Development of a stem taper function using mixed-effects models for Pinus sylvestris in Turkey: selection of fixed parameters to expand

Abstract

Stem taper functions predict diameter variation along the tree stem, enabling to estimate merchantable volume according to market requirements. In this study, a stem taper function for Pinus sylvestris in Turkey was developed using the mixed-effects modelling approach, which allows some parameters to include a fixed part (common to the whole population) and a random effect (individual-specific response). We analyzed different strategies to choose the best combination of fixed parameters to expand with random effects (mixed-effects parameters): (1) expanding fixed parameters that presented the highest variability and (2) all possible combinations of one and two mixed-effects parameters; the best performance was observed in the latter. Given that inclusion of random effects was not enough to account for the existing correlation between the residuals of the same individual, the variance-covariance matrix of the error term was modelled by a first-order autoregressive structure. In addition, we evaluated the response obtained by calibration (estimation of random effects for a new individual), i.e. using a diameter measured at different heights along the stem. The selected mixed-effects model presented the best results both in the fitting and calibration steps. Generally, the mixed-effects model is recommended if an additional stem diameter measurement at 40-90 % of the total tree height is available. Otherwise, and from a predictive point of view, the model fitted by non-linear ordinary least squares is recommended, which only considers fixed parameters.