First-order branch number simulation for Larix olgensis plantation through Poisson regression mixed effect model

In this study, the generalized linear mixed model was used to study the distribution of number of first-order branch for planted Larix olgensis trees. The modeling data were based on 596 first-order branches of 49 branch analysis trees selected from 7 permanent sample plots in Larix olgensis plantation from Mengjiagang Forest Farm, Jiamusi City, Heilongjiang Province of northeastern China. Poisson model was introduced to develop the optimal basic model with the PROC GLIMMIX procedure of SAS. Considering the different tree effects, the generalized linear mixed model of number of first-order branch per 0.5 m was developed on the selected optimal basic model. AIC, BIC, -2log likelihood and LRT test were selected to compare the goodness-of-fit statistics of the models. The results showed that all of the convergence mixed models with the combination of random coefficients fitted better than the basic model. Finally, the one with three random coefficients (including DINC, LnRDINC, RDINC²) was selected as the optimal mixed model to describe the distribution of number of first-order branch per 0.5 m for planted Larix olgensis trees. In this model, the parameter values for LnRDINC and CL were positive; the ones for DINC, RDINC², HT/DBH, DBH were negative. Moreover, there was a peak value for the number of first-order branch per 0.5 m. The fitting result of model showed that the coefficient of determination (R²) was 0.669 and the mean absolute error was 2.250 and the root mean square error was 3.012. All in all, not only could the mixed model describe the mean trend of the branch distribution, but also it reflected the differences among sample trees. It was shown that the generalized linear mixed model could improve the simulation accuracy of the model. As a result, the optimal mixed model would be suitable for predicting the first-order branch quantity and will provide theoretic basis to modeling crown architecture and three-dimension visualization for Larix olgensis plantation.