Using Linear Mixed Model and Dummy Variable Model Approaches to Construct Generalized Single-Tree Biomass Equations in Guizhou

ZENG Wei-sheng; TANG Shou-zheng; XIA Zhong-sheng; ZHU Song; LUO Hong-zhang

Volume 24 Issue 3

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Using Linear Mixed Model and Dummy Variable Model Approaches to Construct Generalized Single-Tree Biomass Equations in Guizhou

1.
Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing 100091,China
2.
Forest Resources Administration Office of Guizhou Province, Guiyang 550001, Guizhou, China

Received Date: 2011-01-05

Abstract

Based on the above-ground biomass data of Chinese fir (Cunninghamia lanceolata) and Masson Pine (Pinus massoniana) plantations in Guizhou Province, the generalized single-tree biomass equations suitable for different species and regions (central region and other region) were established using linear mixed model and dummy variable model methods, which provided effective approaches to simplify the biomass modeling. The results show that the above-ground biomass estimates of individual trees with the same diameter are different in some extent among different tree species and geographic regions, and linear mixed model with random parameters and dummy model with specific (local) parameters are better than population average model; and linear mixed model and dummy variable model approaches are almost same effective and may be applied to develop other generalized models such as tree volume equations.
- above-ground biomass,
- linear mixed model,
- dummy variable model,
- generalized equation,
- compatibility,
- Cunninghamia lanceolata

References

[1]	Tomppo E, Gschwantner T, Lawrence M, et al. National Forest Inventories: Pathways for Common Reporting [M]. Springer, New York, 2010
[2]	Hansen M. Volume and biomass estimation in FIA: National consistency vs. regional accuracy . GTR NC-230, North Central Research Station, Forest Service USDA, 2002: 109-120
[3]	Chojnacky D C. Allometric scaling theory applied to FIA biomass estimation . GTR NC-230, North Central Research Station, Forest Service USDA, 2002: 96-102
[4]	Jenkins J C, Chojnacky D C, Heath L S, et al. National-scale biomass estimators for United States tree species [J]. For Sci, 2003,49(1):12-35
[5]	Snorrason A, Einarsson S F. Single-tree biomass and stem volume functions for eleven tree species used in Icelandic forestry [J]. Icelandic Agric Sci, 2006,19:15-24
[6]	Vallet P, Dhte J-F, Le Moguédec G, et al. Development of total aboveground volume equations for seven important forest tree species in France [J]. Forest Ecology and Management, 2006,229:98-110
[7]	Muukkonen P. Generalized allometric volume and biomass equations for some tree species in Europe [J]. Eur J Forest Res, 2007,126:157-166
[8]	Case B, Hall R J. Assessing prediction errors of generalized tree biomass and volume equations for the boreal forest region of west-central Canada [J]. Can J For Res, 2008,38:878-889
[9]	Návar J. Allometric equations for tree species and carbon stocks for forests of northwestern Mexico [J]. Forest Ecology and Management, 2009, 257: 427-434
[10]	Lappi J, Bailey R L. A height prediction model with random stand and tree parameters: an alternative to traditional site index methods [J]. For Sci, 1988,38(2):409-429
[11]	Gregoire T G, Schabenberger O, Barrett J P. Linear modeling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements [J]. Can J For Res, 1995,25:137-156
[12]	Zhang Y J, Borders B E. Using a system mixed-effects modeling method to estimate tree compartment biomass for intensively managed loblolly pines—an allometric approach [J]. Forest Ecology and Management, 2004,194:145-157
[13]	Calegario N, Daniels R F, Maestri R, et al. Modeling dominant height growth based on nonlinear mixed-effects model: a clonal Eucalyptus plantation case study [J]. Forest Ecology and Management, 2005,204: 11-20
[14]	Meng S X, Huang S, Lieffers V J, et al. Wind speed and crown class influence the height-diameter relationship of lodgepole pine: Nonlinear mixed effects modeling [J]. Forest Ecology and Management, 2008,256:570-577
[15]	Fehrmann L, Lehtonen A, Kleinn C, et al. Comparison of linear and mixed-effect regression models and a k-nearest neighbor approach for estimation of single-tree biomass [J]. Can J For Res, 2008,38:1-9
[16]	郎璞玫. 航空像片冠幅与地面直径的线性混合模型[J]. 林业科学, 2008,44(3): 41-44
[17]	雷相东,李永慈,向玮. 基于混合模型的单木断面积生长模型[J]. 林业科学, 2009,45(1): 74-80
[18]	李春明,张会儒. 利用非线性混合模型模拟杉木林优势木平均高[J]. 林业科学, 2010,46(3): 89-95
[19]	唐守正,李勇.生物数学模型的统计学基础[M].北京:科学出版社,2002
[20]	李丽霞,郜艳晖,张瑛. 哑变量在统计分析中的应用[J]. 数理医药学杂志, 2006,19(1): 51-52
[21]	唐守正,郎奎建,李海奎.统计和生物数学模型计算(ForStat教程)[M].北京:科学出版社,2008
[22]	李希菲,洪玲霞. 用哑变量法求算立地指数曲线族的研究[J]. 林业科学研究, 1997,10(2): 215-219
[23]	李河,麦劲壮,肖敏,等. 哑变量在Logistic回归模型中的应用[J]. 循证医学, 2008,8(1):42-45
[24]	Wang M, Borders B E, Zhao D. An empirical comparison of two subject-specific approaches to dominant heights modeling, the dummy variable method and the mixed model method [J]. Forest Ecology and Management, 2008, 255: 2659-2669
[25]	FAO. Global forest resources assessment 2005: progress towards sustainable forest management . Rome: FAO Forestry Paper 147, Food and Agriculture Organization of the United Nations, 2006
[26]	Ter-Mikaelian M T, Korzukhin M D. Biomass equations for sixty-five North American tree species [J]. Forest Ecology and Management, 1997,97:1-24
[27]	Baskerville G L. Use of logarithmic regression in the estimation of plant biomass [J]. Can J For Res, 1972,2:49-53
[28]	Flewelling J W, Pienaar L V. Multiplicative regression with lognormal errors [J]. For Sci, 1981,27(2):281-289
[29]	Snowdon P. A ratio estimator for bias correction in logarithmic regressions [J]. Can J For Res, 1991,21(5): 720-724
[30]	West G B, Brown J H, Enquist B J. A general model for the structure and allometry of plant vascular systems [J]. Nature, 1999,400: 664-667

