The comparison of the Bayesian method with the classical methods in modeling crown width for Prince Rupprecht larch in northern China

Abstract

Crown width (CW) is a significant variable of tree growth, but measuring crown width is laborious and time-consuming. Diameter at breast height (D) is a commonly used growth variable in crown width prediction. Here, a CW-D model was developed to estimate the crown width of larch.The data of 1,515 larch trees were collected in Guandi mountain, the northern China. We chose linear function, quadratic function, and other form of base functions to develop the CW models, and we introduced non-linear least squares techniques (NLS), non-linear mixed-effect (NLME), and Bayesian method in modeling process. Because the data was from different plot, we added a plot level random effect in NLME method to predict the effect from environment. For equally comparing the Bayesian method with the NLME, we also added the plot level random effect to the Bayesian MCMC procedure. We selected Akaike's information criterion and logarithm likelihood to evaluate NLS and NLME models, and chose deviance information criterion and stationary test to test Bayesian method. These methods had another three same indicators (the determination coefficient, root mean square error, and mean absolute deviation) in model evaluation.Heteroskedasticity wasn't occurred in this study. The model I.2 (quadratic formula) showed a best fitting effect in each method, and Bayesian method with random effect was slightly superior than other methods. Therefore, the selected final model was quadratic function by Bayesian method with plot level random effect, this combination had the highest prediction accuracy in the larch trees' crown width estimation of Guandi mountain.