Modeling Branch Length and Branch Angle with Linear Mixed Effects for Dahurian Larch

In this study,the sample data was based on 2 190 branch length and angle samples of 30 trees from dahurian larch（Larix gmeiinii） plantations located in Wuying Forest Bureau in Heilongjiang Province.The stepwise regression techniques were used to develop branch length and branch angle models:BL= b1 + b2 DINC + b3 DINC2 + b4 DBH·DINC2,BA = b1 + b2 DINC + b3 DINC2 + b4 DBH·DINC.Then,the developed models were fitted using linear mixed-effects modeling approach based on LME procedure of S-PLUS software.Evaluation statistics,such as AIC,BIC, Log Likelihood and Likelihood ratio test were used for model comparisons.The results showed that the branch length and branch angle models with parameters b1,b2,b3 as mixed effects showed the best performance.Exponential and power functions were incorporated into mixed branch length and branch angle model.The addition of the exponential and power functions significantly improved the mixed-effects model.The plots of standardized residuals indicated that the mixed-effect model with exponential and power functions showed more homogeneous residual variance than the mixed-effects model.Validation confirmed that the mixed model with calibration of random parameters could provide more accurate and precise prediction.Therefore,the application of mixed model not only showed the mean trends of branch length and branch angle,but also showed the individual difference based on variance-covariance structure.