Application of Nonlinear Mixed-Effects Modeling Approach in Tree Height Prediction

A nonlinear mixed-effects modeling approach was used to model the individual tree height–diameter relationship based on Chapman-Richards 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 to reduce the number of the parameters in the model. The mixed-effects model provided better model fitting and more precise estimations than the fixed-effects model. Techniques for calibrating the height-diameter model for a particular plot of interest were also explored. The greatest reductions in bias and root mean square error (RMSE) were obtained when comparing the calibration from one randomly selected tree with the calibration from two randomly selected trees. Substantial reductions were obtained with the inclusion of two randomly selected trees, which could reduce the bias and RMSE of the predictions by almost 73% and 63%, respectively. An important characteristic of mixed-effects models is that they permit both mean response prediction and calibrated prediction. The fixedeffects parameters alone can be used to obtain the mean response prediction. More accurate estimates can be obtained by calibration for individual prediction.