Fitting Logistic Growth Curve with Nonlinear Mixed-effects Models

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 b1, b2, b3 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.