Analysis of Nonlinearity Effects in Expected-Value Parameterizations of the von Bertalanffy Equation

Abstract

Using curvature measures, this study provides direction on exploiting the full potential of two expected-value parameterizations of the von Bertalanffy equation in reducing nonlinearity effects. This study also examines the relationship between the curvature measures and characteristics of growth data for these parameterizations. Empirical analysis of a diverse set of growth data suggests that, on average, a threefold reduction in the maximum parameter effects curvature can be achieved by simply defining one parameter as the expected mean size of an intermediate age-class, rather than as the oldest age-class in the sample. It is also found that samples in which there are proportionally more size measurements in the younger age-classes relative to the older age-classes tend to have lower nonlinearity effects. Results can be applied to existing growth data which would otherwise yield unacceptably biased and nonnormal parameter estimates and to reduce the effort required in producing accurate confidence regions.