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通讯作者: 陈斌, bchen63@163.com

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沈阳化工大学材料科学与工程学院沈阳 110142

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Using Linear Mixed Model and Dummy Variable Model Approaches to Construct Generalized Single-Tree Biomass Equations in Guizhou

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

2. Forest Resources Administration Office of Guizhou Province, Guiyang 550001, Guizhou, China

Received Date: 2011-01-05

Abstract: Based on the above-ground biomass data of Chinese fir (Cunninghamia lanceolata) and Masson Pine (Pinus massoniana) plantations in Guizhou Province, the generalized single-tree biomass equations suitable for different species and regions (central region and other region) were established using linear mixed model and dummy variable model methods, which provided effective approaches to simplify the biomass modeling. The results show that the above-ground biomass estimates of individual trees with the same diameter are different in some extent among different tree species and geographic regions, and linear mixed model with random parameters and dummy model with specific (local) parameters are better than population average model; and linear mixed model and dummy variable model approaches are almost same effective and may be applied to develop other generalized models such as tree volume equations.

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[1]	Tomppo E, Gschwantner T, Lawrence M, et al. National Forest Inventories: Pathways for Common Reporting [M]. Springer, New York, 2010
[2]	Hansen M. Volume and biomass estimation in FIA: National consistency vs. regional accuracy . GTR NC-230, North Central Research Station, Forest Service USDA, 2002: 109-120
[3]	Chojnacky D C. Allometric scaling theory applied to FIA biomass estimation . GTR NC-230, North Central Research Station, Forest Service USDA, 2002: 96-102
[4]	Jenkins J C, Chojnacky D C, Heath L S, et al. National-scale biomass estimators for United States tree species [J]. For Sci, 2003,49(1):12-35
[5]	Snorrason A, Einarsson S F. Single-tree biomass and stem volume functions for eleven tree species used in Icelandic forestry [J]. Icelandic Agric Sci, 2006,19:15-24
[6]	Vallet P, Dhte J-F, Le Moguédec G, et al. Development of total aboveground volume equations for seven important forest tree species in France [J]. Forest Ecology and Management, 2006,229:98-110
[7]	Muukkonen P. Generalized allometric volume and biomass equations for some tree species in Europe [J]. Eur J Forest Res, 2007,126:157-166
[8]	Case B, Hall R J. Assessing prediction errors of generalized tree biomass and volume equations for the boreal forest region of west-central Canada [J]. Can J For Res, 2008,38:878-889
[9]	Návar J. Allometric equations for tree species and carbon stocks for forests of northwestern Mexico [J]. Forest Ecology and Management, 2009, 257: 427-434
[10]	Lappi J, Bailey R L. A height prediction model with random stand and tree parameters: an alternative to traditional site index methods [J]. For Sci, 1988,38(2):409-429
