Developent of stem taper equation using nonlinear mixed-effects modeling approach for Taurus fir

The Max and Burkhart segmented taper equation was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual variation in Taurus fir (Abies cilicica Carr.) stem profiles. Totally 327 sample trees measured and about 60% (203 trees) of the trees were randomly selected for model development and the reminder 40% (124 trees) of the trees used for model validation. Based on goodness-of-fit criteria, the model including three random-effects parameters β1, β3, and β4 was the best. An error variance function and a continuous auto correlation structure incorporated in model to within and between-tree residual variances and spatial autocorrelation between residuals. However, most of the residual autocorrelation was accounted for by including random effects. Upper stem diameter measurements were used to estimate random effects parameters using an approximate Bayesian estimator, which localized stem profile curves for individual trees. The procedure was tested with a validation data set. The goodness-of-fit statistics (Bias, precision, and RMSE) showed that upper stem diameter measurements and subsequent estimates of random effects improved the predictive capability of the taper equation mainly in the lower portion of the bole. Accordingly results of this research, there is no big differences between one and two additional upper stem diameter measurements for predictive capability of model. The method can localize stem curves for trees growing under different site and management conditions in natural Taurus fir stands. The results of this study support previous findings that mixed-effect modeling approach increases flexibility and efficiency of taper equations for upper stem diameter prediction