Bayesian modeling of the coffee tree growth curve

Abstract

When modeling growth curves, it should be considered that longitudinal data may show residual autocorrelation, and, if this characteristic is not considered, the results and inferences may be compromised. The Bayesian approach, which considers priori information about studied phenomenon has been shown to be efficient in estimating parameters. However, as it is generally not possible to obtain marginal distributions analytically, it is necessary to use some method, such as the weighted resampling method, to generate samples of these distributions and thus obtain an approximation. Among the advantages of this method, stand out the generation of independent samples and the fact that it is not necessary to evaluate convergence. In this context, the objective of this work research was: to present the Bayesian nonlinear modeling of the coffee tree height growth, irrigated and non-irrigated (NI), considering the residual autocorrelation and the nonlinear Logistic, Brody, von Bertalanffy and Richard models. Among the results, it was found that, for NI plants, the Deviance Information Criterion (DIC) and the Criterion of density Predictive Ordered (CPO), indicated that, among the evaluated models, the Logistic model is the one that best describes the height growth of the coffee tree over time. For irrigated plants, these same criteria indicated the Brody model. Thus, the growth of the non-irrigated and irrigated coffee tree followed different growth patterns, the height of the non-irrigated coffee tree showed sigmoidal growth with maximum growth rate at 726 days after planting and the irrigated coffee tree starts its development with high growth rates that gradually decrease over time.

Bayesian estimation of nonlinear models parameters in the description of growth coffee fruits

“…The nonlinear regression models are able to describe diverse situations, providing a better fit quality and, mainly, present practical interpretation of the parameters. Therefore are been widely used, especially in the study of growth curves ( Growth models are commonly estimated by frequentist approach, however the parameter estimation process is based on asymptotic theory and, when there is small sample data, the obtention of the estimates is very affected, generating atypical growth curves (Pereira et al, 2022;Martins Filho et al, 2008;Salles et al, 2020). However, few longitudinal observations are common in the study of fruit growth, due to the short fruiting period.…”

“…An alternative to the MCMC is the weighted importance resampling, that unlike MCMC, it generates independent samples, requires a short computational time for implementation, and has a more attractive theory (Pereira et al, 2022;Cole et al, 2012;Lopes et al, 2012).…”