Efficiency of nonlinear mixed-effects model in determining height-diameter equations of velvet maple and ironwood trees

Document Type : Research Paper


1 M.Sc. Student, Faculty of Forest Sciences, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, I. R. Iran

2 Assistant Prof., Faculty of Forest Science, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, I. R. Iran.

3 Prof., Faculty of Forest Sciences, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, I. R. Iran

4 Associate Prof., Faculty of Forest Sciences, Gorgan University of Agricultural Sciences and Natural Resources, Gorgan, I. R. Iran

5 Assistant Prof., Faculty of agriculture, Shiraz university, Shiraz, I. R. Iran.



The aim of this study was to develop a mixed-effects model and compare it with nonlinear models for estimating the heights of velvet maple and ironwood trees in the uneven-aged, mixed Shast-kalateh forests of Gorgan. We applied a systematic sampling method to collect field data within a 150×200 m network, comprising of 308 circular sample plots, and measured the height, diameter at breast height (DBH), and tree species in each plot. Model fitting was done in two stages: In the first stage, we used a fixed-effect approach to select candidate models, where height was the dependent variable and DBH was the independent variable. In the second stage, the dominant height, mean DBH, basal area, basal area of trees larger than the desired tree, tree density, and volume of trees were refitted using a mixed-effect approach. We used adjusted coefficient of determination and root mean square error to assess the models. The results of fitting nonlinear models for velvet maple species showed that the Curtis and Michailief models with R2 values of 0.74 and the lowest RMSE values of 3.43 and 3.24, respectively, were the best models. For ironwood trees, the Nassland and Michailoff models with R2 values of 0.42 and the RMSE values of 2.92 and 2.91 m were selected as the best models. The results of fitting the nonlinear mixed-effect model showed that compared to the nonlinear models, the R2 values for velvet maple and ironwood species increased by 20% and 23%, respectively, and the RMSE improved to 1.75 m for velvet maple and 0.45 m for ironwood.

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Volume 14, Issue 4
February 2023
Pages 473-485
  • Receive Date: 20 December 2021
  • Revise Date: 12 April 2022
  • Accept Date: 04 June 2022
  • First Publish Date: 20 February 2023