Forecasting fish yield using statistical nonlinear growth models – A reparameterization concept

Abstract

The concept of reparameterization is rarely employed in forecasting fish yield, even though reparameterization method is computationally more efficient especially when estimation involves an iterative method. Further, a reparameterization of the growth functions whose new parameters correspond to scientifically interesting characteristics of the growth process (Choi et al, 2009). Reparameterization of the same basic model produce the same goodness-of-fit and the same fitted values, etc. but they may differ greatly in their estimation behavior. Further, a class of parameters that exhibits close-to-linear behavior is the class of expected-value parameters. The extent of non-normality and excess variance of the least squares estimates of an expected value parameter is generally small (Ratkowsky, 1990). The only restriction on expected-value parameters is that they should fall within the observed range of the data and not correspond to asymptotes or extrapolations outside the data range. Expected-value parameters outside the range of the observed data are less efficacious. Also, the derived expressions due to expected-value parameters are usually more cumbersome in appearance than the original expressions, and the expected-value parameters may appear more than once. As compensation for this loss of aesthetics, however, parameterizations with expected-value parameters offer three advantages. First, one obtains rapid convergence to the leastsquares estimates using the new parameterization, since the new model close-to-linear. A second benefit is that initial parameter estimates are very easy to obtain. Third, the expected-value parameters are more suitable for inference than the original parameters since their least-squares estimates are close-to being unbiased, normally distributed, minimum variance estimators. Although the role of expected-value parameters is very important, algebraic limitations prevent the universal application of expected-value parameters. However, in most of the cases a few parameters (one or two parameters only) are responsible for the far-from-linear behavior of a nonlinear regression model, it is seldom necessary to replace all the parameters of a model by expected-value parameters (Ratkowsky, 1990). Singh (2011) derived an explicit expression for partial reparameterization of Schaefer model with autoregressive of order one using expected-value parameters and fitted to catch-effort fishery data.