J. For. Sci., 2012, 58(3):101-115 | DOI: 10.17221/69/2011-JFS

Using linear mixed model and dummy variable model approaches to construct compatible single-tree biomass equations at different scales - A case study for Masson pine in Southern China

L.Y. Fu1, W.S. Zeng2, S.Z. Tang1, R.P. Sharma3, H.K. Li1
1 Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing, China
2 Academy of Forest Inventory and Planning, State Forestry Administration, Beijing, China
3 Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, Ås, Norway

The estimation of forest biomass is important for practical issues and scientific purposes in forestry. The estimation of forest biomass on a large-scale level would be merely possible with the application of generalized single-tree biomass models. The aboveground biomass data on Masson pine (Pinus massoniana) from nine provinces in southern China were used to develop generalized single-tree biomass models using both linear mixed model and dummy variable model methods. An allometric function requiring only diameter at breast height was used as a base model for this purpose. The results showed that the aboveground biomass estimates of individual trees with identical diameters were different among the forest origins (natural and planted) and geographic regions (provinces). The linear mixed model with random effect parameters and dummy model with site-specific (local) parameters showed better fit and prediction performance than the population average model. The linear mixed model appears more flexible than the dummy variable model for the construction of generalized single-tree biomass models or compatible biomass models at different scales. The linear mixed model method can also be applied to develop other types of generalized single-tree models such as basal area growth and volume models.

Keywords: aboveground biomass; dummy variable model; linear mixed model; Pinus massoniana

Published: March 31, 2012  Show citation

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Fu LY, Zeng WS, Tang SZ, Sharma RP, Li HK. Using linear mixed model and dummy variable model approaches to construct compatible single-tree biomass equations at different scales - A case study for Masson pine in Southern China. J. For. Sci.. 2012;58(3):101-115. doi: 10.17221/69/2011-JFS.
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    References

