FITTING AND SELECTING TRADITIONAL MODELS FOR TREE’S HEIGHT TIME SERIES DATA

Abstract

Mesuring trees' height is very importance for planning forest production. Usually, it is accomplished through samplings due to the size of the populations and the size of the trees themselves. Measurements along time form a time series data with some problems for the adjustment of equations to describe its growth. Several models were developed with that purpose. The equations used in this paper were linear, logarithmic, and non-linear models. The statistics used for comparison of those models were the determination coefficient (R²), Cp of Mallows, Akaike's information criterion (AIC), Schwarz's Bayesian criterion (SBC/BIC), squared mean of residues and the graphic analysis of residues. The objective of this work was to develop an example of adjustment of growth equations for height, to demonstrate which one adapts better to the population data and to determine which selection criteria have more relationship with the better true model. To do so, a sample of 64 trees was used, submitted to the trunk analysis, from a population of 531 trees of Pinus elliottii Engelm. The statistics of the sample were compared to the statistics of the population, demonstrating which model describes better the data of the population. Quality of the adjustment to the population's data of each model was evaluated through the Chi-square test and graphic analysis of residues. The Akaike's information criterion (AIC) was appropriated to select models for the data. The two better equations were h=b₀+b₁.t+b₂.t⁵ and Chapman-Richards' growth model, which showed no significant differences for the chosen criteria in this study. In this sense, the Akaike's information criterion (AIC) calculated to the sample data showed efficiency as an equations' selection criterion to describe the height of the trees along the time for the population used in this study. The generability, calculated by Qui-square test, in relation to the population, didn't show significant difference between models 3 and 9. Final selection, using the qualitative criteria of connection of the model to the studied process, its interpretability and comprehensibility, determined the choice of the Chapman-Richards' model as the best to describe the height growth for the studied trees.