Page menu:

Lebedev A. V., Kuzmichev V. V. Mixed Effects Regression Models in Forestry Research

models of mixed effects, fixed effect, random effect, tree stand, forestry


UDC 502/504:630*53

How to cite: Lebedev A. V., Kuzmichev V. V. Mixed effects regression models in forestry research // Sibirskij Lesnoj Zurnal (Sib. J. For. Sci.). 2021. N. 1. P. 13–20 (in Russian with English abstract and references).

DOI: 10.15372/SJFS20210102

© Lebedev A. V., Kuzmichev V. V., 2021

A promising method for finding patterns in experimental data is regression models of mixed effects, which have not found wide application in forest science in Russia to date. Over the past two decades, interest in them has grown significantly in the world scientific community. Mixed-effect models are extensions of regression models for data that is collected by group. In forestry, for example, individual stands, trial plots, geographic regions, etc. can be considered as separate groups influencing the resultant trait. Compared to classical fixed effect models, the addition of a random component avoids violating the assumption of independence in repeated measurements. Therefore, parameter estimates are more reliable. Mixed-effect models are used to solve a wide range of problems in forestry, from describing pairwise relationships between individual tree variables to reflecting the dynamics of forest stands. By giving more accurate forecasts of variables in comparison with traditional models, which include only fixed effects, their introduction into production activities can increase labor productivity and economic efficiency of forestry. A large positive experience of using models of mixed effects abroad should not go unnoticed in the domestic forestry science. Their active use makes it possible to reveal new or hidden patterns in experimental data, thereby giving a new vector in the development of forestry, forest inventory and other forestry scientific disciplines.



Грабарник П. Я., Шанин В. Н., Чертов О. Г., Припутина И. В., Быховец С. С., Петропавловский Б. С., Фролов П. В., Зубкова Е. В., Шашков М. П., Фролова Г. Г. Моделирование динамики лесных экосистем как инструмент прогнозирования и управления лесами // Лесоведение. 2019. № 6. С. 488–500 [Grabarnik P. Ya., Shanin V. N., Chertov O. G., Priputina I. V., Bykhovets S. S., Petropavlovsky B. S., Frolov P. V. Zubkova E. V., Shashkov M. P., Frolova G. G. Modelirovanie dinamiki lesnykh ekosistem kak instrument prognozirovaniya i upravleniya lesami (Modelling of forest ecosystem dynamics: an instrument for forest prediction and management) // Lesovedenie (For. Sci.). 2019. N. 6. P. 488–500 (in Russian with English abstract)].

Усольцев В. А., Шубаири С. О., Дар Дж. А., Цепордей И. С., Часовских В. П., Колчин К. В. Проблемы оценки биопродуктивности лесов в аспекте биогеографии: 2) модели смешанных эффектов // Эко-Потенциал. 2018. № 1(21). С. 9–27 [Usoltsev V. A., Shobairi S. O., Dar J. A., Tsepordey I. S., Chasovskikh V. P., Kolchin K. V. Problemy otsenki bioproduktivnosti lesov v aspekte biogeografii: 2) modeli smeshannykh effektov (Problems of estimating forest biological productivity in the aspect of biogeography: 2) mixed-effects models) // Eco-Potential. 2018. N. 1 (21). P. 9–27 (in Russian with English abstract)].

Arcangeli C., Klopf M., Hale S. E., Jenkins T. A., Hasenauer H. The uniform height curve method for height-diameter modelling: an application to Sitka spruce in Britain // Forestry. 2014. V. 87. Iss. 1. P. 177–186.

Bailey R. L., Clutter J. L. Base-age invariant polymorphic site curves // For. Sci. 1974. V. 20. Iss. 2. P. 155–159.

Bolker B. M., Brooks M. E., Clark C. J., Geange S. W., Poulsen J. R., Stevens M. H., White J.-S. S. Generalized linear mixed models: a practical guide for ecology and evolution // Trends Ecol. Evolut. 2009. V. 24. Iss. 3. P. 127–135.

