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Citation:

Multilevel Nonlinear Mixed-effects Basal Area Models for Individual Trees of Quercus mongolica

  • Received Date: 2014-01-28
  • Taking 10 111 Q. mongolica individuals obtained from 184 plots in Wangqing Forestry Bureau in Jilin Province as test materials, this study is to develop individual basal area increment model for Quercus mongolica Fisch by mixed effects model approach. The relationship between four dependent variables (the later diameter at breast height, the later basal area at breast height, the diameter increment and the basal area increment) and earlier stage diameter at breast height were analyzed using seven functions commonly used, i.e. linear function, Richards function, logistic function, exponential function etc. The best model was selected as the base model to develop mixed effects model. And then, the best combination form of formal parameters in the base model was determined with considering both the random effects of forest farms and the plot simultaneously. Forest variables contained in the formal parameters of the model were determined by stepwise regression method. Three kinds of residual variance functions (exponential function, power function and constant plus power function) that used to eliminate heteroskedasticity were analyzed and compared and the prediction efficiency of model was tested. The results are as follows. The Wykoff model that the dependent variable was later basal area at breast height had a better fit effect and used as the base model. In addition to the early diameter at breast height (D), the model included the stand variables, such as the tangent of slope (ST), the ratio of D of target tree to arithmetical mean diameter of plot (RAD), the total basal area of plots (TBA), the sum of basal area of trees with diameter larger than target tree (GSBA), the ratio of basal area of target tree to arithmetical mean basal area of plot (RABA) and the ratio of basal area of target to total basal area of plot (RBA), had a better prediction accuracy. For residual variance, the exponential function, power function and constant plus power function could eliminate the heteroskedasticity, but the power function was the best. The mixed effects model taking forest farm and plot effects into account has the highest prediction accuracy.
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Multilevel Nonlinear Mixed-effects Basal Area Models for Individual Trees of Quercus mongolica

  • 1. Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091, China

Abstract: Taking 10 111 Q. mongolica individuals obtained from 184 plots in Wangqing Forestry Bureau in Jilin Province as test materials, this study is to develop individual basal area increment model for Quercus mongolica Fisch by mixed effects model approach. The relationship between four dependent variables (the later diameter at breast height, the later basal area at breast height, the diameter increment and the basal area increment) and earlier stage diameter at breast height were analyzed using seven functions commonly used, i.e. linear function, Richards function, logistic function, exponential function etc. The best model was selected as the base model to develop mixed effects model. And then, the best combination form of formal parameters in the base model was determined with considering both the random effects of forest farms and the plot simultaneously. Forest variables contained in the formal parameters of the model were determined by stepwise regression method. Three kinds of residual variance functions (exponential function, power function and constant plus power function) that used to eliminate heteroskedasticity were analyzed and compared and the prediction efficiency of model was tested. The results are as follows. The Wykoff model that the dependent variable was later basal area at breast height had a better fit effect and used as the base model. In addition to the early diameter at breast height (D), the model included the stand variables, such as the tangent of slope (ST), the ratio of D of target tree to arithmetical mean diameter of plot (RAD), the total basal area of plots (TBA), the sum of basal area of trees with diameter larger than target tree (GSBA), the ratio of basal area of target tree to arithmetical mean basal area of plot (RABA) and the ratio of basal area of target to total basal area of plot (RBA), had a better prediction accuracy. For residual variance, the exponential function, power function and constant plus power function could eliminate the heteroskedasticity, but the power function was the best. The mixed effects model taking forest farm and plot effects into account has the highest prediction accuracy.

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