Comparison of six statistical approaches in the selection of appropriate fish growth models

The performance of six statistical approaches, which can be used for selection of the best model to describe the growth of individual fish, was analyzed using simulated and real length-at-age data. The six approaches include coefficient of determination (R-2), adjusted coefficient of determination (adj.-R-2), root mean squared error (RMSE), Akaike's information criterion (AIC), bias correction of AIC (AIC(c)) and Bayesian information criterion (BIC). The simulation data were generated by five growth models with different numbers of parameters. Four sets of real data were taken from the literature. The parameters in each of the five growth models were estimated using the maximum likelihood method under the assumption of the additive error structure for the data. The best supported model by the data was identified using each of the six approaches. The results show that R-2 and RMSE have the same properties and perform worst. The sample size has an effect on the performance of adj.-R2, AIC, AIC(c) and BIC. Adj.-R-2 does better in small samples than in large samples. AIC is not suitable to use in small samples and tends to select more complex model when the sample size becomes large. AIC(c) and BIC have best performance in small and large sample cases, respectively. Use of AIC(c) or BIC is recommended for selection of fish growth model according to the size of the length-at-age data.