Evidence of parameters underestimation from nonlinear growth models for data classified as limited

Abstract

Some growth data in aquaculture have peculiar characteristics that generate consequences in the analysis and modeling. They are usually incomplete or limited, as classified in this article. This means data are restricted to a few observations and often are limited to observations below the curve’s inflection point due to economic interests in farm settings, or due to limitation of physical space in controlled research laboratories, for example. This possibly causes under and/or overestimation in the inference of nonlinear models. Through shrimp growth simulations from the Michaelis–Menten curve, the limited data were synthesized with threshold observation up to the first 7, 13, 18, 36, and 82 weeks. Seven sigmoid growth functions (Logistic, Gompertz, von Bertalanffy, Richard, Weibull, Morgan–Mercer–Flodin, and the own Michaelis–Menten growth) were fitted to respective limited data, in order to assess the research hypothesis. Taking the scenarios with incompleteness in the first 7, 13 and 18 weeks, the parameters of all growth curves modeled under a frequentist approach were underestimated. Thus, we propose a correction for this possible problem through a hierarchical Bayesian approach. Real data from shrimp farming in northeastern Brazil were used to compare it with the traditional frequentist approach employed. The sensitivity in detecting outstanding treatment (pond or batch level hierarchy) can make the new method a powerful management tool in animal production, and also in trials designed for scientific research.