Improving taper equations of loblolly pine with crown dimensions in a mixed-effects modeling framework

A mixed-effects modeling framework was applied to Max and Burkhart's (1976) (MB) taper equation for loblolly pine (Pinus taeda L.). The advantages of such a strategy over ordinary least squares were: (1) more accurate specification of the correlation structure of the data and (2) the ability to assess the potentially explainable variation at the tree level. Significant relationships were established between tree-level crown dimensions and parameter estimates. The study data comprised 197 plantation-grown loblolly pine trees of 10 different ages in Uruguay. Four versions of MB were evaluated: (1) the original equation, (2) the original equation fitted with mixed effects, and two adapted versions: (3) the first included crown variables and fixed effects, (4) the second included crown variables and mixed effects. The crown variables were tree-level crown length and crown length ratio. The best of the four competing equations included both of the crown variables as well as tree-level random effects, suggesting that some linear tree-level variability may yet be explained by variables not considered in this study. Testing on an independent validation data set did not show over-fitting problems. For prediction purposes, the equations with added crown variables were more precise but not less biased.