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



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Table 14 



Summai'v of model fits for estimating indices of abundance 

 from empirical MRFSS (Marine Recreational Fishery Sta- 

 tistics Survey) scup catch per trip (including zero catches), 

 1981-98. Total model degrees of freedom (df) were 17,604; 

 for the positive catches component of the delta models, 

 degrees of freedom were 11,124. All model fits and classifi- 

 cation effects were highly significant (P<0.001). 



Delta models: binomial proportion positive catch 



Deviance 22,027 1.2512 



Log-likelihood -11,013 



Year chi-square 174 



Delta-lognormal model: lognormal positive catches 

 Deviance 14,340 1.2891 



Log-likelihood -17,225 



Year chi-square 350 



Delta-Poisson model: Poisson positive catches 



Deviance 212,250 19.0804 



Log-likelihood 391,327 



Year chi-square 8793 



rates of change in abundance than do the unstandardized, 

 Poisson, or negative binomial indices, with the CV of the 

 lognormal series about 25-50'7f of the CV of the unstan- 

 dardized indices (Figs. 10-14). In effect, the lognormal 

 standardization of MRFSS per trip catch rates had an 

 unintended (and undesirable) smoothing effect on the 

 independent annual indices abundance. The Poisson and 

 negative binomial models generally provided interpreta- 

 tions of the trend and annual changes in abundance very 

 similar to those of the unstandardized indices. 



For bluefish, the delta-lognormal, and delta-Poisson 

 models provided time series of indices with about the 

 same variability and trend, but slightly different annual 

 changes, as those from the unstandardized, Poisson, and 

 negative binomial models. For summer flounder, Atlantic 

 cod, scup, and all species, the delta-lognormal and delta- 

 Poisson models provided time series of abundance indices 

 that were more variable, with slightly different trends and 



annual changes, than the unstandardized, Poisson, and 

 negative binomial series. This last result is comparable to 

 that observed for the delta models used with the simulated 

 data and is therefore likely due in part to model misspecifi- 

 cation of the positive catch-per-trip component (recall that 

 catch per trip for these examples is best characterized 

 by the negative binomial distribution) and a comparable 

 interaction of the binomial, lognormal, and Poisson model 

 year coefficients. 



Discussion 



The frequency distributions of recreational fishery catch- 

 rate data as sampled by the MRFSS are highly skewed, 

 often with a significant proportion of zero catch observa- 

 tions. The present study indicates that MRFSS catch rates 

 generally are not normally or lognormally distributed 



