Multilevel nonlinear mixed-effects models for the modeling of earlywood and latewood microfibril angle

Abstract

Earlywood and latewood microfibril angle (MFA) was determined at 1-millimeter intervals from disks at 1.4 meters, then at 3-meter intervals to a height of 13.7 meters, from 18 loblolly pine (Pinus taeda L.) trees grown in southeastern Texas. A modified three-parameter logistic function with mixed effects is used for modeling earlywood and latewood MFA. By making the parameters of the logistic function linear functions of height, a three-dimensional model was developed that describes the changes of earlywood and latewood MFA within the tree. A first-order autoregressive correlation structure and a variance model corresponding to a variance covariate given by the fitted values for each wood type, but in which the proportionality constant differs according to the level of wood type, was identified as the within-group correlation and variance structures. Cross-validation was used to determine model accuracy and precision. The methods of model development including determination of the height structure, which parameters should be considered random or fixed, determination of an appropriate variance-covariance structure, and prediction are addressed. Model performance was evaluated utilizing informative statistics including likelihood ratio tests (LRTs), Akaike information criterion (AIC), and Bayesian information criterion (BIC). Copyright © 2005 by the Society of American Foresters.