FITTING AND CALIBRATING A MIXED-EFFECTS SEGMENTED TAPER MODEL FOR BRUTIAN PINE

ABSTRACT Taper models are one of several necessary tools in modern forest inventory, giving information on diameter at any point along the tree stem and this information can also be used to estimate stem volume. In this study, we used nonlinear mixed-effects (NLME) modeling approach to minimize existing statistical problems in constructing taper equations. A segmented taper model of Max and Burkhart (1976) was fitted using this approach to consider for within- and between-tree variation in brutian pine (Pinus brutia Ten.) stem taper. Based on evaluation statistics, the model including random-effects parameters β 1, β 3 and β 4 were found to be the best. Inclusion of random parameters were not completely eliminated heterogenous variance and autocorrelation in residuals. Incorporating variance function and a continuous autoregressive error structure (CAR(1)) to NLME Max and Burkhart model removed the heteroscedasticity and autocorrelation in residuals. Upper stem diameters were used to localized stem taper model to individual tree. For this, two different measurement scenarios were evaluated as one and two upper stem diameter measurements. Inclusion of random parameters were improved the predictive capability of taper model in particularly the middle and lower sections of stem based on upper stem diameter measurements. The calibration using upper stem diameter measurements can improve the tree-level accuracy of stem taper model is therefore recommended.