Burkhart H. E., Tomé M. Modeling forest trees and stands. Dordrecht, Netherlands: Springer Sci., Business Media, 2012. 458 p.

Calama R., Montero G. Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach // Silva Fenn. 2005. V. 39. N. 1. P. 37–54.

Chen D., Huang X., Zhang S., Sun X. Biomass modeling of larch (Larix spp.) plantations in China based on the mixed model, dummy variable model, and Bayesian hierarchical model // Forests. 2017. V. 8. N. 8. Article number: 268.

Clutter J. L. The development of compatible analytic models for growth and yield of Loblolly pine. PhD. dissertation, Duke Univ., 1961.

Fang Z., Bailey R. L. Nonlinear mixed effects modeling for slash pine dominant height growth following intensive silvicultural treatments // For. Sci. 2001. V. 47. Iss. 3. P. 287–300.

Fu L., Zeng W., Zhang H., Wang G., Lei Y., Tang S. Generic linear mixed-effects individual-tree biomass models for Pinus massoniana in southern China // Southern Forests: J. For. Sci. 2014. V. 76. Iss. 1. P. 47–56.

Gałecki A., Burzykowski T. Linear mixed-effects models using R: A step-by-step approach. New York: Springer Verlag 2013. 542 p.

Guangyi M., Yujun S., Hao X., de-Miguel S. A mixed-effects model with different strategies for modeling volume in Cunninghamia lanceolata plantations // PLoS One. 2015. V. 10. N. 10. Article number: e0140095.

Harrington T. B. Silvicultural approaches for thinning southern pines: Method, intensity, and timing. Georgia For. Commission: Macon, GA, USA, 2000.

Harrison X. A., Donaldson L., Correa-Cano M. E., Evans J., Fisher D. N., Goodwin C. Е., Robinson B. S., Hodgson D. J., Inger R. A brief introduction to mixed effects modelling and multi-model inference in ecology // Peer J. 2018. N. 6 (1). Article number: e4794.

Huang S., Meng S. X., Yang Y. Using nonlinear mixed model technique to determine the optimal tree height prediction model for black spruce // Modern Appl. Sci. 2009. V. 3. N. 4. P. 3–18.

Huy B., Kralicek K., Poudel K. P., Phuong V. T., Khoa P. V., Hung N. D., Temesgen H. Allometric equations for estimating tree aboveground biomass in evergreen broadleaf forests of Vietnam // For. Ecol. Manag. 2016. N. 382. P. 193–205.

Kalbi S., Fallah A., Bettinger P., Shataee S., Yousefpour R. Mixed-effects modelling for tree height prediction models of Oriental beech in the Hyrcanian forests // J. For. Res. 2018. N. 29. P. 1195–1204.

Lappi J., Bailey R. L. A height prediction model with random stand and tree parameters: an alternative to traditional site index methods // For. Sci. 1988. V. 34. N. 4. P. 907–927.

Lindstrom M. J., Bates D. M. Nonlinear mixed effects models for repeated measures data // Biometrics. 1990. V. 46. N. 3. P. 673–687.

Mehtätalo L., Miguel S. de, Gregoire T. G. Modeling height-diameter curves for prediction // Can. J. For. Res. 2015. N. 45. P. 826–837.

Ni C., Nigh G. D. An analysis and comparison of predictors of random parameters demonstrated on planted loblolly pine diameter growth prediction // Forestry. 2012. V. 85. Iss. 2. P. 271–280.

Nicoletti M. F., Carvalho S. P., Machado S. A., Filho A. F., Oliveira G. S. Partial volume prediction through nonlinear mixed modeling // Floresta e Ambiente. 2019. V. 26. N. 4. Article number: e20170329.

Njana M. A., Bollandsås O. M., Eid T., Zahabu E., Malimbwi R. E. Above- and belowground tree biomass models for three mangrove species in Tanzania: a nonlinear mixed effects modelling approach // Ann. For. Sci. 2016. V. 73. Iss. 2. P. 353–369.

Ogana F. N., Corral-Rivas S., Gorgoso-Varela J. J. Nonlinear mixed-effect height-diameter model for Pinus pinaster Ait. and Pinus radiata D. Don // Cerne. 2020. V. 26. N. 1. P. 150–161.

