Interpretable Statistical Tests for Growth Comparisons using Parameters in the von Bertalanffy Equation

Abstract

Likelihood ratio, t-, univariate χ2-, and T2-tests have been proposed to compare von Bertalanffy parameters among stocks. As commonly applied, all of these tests are approximate, with the accuracy of each dependent on the nonlinearity of the von Bertalanffy equation, sample size, and if present, the degree of heterogeneity in the error variances. An empirical comparison of these procedures shows that the likelihood ratio test often differs in outcome from the others. Analysis of the conflicting cases by confidence region comparisons and Monte Carlo simulations almost always resolved the outcome in favor of the likelihood ratio test. The parameter effects component of nonlinearity was found to be the principal factor biasing the t-, univariate χ2-, and T2-tests. Reparameterizations of the von Bertalanffy equation substantially reduced, but did not completely eliminate, conflicting outcomes. It is concluded that the likelihood ratio test is the most accurate of the procedures considered in this study, and whenever possible, it should be the approach of choice.