Open AccessTHE USE OF CONTRASTS IN MULTIVARIATE NONLINEAR MIXED MODELS TO COMPARE TREATMENTS IN LONGITUDINAL FACTORIAL EXPERIMENTS
Author(s) -
Lídia Raquel de Carvalho,
Martha Maria Mischan,
José Raimundo de Souza Passos,
Sheila Zambello de Pinho
Publication year - 2018
Publication title -
revista de matemática e estatística
Language(s) - English
Resource type - Journals
eISSN - 1980-4245
pISSN - 0102-0811
DOI - 10.28951/rbb.v36i4.314
Subject(s) - mathematics , bivariate analysis , statistics , gompertz function , mixed model , factorial , multivariate statistics , context (archaeology) , inflection point , factorial experiment , covariate , nonlinear system , asymptote , econometrics , bivariate data , mathematical analysis , paleontology , physics , geometry , quantum mechanics , biology
The purpose of this study was to establish contrasts in multivariate nonlinear mixed models to verify the effects of treatments in experiments with longitudinal data and multiple responses. The evaluated nonlinear functions were the three parameters curves logistic, Gompertz and von Bertalanffy. The random variables were added to the fixed parameters, asymptote α , abscissa of the inflection point β, and parameter γ. The best fitted model was expanded with covariates, which establish orthogonal contrasts, in order to verify main effects and interactions in factorial experiments. The methodology was applied to analyse data of an experiment with citrus, in which case the logistic bivariate mixed effects model was the best fit. The chosen model allowed comparisons between treatments in a global context of more than one dependent variable and throughout the measurement period.