Prediction of tree diameter growth using quantile regression and mixed-effects models

• Future tree diameters were predicted from past diameters by localizing a mixed-effects model.
• A second approach involved the use of a set of quantile regression models.
• Quantile regression based on three quantiles was deemed adequate in predicting diameter growth.
• Results for mixed-effects and quantile regression models were similar, but mixed model was less biased.

A tree diameter growth function is an important component of an individual-tree model. This function can be considered as a mixed-effects model, in which a diameter measurement can be used to calibrate (or localize) the equation to produce improved diameter predictions for the same tree in the future. Another approach considered in this study involved a system of quantile regressions, in which future diameters can be determined through interpolation, based on a current diameter measurement. The aim of this study was to evaluate the use of quantile regression and mixed-effects models in predicting tree diameter growth. Tree diameter at the end of each growth period was predicted from diameter at the beginning of the period by use of one of the four methods: the mixed-effects model and three quantile regression methods that were based on nine quantiles, five quantiles, and three quantiles. The mixed-effects model performed as well as the three quantile regression methods, based on the mean absolute difference and fit index, but was far superior in terms of the mean difference. The mixed-effects model produced an unbiased prediction of future diameter, up to ten years into the future, when calibrated with a current diameter measurement.