Modeling stem profile of caucasian fir and oriental spruce mixed stands in Turkey using nonlinear mixed-effects models

Abstract

The objective of this study is to develop segmented polynomial taper equations using the nonlinear mixed-effects modeling approach for Caucasian fir (Abies nordmanniana (Steven) Spach. subsp. nordmanniana) - Oriental spruce (Picea orientalis (L.) Link.) mixed stands in Artvin-Ardanuc region of Turkey. For this purpose, the data obtained from 213 felled sample trees in total, which are 107 fir and 106 spruce, were used. Jiang et al.'s (2005) stem profile model produced the best prediction results for both tree species. The R-adj(2), RMSE, (E) over bar, MAE, AIC and BIC values of the model were found as 98.7% and 98.3%, 1.700 and 1.814 cm, 0.143 and 0.167 cm, 1.179 and 1.269 cm, 4142.2 and 3951.7, 4148.5 and 3957.8 for fir and spruce, respectively. Based on AIC, BIC and -2LnL criteria, the model including random-effects in two parameters (b(3) and b(4)) were the best for both tree species. This mixed-effects model with two random parameters showed homogeneous residual variance and autocorrelation was almost removed. Mixed-effects models provided much better fits than their fixed model counterparts for both species. In addition, among 12 different calibration choices, the best results were obtained with the choice involving the measurement of five diameters that divide the sample tree measurements into two equal parts for fir and of four diameters that bottom of the sample tree for spruce.