Application of Additive Mixed Effects Models to Study the Stem Radial Growth of Eucalyptus Tree

Abstract

Classical techniques such as simple and multiple parametric regression analyses assume the linearity of the relationship between the response and independent variables. Moreover, these classical techniques rely on the rigid assumptions of constant variance and the independent and identical distributions of the error terms. Consequently, a consideration of a more flexible approach can greatly influence the accuracy of our analysis. The objectives of this study are to evaluate and suggest an alternative approach to the classical parametric methods. The stem radius data obtained from Sappi landholdings in eastern South Africa were used. The stem radius of two hybrid clones, namely Eucalyptus Grandis × Eucalyptus urophylla and E. Grandis × E. Camaldulensis clone was used as the response variable. An additive mixed-effects model that incorporates a non-parametric smooth function is used. Different additive mixed models were fitted to show the functional relationship between stem radius and tree age. The relationship between stem radius and tree age depends on clone and season. This study suggests a semi-parametric approach as an alternative to the usual parametric approaches especially when the functional relationship between the response and the covariate is not known.