Modelling longitudinal proportion data from successful grafting on Camu-Camu

Silvano Cesar da COSTA[1]

Clarice Garcia Borges DEMÉTRIO[2]

Eduardo SUGUINO[3]

Suely Ruiz GIOLO[4]

§    ABSTRACT: Proportion data are very common in several research areas, specially in agriculture. The standard distribution used for analysing this kind of data is the binomial distribution, a particular case of generalized linear models (McCullagh e Nelder, 1989; Demétrio, 2001). In this paper repeated proportion data over time are analysed using four models. The first model is a logistic split-plot in time while the second incorporates a heterogeneity factor in the variance function to account for (under) overdispersion. The third one is a logistic model with an AR(1) correlation structure which is incorporated in the variance-covariance matrix using generalized estimating equations. In the last model the correlation existing over time is incorporated by means of a latent variable, assumed to have a priori distribution, and the individual variability is modelled with a heterogeneity factor in the variance function estimated from the logistic split-plot in a time model. The methodology is applied to a data set obtained from an experiment with Camu-Camu, the major source of vitamin C in Brazil. The plants were collected from low and flat lands alongside a watercourse located in the North of Brazil. The aim of the experiment was to evaluate grafting methods and understock types to be used for propagating the plant in dry lands.

§    KEYWORDS: Generalized linear models, generalized estimating equations; longitudinal analysis; random effects; generalized linear mixed models.



[1] Departamento de Estatística e Matemática Aplicada, Universidade Estadual de Londrina - UEL, CEP: 86051-990, Londrina, PR, Brasil.

[2] Departamento de Ciências Exatas, Escola Superior de Agricultura Luiz de Queiroz - ESALQ, Universidade de São Paulo - USP, CEP 13418-900, Piracicaba, SP, Brasil.

[3] Departamento de Produção Vegetal, Escola Superior de Agricultura Luiz de Queiroz - ESALQ, Universidade de São Paulo - USP, CEP 13418-900, Piracicaba, SP, Brasil.

[4] Departamento de Estatística, Universidade Federal do Paraná - UFPR, CEP 81531-990, Curitiba, PR, Brasil.