Estimação de parâmetros de modelos não lineares com resíduos autocorrelacionados

Abstract

Due to the economic importance of coffee for Brazil, one of the main focuses of research in the agricultural sector refers to the coffee development. In such research, the height of plants is a relevant variable to be considered, as well as being representative of the vegetative growth it is correlated with productivity. For the coffee grower, it is essential to characterize the growth pattern of the crop, since the management and production are related to its development over time. The non-linear regression models stands out among the models that can be used to model the growth. However, in order to obtain coherent estimates and thus to correctly model the growth pattern of the coffee tree, it should be considered that longitudinal data may present residual autocorrelation, and if this characteristic is not considered, the results and inferences can be compromised. The objectives of this study were: In the first chapter, present a summary on non-linear models and their main characteristics. In the second chapter to identify among Logistic, Brody, von Bertalanffy and Richards non-linear models that best describles the height growth pattern of irrigated and non-irrigated coffee plants over time, considering the residual autocorrelation, performing the estimation of the parameters by the method of least squares (classical approach). In the third chapter, we present the Bayesian nonlinear modeling of growth in height of irrigated and non-irrigated coffee plants, also considering the residual autocorrelation and Logistic, Brody, von Bertalanffy and Richards non-linear models. We also present a simulation study with the purpose of validating the weighted resampling method in the parameters estimation, considering a likelihood approximation as candidate distribution. In the results of chapter 2, we verified that among the studied models, the Brody model is the one that best represents the growth pattern of irrigated and non-irrigated coffee plants over time based on the criteria of residual standard deviation and Akaike’s information criterion. Among the results of chapter 3, we found that the high posterior density intervals obtained for all the parameters of the evaluated models, including the parameters of residual autocorrelation, contained the preestablished parametric values, validating the efficiency of the weighted resampling method for parameter estimation, considering as candidate distribution an approximation of likelihood. For non-irrigated system, the Bayesian information criterion and the criterion of ordered predictive density indicated, among the studied models, the Logistic model as the one that best describes the growth of the coffee plant height over time. In addition, for the irrigated system, the same criteria indicated the Brody model.