Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey

Height-diameter models were developed for Brutian pine (Pinus brutia Ten.) and Taurus cedar (Cedrus libani A. Rich.) in Turkey. A modified Chapman-Richards model that includes dominant height was used to predict tree height from diameter. Using the twofold evaluation scheme, five alternative modeling approaches were evaluated: (1) fixed-effects model, (2) calibrated fixed-effects model, (3) calibrated mixed-effects model, (4) three-quantile regression method, and (5) five-quantile regression method. Parameters of fixed-effects, mixed-effects and quantile regression models were calibrated by use of a subset of height measurements, ranging from 1 to 10 sample trees per plot. Evaluation statistics show that both quantile regression models produced similar results, and that the mixed-effects model approach yielded the best results in predicting tree heights. Model performance improved with increasing sample size; but gains in performance generally increased at a decreasing rate. A sample size of four trees per plot appears to be a good compromise between sampling cost and predictive accuracy and precision.