Özçelika R., Caob Q. V., Trincadoc G., Göçer N. Predicting tree height from tree diameter and dominant height using mixed-effects and quantile regression models for two species in Turkey // For. Ecol. Manag. 2018. V. 419–420. P. 240–248.

Pinheiro J. C., Bates D. M. Mixed-effects models in S and S-PLUS. New York: Springer Verlag, 2000. 528 p.

Pokharel B., Dech J. P. Mixed-effects basal area increment models for tree species in the boreal forest of Ontario, Canada using an ecological land classification approach to incorporate site effects // Forestry. 2012. V. 85. Iss. 2. P. 255–270.

Pretzsch H. Density and growth of forest stands revisited. Effect of the temporal scale of observation, site quality, and thinning // For. Ecol. Manag. 2020. V. 460. Article number: 117879.

Pretzsch H., Biber P., Schütze G., Bielak K. Changes of forest stand dynamics in Europe. Facts from long-term observational plots and their relevance for forest ecology and management // For. Ecol. Manag. 2014a. V. 316. P. 65–77.

Pretzsch H., Biber P., Schütze G., Uhl E., Rötzer T. Forest stand growth dynamics in Central Europe have accelerated since 1870 // Nature Comm. 2014b. N. 5. Article number: 4967.

Pretzsch H., Biber P., Schütze G., Kemmerer J., Uhl E. Wood density reduced while wood volume growth accelerated in Central European forests since 1870 // For. Ecol. Manag. 2018. V. 429. P. 589–616.

R Core Team. R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing, 2016.

Richards F. J. A flexible growth function for empirical use // J. Exp. Bot. 1959. V. 10. N. 29. P. 290–300.

Sánchez-González M., Cañellas I., Montero G. Generalized height-diameter and crown diameter prediction models for cork oak forests in Spain // Invest. Agr. Sist. Recur. For. 2007. V. 16. N. 1. P. 76–88.

Sharma R. P., Vacek Z., Vacek S. Nonlinear mixed effect height-diameter model for mixed species forests in the central part of the Czech Republic // J. For. Sci. 2016. V. 62. N. 10. P. 470–484.

Sharma R. P., Vacek Z., Vacek S. Generalized nonlinear mixed-effects individual tree crown ratio models for Norway Spruce and European Beech // Forests. 2018. N. 9. Article number: 555.

Sharma R. P., Vacek Z., Vacek S., Kučera M. Modelling individual tree height-diameter relationships for multi-layered and multi-species forests in central Europe // Trees. 2019. V. 33. P. 103–119.

Schumacher F. X., Hall F. S. Logarithmic expression of timber-tree volume // J. Agr. Res. 1933. V. 47. N. 9. P. 719–734.

Vismara E. S., Mehtätalo L., Batista J. L. Linear mixed-effects models and calibration applied to volume models in two rotations of Eucalyptus grandis plantations // Can. J. For. Res. 2015. V. 46. N. 1. P. 132–141.

Wang W., Chen X., Zeng W.-S., Wang J., Meng J. Development of a mixed-effects individual-tree basal area increment model for oaks (Quercus spp.) considering forest structural diversity // Forests. 2019. V. 10. N. 6. Article number: 474. 19 p.

Xu H., Sun Y., Wang H., Fu Y., Dong Y., Li Y. Nonlinear Mixed-Effects (NLME) diameter growth models for individual China fir (Cunninghamia lanceolata) trees in Southeast China // PLoS ONE. 2014. V. 9. N. 8. Article number: e104012.

Zheng C., Mason E. G., Jia L., Wei S., Sun C., Duan J. A single-tree compatible biomass model of Quercus variabilis Blume forests in North China // Trees. 2015. V. 29. Iss. 3. P. 705–716.

Zuur A. F., Ieno E. N., Walker N., Saveliev A. A., Smith G. M. Mixed effects models and extensions in ecology with R. New York: Springer Sci. Business Media, LLC, 2009. 563 p.

Return to list