Abstract
A nonlinear mixed-effects modeling approach was used to model individual tree diameter increment based on Logistic growth function for dahurian larch (Larix gmelinii Rupr.) plantations in northeastern China. The study involved the estimation of fixed and random parameters, as well as procedures for determining random effects variance-covariance matrices. Results showed that the mixed-effects model provided better model fitting than the fixed-effects model. The logistic model with three random parameters b<sub>1</sub>, b<sub>2</sub>, b<sub>3</sub> was considered the best mixed model. Time series correlation structures included Autoregressive correlation structure AR (1) and AR (2), Moving Average correlation structure MA (1) and MA (2) and Autoregressive-Moving Average correlation structure [ARMA (1, 1)] and ARMA (2, 2) were incorporated into the best mixed model. The mixed model with MA (2) correlation structure showed lower AIC and BIC values and significantly improved model performance (LRT = 545.6, p<0.0001). Techniques for calibrating the diameter growth model for a particular tree of interest were also explored. The results indicated that the mixed-effects model provided better diameter predictions than the models using only fixed-effects parameters.
Highlights
Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular (Wolfinger, 1999). These models have a wide variety of applications in many areas such as agriculture, forestry, biology, ecology, biomedicine, sociology, economics, pharmacokinetics and other areas (Pinheiro and Bates, 1998)
A number of growth functions have been used for modeling tree growth variables (Huang and Titus, 1995; Colbert et al, 2002)
Tree diameter increment data are generally taken from trees growing in plots located in different stands. This hierarchical structure results in a lack of independence between observations, which results in biased estimates for the confidence interval of the parameters if ordinary least squares regression techniques are used. To deal with this problem, mixed model approaches have been used in tree growth modeling (Fang and Bailey, 2001; Jiang and Li, 2008, 2010; Gregoire and Schabenberger, 1996)
Summary
Statistical models in which both fixed and random effects enter nonlinearly are becoming increasingly popular (Wolfinger, 1999). Tree diameter increment data are generally taken from trees growing in plots located in different stands This hierarchical structure results in a lack of independence between observations, which results in biased estimates for the confidence interval of the parameters if ordinary least squares regression techniques are used. To deal with this problem, mixed model approaches have been used in tree growth modeling (Fang and Bailey, 2001; Jiang and Li, 2008, 2010; Gregoire and Schabenberger, 1996). Evaluate the predictability of the mixed-effects model based on the calibration
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