    1. Baskerville G.L. (1972): Use of logarithmic regression in the estimation of plant biomass. Canadian Journal of Forest Research, 2: 49-53. Go to original source...
    2. Case B., Hall R.J. (2008): Assessing prediction errors of generalized tree biomass and volume equations for the boreal forest region of west-central Canada. Canadian Journal of Forest Research, 38: 878-889. Go to original source...
    3. Chojnacky D.C. (2002): Allometric scaling theory applied to FIA biomass estimation. In: McRoberts R.E., Reams G.A., Van Deusen P.C., Moser J.W. (eds): Proceedings of 3rd Annual Forest Inventory and Analysis Symposium. Traverse City, 17.-19. October 2001. St. Paul, North Central Research Station, Forest Service USDA, General Technical Report NC-230: 96-102.
    4. FAO (2006): Global Forest Resources Assessment 2005: Progress Towards Sustainable Forest Management. FAO Forestry Paper 147. Rome, Food and Agriculture Organization of the United Nations.
    5. Fehrmann L., Lehtonen A., Kleinn C., Tomppo R. (2008): Comparison of linear and mixed-effect regression models and a k-nearest neighbor approach for estimation of singletree biomass. Canadian Journal of Forest Research, 38: 1-9. Go to original source...
    6. Flewelling J.W., Pienaar L.V. (1981): Multiplicative regression with lognormal errors. Forest Science, 27: 281-289.
    7. Fu L.Y., Zeng W.S., Tang S.Z. (2011): Analysis the effect of region impacting on the biomass of domestic Masson pine using mixed model. Acta Ecologica Sinica, 31: 5797-5808. (in Chinese)
    8. Gregoire T.G., Schabenberger O., Barrett J.P. (1995): Linear modeling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements. Canadian Journal of Forest Research, 25: 137-156. Go to original source...
    9. Hansen M. (2002): Volume and biomass estimation in FIA: National consistency vs. regional accuracy. In: McRoberts R.E., Reams G.A., Van Deusen P.C., Moser J.W. (eds): Proceedings of 3rd Annual Forest Inventory and Analysis Symposium. Traverse City, 17.-19. October 2001. St. Paul, North Central Research Station, Forest Service USDA, General Technical Report NC-230: 109-120.
    10. Jenkins J.C., Chojnacky D.C., Heath L.S., Birdsey R.A. (2003): National-scale biomass estimators for United States tree species. Forest Science, 49: 12-35.
    11. Laird N., Lange N., Stram D. (1987): Maximum likelihood computations with repeated measures: Application of the EM algorithm. Journal of the American Statistical Association, 82: 97-105. Go to original source...
    12. Lang P.M. (2008): Linear mixed model of aerial photo crown width and ground diameter. Scientia Silvae Sinicae, 44: 41-44. (in Chinese) Go to original source...
    13. Lappi J., Bailey R.L. (1988): A height prediction model with random stand and tree parameters: an alternative to traditional site index methods. Forest Science, 38: 409-429.
    14. Lei X.D., Li Y.C., Xiang W. (2009): Individual basal area growth model using multi-level linear mixed model with repeated measurements. Scientia Silvae Sinicae, 45: 74-80. (in Chinese)
    15. Li X.H., Hong L.X. (1997): Research on the use of dummy variables method to calculate the family of site index curves. Forest Research, 10: 215-219. (in Chinese)
    16. Li C.M., Zhang H.R. (2010): Modeling dominant height for Chinese fir plantation using a nonlinear mixed-effects modeling approach. Scientia Silvae Sinicae, 46: 89-95. (in Chinese)
    17. Li L.X., Hao Y.H., Zhang Y. (2006): The application of dummy variable in statistic analysis. The Journal of Mathematical Medicine, 19: 51-52. (in Chinese)
    18. Li H., Mai J.Z., Xiao M. (2008): Application of dummy variable in logistic regression models. The Journal of EvidenceBased Medicine, 8: 42-45. (in Chinese)
    19. Meng S.X., Huang S. (2009): Improved calibration of nonlinear mixed-effects models demonstrated on a height growth function. Forest Science, 55: 239-248.
    20. Meng S.X., Huang S., Lieffers V.J. (2008): Wind speed and crown class influence the height-diameter relationship of lodgepole pine: Nonlinear mixed effects modeling. Forest Ecology and Management, 256: 570-577. Go to original source...
    21. Muukkonen P. (2007): Generalized allometric volume and biomass equations for some tree species in Europe. European Journal of Forest Research, 126: 157-166. Go to original source...
    22. Návar J. (2009): Allometric equations for tree species and carbon stocks for forests of northwestern Mexico. Forest Ecology and Management, 257: 427-434. Go to original source...
    23. Pinherio J.C., Bates D.M. (2000): Mixed-Effects Models in S and S-PLUS. New York, Springer-Verlag: 528. Go to original source...
    24. Repola J., Ojansuu R., Kukkola M. (2007): Biomass functions for Scots pine, Norway spruce and birch in Finland. Working Papers of the Finnish Forest Research Institute, 53: 28. Available at http://www.metla.fi/julkaisut/workingpapers/2007/mwp053.htm
    25. SAS Institute Inc. (1999): SAS/STAT user's guide, Version 8. Cary, SAS Institute Inc.
    26. Snorrason A., Einarsson S.F. (2006): Single-tree biomass and stem volume functions for eleven tree species used in Icelandic forestry. Icelandic Agriculture Science, 19: 15-24.
    27. Snowdon P. (1991): A ratio estimator for bias correction in logarithmic regressions. Canadian Journal of Forest Research, 21: 720-724. Go to original source...
    28. Tang S.Z., Li Y. (2002): Statistical Foundation for Biomathematical Models. Beijing, Science Press: 168-194. (in Chinese)
    29. Tang S.Z., Lang K.J., Li H.K. (2008): Statistics and Computation of Biomathematical Models (ForStat Course). Beijing, Science Press: 115-261. (in Chinese)
    30. Ter-Mikaelian M.T., Korzukhin M.D. (1997): Biomass equations for sixty-five North American tree species. Forest Ecology and Management, 97: 1-24. Go to original source...
    31. Tomppo E., Gschwantner T., Lawrence M., McRoberts R.E. (2010): National Forest Inventories: Pathways for Common Reporting. 1st Ed. New York, Springer: 610. Go to original source...
    32. Vallet P., Dhôte J-F., Le Moguédec G., Ravart M., Pignard G. (2006): Development of total aboveground volume equations for seven important forest tree species in France. Forest Ecology and Management, 229: 98-110. Go to original source...
    33. Wang M., Borders B.E., Zhao D. (2008): An empirical comparison of two subject-specific approaches to dominant heights modeling the dummy variable method and the mixed model method. Forest Ecology and Management, 255: 2659-2669. Go to original source...
    34. West G.B., Brown J.H., Enquist B.J. (1999): A general model for the structure and allometry of plant vascular systems. Nature, 400: 664-667. Go to original source...
    35. Zhang Y.J., Borders B.E. (2004): Using a system mixedeffects modeling method to estimate tree compartment biomass for intensively managed loblolly pines- an allometric approach. Forest Ecology and Management, 194: 145-157. Go to original source...

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