Aplicação de modelos lineares mistos com regressão quantílica na projeção do crescimento e produção de Eucalyptus spp.

Abstract

The correct inference of growth and forest production are important factors for decision making in planning, with different models based on regression statistics. These models are used to determine the technical and economic age of the cut, to generate production tables for the stands and growth curves. Due to its importance and the search for more accurate estimates, the development of more complex models has been applied in the forestry sector, among which we can mention the mixed modeling and the use of quantile regression. The aim of this work was to evaluate the use of a new technique using linear mixed models with quantile regression in the projection of growth and production in an eucalyptus stand and also to compare the volumetric estimates with those obtained by the traditional Clutter model and mixed modelling. The data came from a clonal Eucalytpus spp. stand, located in the interior of São Paulo state, aged between 24 and 64 months. Adjustments to the equations of the Clutter model, as well as the mixed-effect models and the linear mixed-effect models with quantile regression, as well as the linear mixed model with quantile regression and mixed-effect models were performed using the statistical software R. To check the accuracy of the methods, the last measurement was selected as a reference and, based on this, classes of projection periods were created at 12-month intervals, which are: (6,18], (18,30] and (30,42] months. The evaluation was carried out through the residual plot, as well as through the square root of the average error (RMSE %). It was found that the mixed model and linear mixed model with quantile regression obtained a lower RMSE of 3.94% and 4.20%, respectively, for (6,18] month class. For the classes (18.30] and (30.42) months, the traditional Clutter model that presented lower values of RMSE, being 4.28% and 4.75%, respectively. After the analyzes were carried out, it was defined that for the class of (6,18) months the use of the linear mixed model with quantile regression due to the RMSE is indicated and also present the best dispersion of the residues. For the classes (18,30] months, despite the traditional Clutter model presenting the lowest RMSE, after analyzing the dispersion of the residues it was found that the use of the mixed model is the most suitable due to better dispersion, and for the class of ( 30,42] months, the traditional model of Clutter is the most suitable.