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Fishery Bulletin 101(3) 



Standardized annual indices of abundance derived from 

 the simulated recreational and empirical MRFSS data 

 were calculated by using maximum likelihood estimation 

 to fit generalized linear models with the SAS GENMOD 

 procedure (SAS, 2000). The SAS (2000) defaults for model 

 specification were generally followed. An identity link func- 

 tion was used under the lognormal distribution assump- 

 tion (catch rates were In-transformed prior to analysis). A 

 logistic link function was used under the binomial distri- 

 bution assumption applied for the probability of positive 

 catch component in the delta-lognormal and delta-Poisson 

 model approaches. A logarithmic link function was used 

 under the Poisson and negative binomial assumptions 

 (SAS, 2000). Type-3 general linear models were fitted in 

 all cases because the results of this type of analysis do not 

 depend on the order in which the terms of the model are 

 specified. The significance of the individual classification 

 effects (factors) in the models was judged by the chi-square 

 statistic (Searle, 1987; SAS, 2000). 



The overall goodness of fit of the standardization mod- 

 els was evaluated by using the deviance and log-likelihood 

 statistics. The deviance is defined to be twice the difference 

 between the maximum achievable log likelihood and the 

 log likelihood at the maximum likelihood estimates of the 

 model parameters (McCullagh and Nelder, 1989). The devi- 

 ance has a limiting chi-square distribution, and so signifi- 

 cance is judged by comparison to critical values of the chi- 

 square distribution. The scale parameter (i.e. for normal 

 distributions) was held fixed at 1 for all models to facilitate 



evaluation of goodness of fit and the degree of overdisper- 

 sion for models with different error distribution assump- 

 tions. Holding the scale parameter fixed has no effect on the 

 estimated intercept or model regression coefficients (e.g. 

 in the study, the year coefficients that serve as the annual 

 indices of abundance), but allows equivalent calculation 

 among models of a "dispersion estimate" (SAS, 2000). This 

 "dispersion estimate," measured after model fitting as the 

 deviance divided by the degrees of freedom (deviance/df), 

 is used to judge whether the data are overdispersed or un- 

 derdispersed with respect to the error distribution used in 

 model fitting and is therefore useful in evaluating whether 

 the correct error distribution assumption has been used in 

 the model (McCullagh and Nelder, 1989; SAS, 2000). 



Descriptive statistics for MRFSS catch rates 



The descriptive statistics (mean, median, variance, skew- 

 ness, and Kolmolgorov-Smirnov (D) normality test statis- 

 tic) and frequency distributions of MRFSS sample catch 

 rates for 1981, 1988, and 1996 were examined for four 

 species from U.S. Atlantic coast waters (Maine to the east 

 coast of Florida), and in aggregate for all species sampled 

 along the U.S. Atlantic coast. The following individual 

 species were considered: bluefish (Pomatomus saltatrix, 

 an example of a Atlantic coast predatory "gamefish"); 

 summer flounder (Paralichthys dentatus, a Mid Atlantic 

 Bight demersal flatfish); Atlantic cod (Gadus morhua, a 

 New England demersal roundfish); and scup (Stenotomus 



