A generalized height–diameter model including random components for radiata pine plantations in northwestern Spain

A generalized height–diameter (h–d) model based on Schnute's function was developed for radiata pine (Pinus radiata D. Don) plantations in Galicia (northwestern Spain). The study involved the estimation of fixed and random parameters by mixed-model techniques. The hierarchical structure of the data set, trees within plots, justifies the application of mixed-effects modelling. Techniques for calibrating the generalized height–diameter model for a particular plot of interest were also applied. For the experimental data analyzed, calibration can be used to obtain h–d relationships tailored to individual plots after measuring the height of only the three smallest trees in a plot. The main reason for the high predictive ability using this subsample of trees is that the dominant height of each plot was already considered as a fixed-effect in the height–diameter model formulation; therefore, heights corresponding to the largest trees did not provide much more additional information for calibrations. The model also included an unstructured random component to mimic the observed natural variability in heights within diameter classes for the same plot. This is an important aspect because the model will be applied to fill in the missing height measurements, subsequently used for assessing variables (e.g., volume, biomass, etc.) that depend on the estimated heights.