GAMLSS Modeling on stem taper of Tectona grandis L.f

Abstract

In this study we propose GAMLSS to fit  taper functions. We measured 52 Tectona grandis trees for fiting of the 5^th degree polynomial by multiple linear regression and by the theory of generalized additive model for location, scale and shape (GAMLSS). The goodness of fit was determined by the statistics: squared coefficient of correlation (R²), standard error of the estimate (S_yx and S_yx(%)), Akaike information criterion (AIC), worm plot, quantile-quantile plots, residual dispersion and statistics Deviation (Bias), Root Sum Squared Residues (RMSE) and Percentage Residues (RP). Pre-established assortment sections were assessed by numeric integrals in both adjustment methods, as well as volume and height for a given diameter of each assortment section. The classic linear model was more efficient according to R², S_yx and S_yx(%). However, the GAMLSS model was more efficient according to AIC, auxiliary statistics and graphical analysis of residuals. Assessing the practical effect of the different methods, we verified no differences in the classification of the products, morever, the volume obtained from the classic linear model was 5.47% greater in relation to the GAMLSS for the first product and the heights occurrence of diameters reached up to 37 cm. The  GAMLSS model, in general, presented diameter estimates with greater efficiency in estimating the actual values.