Mixed effect models for predicting breast height diameter from stump diameter of Oriental beech in Göldağ

Diameter at breast height (DBH) is the simplest, most common and most important tree dimension in forest inventory and is closely correlated with wood volume, height and biomass. In this study, a number of linear and nonlinear models predicting diameter at breast height from stump diameter were developed and evaluated for Oriental beech (Fagus orientalisLipsky) stands located in the forest region of Ayancık, in the northeast of Turkey. A set of 1,501 pairs of diameter at breast height-stump measurements, originating from 70 sample plots of even-aged Oriental beech stands, were used in this study. About 80 % of the otal data (1,160 trees in 55 sample plots) was used to fit a number of linear and nonlinear model parameters; the remaining 341 trees in 15 sample plots were randomly reserved for model validation and calibration response. The power model data set was found to produce the most satisfactory fits with the Adjusted Coefficient of Determination, R2adj (0.990), Root Mean Square Error, RMSE (1.25), Akaike’s Information Criterion, AIC (3820.5), Schwarz’s Bayesian Information Criterion, BIC (3837.2), and Absolute Bias (1.25). The nonlinear mixed-effect modeling approach for power model with R2adj(0.993), AIC (3598), BIC (3610.1), Absolute Bias (0.73) and RMSE (1.04) provided much better fitting and precise predictions for DBH from stump diameter than the conventional nonlinear fixed effect model structures for this model. The calibration response including tree DBH and stump diameter measurements of the four largest trees in a calibrated sample plot in calibration produced the highest Bias, -5.31 %, and RMSE, -6.30 %, the greatest reduction percentage