A Generalized Approach for Modeling and Localizing Stem Profile Curves
The Max and Burkhart segmented taper equation was fitted using nonlinear mixed-effects modeling techniques to account for within- and between-individual variation in loblolly pine (Pinus taeda L.) stem profiles. Within- and between-tree residual variances and spatial autocorrelation between residuals were incorporated in the model with an error variance function and a continuous autocorrelation structure, respectively. 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 an independent data set. Measures of precision and bias 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. The method can localize stem curves for trees growing under different site and management conditions. It also represents a general framework that can be applied to other taper equation forms, increasing their flexibility and efficiency in prediction for local conditions.