[11]	Gregoire T G, Schabenberger O, Barrett J P. Linear modeling of irregularly spaced, unbalanced, longitudinal data from permanent-plot measurements [J]. Can J For Res, 1995,25:137-156
[12]	Zhang Y J, Borders B E. Using a system mixed-effects modeling method to estimate tree compartment biomass for intensively managed loblolly pines—an allometric approach [J]. Forest Ecology and Management, 2004,194:145-157
[13]	Calegario N, Daniels R F, Maestri R, et al. Modeling dominant height growth based on nonlinear mixed-effects model: a clonal Eucalyptus plantation case study [J]. Forest Ecology and Management, 2005,204: 11-20
[14]	Meng S X, Huang S, Lieffers V J, et al. Wind speed and crown class influence the height-diameter relationship of lodgepole pine: Nonlinear mixed effects modeling [J]. Forest Ecology and Management, 2008,256:570-577
[15]	Fehrmann L, Lehtonen A, Kleinn C, et al. Comparison of linear and mixed-effect regression models and a k-nearest neighbor approach for estimation of single-tree biomass [J]. Can J For Res, 2008,38:1-9
[16]	郎璞玫. 航空像片冠幅与地面直径的线性混合模型[J]. 林业科学, 2008,44(3): 41-44
[17]	雷相东,李永慈,向玮. 基于混合模型的单木断面积生长模型[J]. 林业科学, 2009,45(1): 74-80
[18]	李春明,张会儒. 利用非线性混合模型模拟杉木林优势木平均高[J]. 林业科学, 2010,46(3): 89-95
[19]	唐守正,李勇.生物数学模型的统计学基础[M].北京:科学出版社,2002
[20]	李丽霞,郜艳晖,张瑛. 哑变量在统计分析中的应用[J]. 数理医药学杂志, 2006,19(1): 51-52
[21]	唐守正,郎奎建,李海奎.统计和生物数学模型计算(ForStat教程)[M].北京:科学出版社,2008
[22]	李希菲,洪玲霞. 用哑变量法求算立地指数曲线族的研究[J]. 林业科学研究, 1997,10(2): 215-219
[23]	李河,麦劲壮,肖敏,等. 哑变量在Logistic回归模型中的应用[J]. 循证医学, 2008,8(1):42-45
[24]	Wang M, Borders B E, Zhao D. An empirical comparison of two subject-specific approaches to dominant heights modeling, the dummy variable method and the mixed model method [J]. Forest Ecology and Management, 2008, 255: 2659-2669
[25]	FAO. Global forest resources assessment 2005: progress towards sustainable forest management . Rome: FAO Forestry Paper 147, Food and Agriculture Organization of the United Nations, 2006
[26]	Ter-Mikaelian M T, Korzukhin M D. Biomass equations for sixty-five North American tree species [J]. Forest Ecology and Management, 1997,97:1-24
[27]	Baskerville G L. Use of logarithmic regression in the estimation of plant biomass [J]. Can J For Res, 1972,2:49-53
[28]	Flewelling J W, Pienaar L V. Multiplicative regression with lognormal errors [J]. For Sci, 1981,27(2):281-289
[29]	Snowdon P. A ratio estimator for bias correction in logarithmic regressions [J]. Can J For Res, 1991,21(5): 720-724
[30]	West G B, Brown J H, Enquist B J. A general model for the structure and allometry of plant vascular systems [J]. Nature, 1999,400: 664-667

Using Linear Mixed Model and Dummy Variable Model Approaches to Construct Generalized Single-Tree Biomass Equations in Guizhou

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通讯作者: 陈斌, bchen63@163.com

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Using Linear Mixed Model and Dummy Variable Model Approaches to Construct Generalized Single-Tree Biomass Equations in Guizhou

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