Modelo de regressão não linear misto para a descrição do crescimento vegetativo do cafeeiro

Abstract

In this study, we model the growth in height of coffee plants using mixed models. We tested the Logistic and Gompertz models with different structures for the variance-covariance matrix of the random effects, as well as the need for random effects in the parameters and for modeling the heterogeneity of variance and autocorrelation of the experimental errors. Finally, the parameter estimates of the best models were compared between experimental treatments, and with those obtained by the usual nonlinear fixed model. The data came from an experiment implemented at the Department of Engineering of Universidade Federal de Lavras - UFLA, in Lavras, Minas Gerais, Brazil. The experiment was implemented in March 1999, using the coffee cultivar (Coffea arabica L.) Rubi. From that date, twenty measures of the height of plants were collected once about every three months. A completely randomized block designed experimented was carried out using three replicates and six treatments, the latter corresponding to water depths applied as irrigation. We observed that the nonlinear mixed modeling approach is a powerful tool to study coffee height growth of the Rubi cultivar, resulting in more reliable and accurate estimates than those obtained from usual nonlinear models. The use of design effect in the logistic models and the inclusion of random effect on all parameters of both logistic and Gompertz models have led to good parameters estimates. We also observed that the unstructured variance-covariance matrix have led to the best results while modeling the random effects, given the lower standard error of estimates and lower values of AIC and BIC. We recommend the Logistic model with random effects in all parameters, unstructured variancecovariance matrix for the random effects and modeling of variance heterogeneity through the varPower function of the R nlme package, as well as the design effect in the model parameters. We also recommend the Gompertz model with random effects in all parameters, unstructured variance-covariance matrix for random effects, checking the need for modeling intra-individual variance and autocorrelation over time.