 
We performed simulations at a finer scale of /3 to de- 
termine the size of a vessel effect that could be detected 
with a power of 0.8 or 0.95, based on the VM model. 
The power was computed from the proportion of CIs 
that did not cover zero. The results are shown in Table 
4, expressed in terms of percent change, 100x(p-l). 
For example, when o 2 = 0.5 there was a 95% chance of 
detecting a 44% increase in catchability with data like 
that for American plaice. 
Vessel and length effects The VLO model performed 
poorly compared to the mixed models and those results 
are not presented. We examined statistical inferences 
for p(l 8td ) based on the VLM,, VLP,, VLM is , and VLP is 
models. Note that simulated data were generated by 
using Equation 7 but fitted with both Equation 6 and 
Equation 7; hence, the results based on Equation 6, i.e. 
VLMj and VLP ; , will reflect model mis-specification 
biases. Results were similar for each simulation scenario 
(i.e., species). We present results for p (l std ) only for the 
Atlantic cod scenario, small and medium spatial vari- 
ability (a =0.1, 0.5), no or large lengths effects (/3j = 0, 
1), and at the center of the length distribution (l std =0; 
Fig. 6 or at a larger value (l std = 1; Fig. 7). 
The random intercept models gave unreliable results 
especially when l std = 1. The total random effect variance 
based on Equation 7 increased with length and this was 
not accounted for by the VLM i or VLPj models. The poor 
performance of CIs for P(l std ) derived from the VLMj 
and VLP, models was caused by both bias in estimates 
of /3 (l std ) and bias in estimates of the variance of the 
estimator for P(l std )- These biases are a complicated 
function of /3 0 , p v o 2 and l std . 
The PQL estimation bias was similar to the results of 
the vessel effects only simulation (not shown for Atlan- 
tic cod) when l std = 0, which is not surprising because the 
conditional distributions based on Equation 5 and Equa- 
tion 7 are essentially the same in this case. However, 
when l std = 1 the VLP is model gave less accurate results 
compared to those when l std = 0. The VLM is model gave 
reliable results in all simulation settings. 
The worst case VLM is result for the lower 95% Cl cov- 
erage was for the deepwater redfish ( Sebastes mentella) 
scenario in which the simulation coverage was 0.057 
(nominal value is 0.025) when /3 0 = 0.5, j3 1 =l, o 2 - 0.5, 
and l std = 0. The worst case result for the upper interval 
