Mixed-effects modeling for tree height prediction models of Oriental beech in the Hyrcanian forests

Height–diameter relationships are essential elements of forest assessment and modeling efforts. In this work, two linear and eighteen nonlinear height–diameter equations were evaluated to find a local model for Oriental beech (Fagus orientalis Lipsky) in the Hyrcanian Forest in Iran. The predictive performance of these models was first assessed by different evaluation criteria: adjusted R2 (Radj2), root mean square error (RMSE), relative RMSE (%RMSE), bias, and relative bias (%bias) criteria. The best model was selected for use as the base mixed-effects model. Random parameters for test plots were estimated with different tree selection options. Results show that the Chapman–Richards model had better predictive ability in terms of adj R2 (0.81), RMSE (3.7 m), %RMSE (12.9), bias (0.8), %Bias (2.79) than the other models. Furthermore, the calibration response, based on a selection of four trees from the sample plots, resulted in a reduction percentage for bias and RMSE of about 1.6–2.7%. Our results indicate that the calibrated model produced the most accurate results.