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Fishery Bulletin 101(3) 



£ 2.0 



1.5 



Simulated catch per trip 

 scales to series means 



123456789 10 11 



1.0 



0.5 



12 3 4 5 6 7 



Year 



9 10 11 



Figure 9 



Simulated recreational fishery indices of abundance mod- 

 eled under different error distribution assumptions. 



statistics indicated a better determined year effect (more 

 precise year coefficients) for the Poisson than for the nega- 

 tive binomial. However, the dispersion estimate (deviance/ 

 df) for the Poisson model was much greater than 1.0, indi- 

 cating that the input data were overdispersed with respect 

 to the Poisson distribution (Table 10). The latter was the 

 expected result, given that the variance of the annual 

 simulated data sets was much larger than the mean. The 

 results indicated that the negative binomial was a more 

 appropriate model, with a dispersion estimate closer to 1.0, 

 which was also the expected result given the true negative 

 binomial distribution of the simulated data (SAS, 2000). 



The consequence of assuming a lognormal model for the 

 true underlying negative binomial distribution was a more 

 extreme smoothing of the true time series trends than with 

 the other model assumptions, with a decline of only 28% 

 over the time series (Fig. 9). The diagnostic statistics for the 

 lognormal model indicated a significant model fit, but the 

 dispersion estimate was much less than 1.0, indicating that 

 the input data were underdispersed with respect to the 

 lognormal distribution (Table 10). This finding is reflective 

 of the large number of and 1 catch-per-trip observations, 

 and a lack of observations near the mean of the input prob- 

 ability distribution (SAS, 2000). In this simulation exercise, 

 therefore, the lognormal model dispersion estimate of much 

 less than 1.0 is indicative of model misspecification. 



As noted in the "Materials and methods" section, the in- 

 dices of abundance from the delta models are calculated as 

 the product of the year-effect coefficients from the two com- 

 ponent models. The interaction of the year coefficients from 

 the binomial proportion positive catches and lognormal or 

 Poisson positive catches components of the delta models 



