Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.