Terceiro The statistical properties of recreational catch data off the northeastern U.S. coast 



667 



Table 11 



Summary of model fits for estimating indices of abundance 

 from empirical MRFSS (Marine Recreational Fishery 

 Statistics Survey) bluefish catch per trip (including zero 

 catches), 1981-98. Total model degrees of freedom (df) were 

 130,300; for the positive catches component of the delta 

 models, degrees of freedom were 48,447. All model fits and 

 classification effects were highly significant (P<0.001). 



Delta models: binomial proportion positive catch 



Deviance 157,674 1.2101 



Log-likelihood -78,837 



Year chi-square 854 



Delta-lognormal model: lognormal positive catches 



Deviance 39,963 0.8249 



Log-likelihood -64,129 



Yera chi-square 1240 



Delta-Poisson model: Poisson positive catches 



Deviance 249,112 5.1419 



Log-likelihood 193,660 



Year chi-square 10,501 



provided some interesting results in this simulation exer- 

 cise. The binomial model component, common to both delta 

 models, provided a highly significant year effect and indi- 

 cated a 41% decline in abundance over the time series. The 

 dispersion estimate indicated some overdispersion of the 

 data with respect to the binomial distribution (Table 10). 



The lognormal positive catches component of the delta- 

 lognormal model also provided a highly significant year 

 effect and indicated a 39% decline in abundance over 

 the time series, producing a smoothing effect similar to 

 that observed for the lognormal model of catch per trip 

 including zeroes. The dispersion estimate indicated some 

 underdispersion of the data with respect to the lognormal 

 distribution (Table 10). The product of the annual year coef- 

 ficients from the two delta-lognormal model components, 

 which individually indicated less decline than the unstan- 

 dardized indices, provided final indices of abundance that 

 declined 64% over the time series (due to the product of two 

 positive fractional values <1 providing a even smaller value 



<1) — nearly identical to the unstandardized, Poisson, and 

 negative binomial series (Fig. 9). 



The Poisson positive catches component of the delta- 

 Poisson model provided a highly significant year effect and 

 indicated a 51% decline in abundance over the time series. 

 The dispersion estimate was much greater than 1.0, indicat- 

 ing overdispersion of the data with respect to the Poisson 

 model (Table 10). The product of the annual year coefficients 

 from the two delta-Poisson model components provided in- 

 dices of abimdance that dechned 71% over the time series, 

 a slightly greater decrease than for the other models (Fig. 

 9). Note again that the delta-lognormal and delta-Poisson 

 models share the same binomial proportion positive catch 

 model components, and therefore annual year coefficients 

 for this component. The decrease estimated by the delta- 

 Poisson model was greater than that for the delta-lognor- 

 mal because the year coefficients from the Poisson positive 

 catch model were all smaller, and more closely matching the 

 unstandardized positive catch series, than the comparable 



