Multilevel nonlinear mixed-effects model and machine learning for predicting the volume of Eucalyptus spp. trees

Abstract

Volumetric equations is one of the main tools for quantifying forest stand production, and is the basis for sustainable management of forest plantations. This study aimed to assess the quality of the volumetric estimation of Eucalyptus spp. trees using a mixed-effects model, artificial neural network (ANN) and support-vector machine (SVM). The database was derived from a forest stand located in the municipalities of Bom Jardim de Minas, Lima Duarte and Arantina in Minas Gerais state, Brazil. The volume of 818 trees was accurately estimated using Smalian’s Formula. The Schumacher and Hall model was fitted by fixedeffects regression and by including multilevel random effects. The mixed model was fitted by adopting 14 different structures for the variance and covariance matrix. The best structure was selected based on the Akaike Information Criterion, Maximum Likelihood Ratio Test and Vuong’s Closeness Test. The SVM and ANN training process considered diameter at breast height and total tree height to be the independent variables. The techniques performed satisfactorily in modeling, with homogeneous distributions and low dispersion of residuals. The quality analysis criteria indicated the superior performance of the mixed model with a Huynh-Feldt structure of the variance and covariance matrix, which showed a decrease in mean relative error from 13.52% to 2.80%, whereas machine learning techniques had error values of 6.77% (SVM) and 5.81% (ANN). This study confirms that although fixed-effects models are widely used in the Brazilian forest sector, there are more effective methods for modeling dendrometric variables.