Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain

An individual-tree height–diameter model was developed for stone pine (Pinus pinea L.) in Spain. Five biparametric nonlinear equations were fitted and evaluated based on a data set consisting of 8614 trees from 455 plots located in the four most important regions where the species occurs in Spain. Because of the problem of high correlation among observations taken from the same sampling unit, a mixed-model approach, including random coefficients, is proposed. Several stand variables, such as density, dominant height, or diametric distribution percentiles, were included in the model as covariates to explain among plot variability. To determine interregional variability among the regions studied, regional effects were included in the model using fixed dummy variables. Two models, one for inland regions and one for coastal regions, were found to be sufficient to explain regional variability in the height–diameter relationship for the species in Spain. Mixed models allow predictive role in two ways: a typical response, including only fixed effects, and a calibrated response, where random effects are predicted and included in the model from the prior measurement of the height in a subsample of trees. Different alternatives were tested to determine optimum subsample size. Measurement of the height of the 20% largest trees in the plot has been shown to be a useful approach.