Modeling Branch Diameter with Linear Mixed Effects for Dahurian Larch

JIANG Li-chun; LI Feng-ri; ZHANG Rui

In this study, based on the data of 2190 branch diameter samples of 30 trees from Dahurian larch (Larix gmelini Rupr.) plantations located in Wuying Forest Bureau in Heilongjiang Province, the stepwise regression techniques were used to develop a branch diameter model: BD=b1+b2DINC+b3DINC2+b4DBH·DINC2. The developed model was 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 indicated that the branch diameter model with parameters b1, b2, b3as mixed effects showed the best performance. Exponential and power functions were incorporated into the mixed branch diameter model. The addition of the power function significantly improved the mixed-effects model. The plots of residuals indicated that the mixed-effects model with power function showed more homogeneous residual variance than the mixed-effects model. Branch diameters increased with the depth into crown (DINC) increasing for trees with similar DBH. Branch diameters increased with the DBH increasing for different trees. DBH is adequate variable of tree for describing branch diameter variations with different trees. Branch diameters can be predicted from the measurement of some tree-level variables without detailed knowledge of the stand history for Dahurian larch plantations.

1. College of Forestry, Northeast Forestry University, Harbin 150040,Heilongjiang, China

Received Date: 2011-06-10

Available Online: 2012-08-20

Abstract: In this study, based on the data of 2190 branch diameter samples of 30 trees from Dahurian larch (Larix gmelini Rupr.) plantations located in Wuying Forest Bureau in Heilongjiang Province, the stepwise regression techniques were used to develop a branch diameter model: BD=b1+b2DINC+b3DINC2+b4DBH·DINC2. The developed model was 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 indicated that the branch diameter model with parameters b1, b2, b3as mixed effects showed the best performance. Exponential and power functions were incorporated into the mixed branch diameter model. The addition of the power function significantly improved the mixed-effects model. The plots of residuals indicated that the mixed-effects model with power function showed more homogeneous residual variance than the mixed-effects model. Branch diameters increased with the depth into crown (DINC) increasing for trees with similar DBH. Branch diameters increased with the DBH increasing for different trees. DBH is adequate variable of tree for describing branch diameter variations with different trees. Branch diameters can be predicted from the measurement of some tree-level variables without detailed knowledge of the stand history for Dahurian larch plantations.

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Reference (18)

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Modeling Branch Diameter with Linear Mixed Effects for Dahurian Larch

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