668 



Fishery Bulletin 101(3) 



Table 12 



Summary of model fits for estimating indices of abundance 

 from empirical MRFSS (Marine Recreational Fishery Sta- 

 tistics Survey) summer flounder catch per trip (including 

 zero catches), 1981-98. Total model degrees of freedom 

 (df) were 102,162; for the positive catches component 

 of the delta models, degrees of freedom were 52,507. All 

 model fits and classification effects were highly significant 

 (P<0.001). 



Delta models: binomisil proportion positive catch 



Deviance 130,341 1.2758 



Log-likelihood -65,171 



Year chi-square 2498 



Delta-lognormal model: lognormal positive catches 

 Deviance 36,780 0.7005 



Log-likelihood -65,202 



Year chi-square 1203 



Delta-Poisson model: Poisson positive catches 



Deviance 183,019 3.4856 



Log-likelihood 115,991 



Year chi-square 5675 



Table 13 



Summary of model fits for estimating indices of abundance 

 from empirical MRFSS (Marine Recreational Fishery 

 Statistics Survey) Atlantic cod catch per trip (including 

 zero catches), 1981-98. Total model degrees of freedom 

 (df) were 20,629; for the positive catches component of 

 the delta models, degrees of freedom were 13,160. All 

 model fits and classification effects were highly significant 

 (P<0.001). 



Delta models: binomial proportion positive catch 



Deviance 24,997 1.2117 



Log-likelihood -78,837 



Year chi-square 191 



Delta-lognormal model: lognormal positive catches 

 Deviance 11,657 0.8858 



Log-likelihood -17,920 



Year chi-square 353 



Delta-Poisson model; Poisson positive catches 



Deviance 75,359 5.7264 



Log-likehhood 88,239 



Year chi-square 2805 



lognormal positive catch year coefficients over the course 

 of the time series. For example, the year- 11 coefficient from 

 the binomial proportion positive catches model was 0.59; 

 the year-11 lognormal positive catches coefficient was 0.61, 

 providing a product for the year-11 index of 0.36. In con- 

 trast, the year-11 Poisson positive catches coefficient was 

 0.49, providing a product for the year-1 1 index of 0.29. When 

 these and the other annual coefficients were scaled to the 

 respective series means, the delta-Poisson model indicated 

 a slightly greater decline over the time series. 



MRFSS standardized indices of abundance, 

 1981-98 



All standardization models of the MRFSS catch per trip 

 (including zero catches), for the four individual species 

 and for all species, fitted well. In part because of the large 



number of observations, the overall model fits and the indi- 

 vidual classification effects (year, mode, state, wave, and 

 days 12 ) were all highly significant. Only the year effect chi- 

 square statistics are tabulated because the year effect coef- 

 ficients serve as the annual indices of abundance (Tables 

 11-15). The year effect was generally the second or third 

 most important effect in the models, after mode and state. 

 The dispersion estimates (deviance/df) for the lognormal 

 models indicated the data were generally underdispersed 

 with respect to the lognormal; the dispersion estimates for 

 the Poisson models indicated overdispersion with respect 

 to that distribution. The dispersion estimates for the nega- 

 tive binomial models and binomial components of the delta 

 models were generally close to 1.0, indicating appropriate 

 model specification (Tables 11-15). 



As in the simulated catch-rate exercise, the lognormal 

 standardized abundance indices generally show lower 



