Comparison of linear mixed effects model and generalized model of the tree height-diameter relationship Z. (2015): Comparison of linear mixed effects model and generalized model of the tree height-diameter relationship. J. For. Sci., 61: 439-447.
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Models of height curves generated using a linear mixed effects model and generalized model were compared. Both tested models were also compared with local models of height curves, which were fitted using a nonlinear regression. In the mixed model two versions of calibration were tested. The first calibration approach was based on measurement of heights only in trees of the mean diameter interval, while the second calibration approach was based on measurement of tree heights in three diameter intervals. Generalized model is the mathematical formulation of a system of uniform height curves, which is commonly used in the Czech Republic. The study took place at Training Forest Enterprise called Masaryk Forest at Křtiny and was carried out for Norway spruce (Picea abies [L.] Karst.). It was found that the mixed model behaves correctly only in the case of calibration based on selection of trees in three diameter intervals. Selection of a total of nine trees was confirmed as the most suitable to calibrate the model. In most of the calculated quality criteria, the mixed model achieved better results than the generalized model, even with a smaller number of measured heights. The bias of both models from the local model was very similar (0.54 m for the mixed model and 0.44 m for the generalized model). The mixed model can therefore fully replace the commonly used generalized model even with a smaller number of measured heights.
Adame Patricia, del Río Miren, Cañellas Isabel (2008): A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.). Forest Ecology and Management, 256, 88-98
Adamec Z., Drápela K. (): Generalized additive models as an alternative approach to the modelling of the tree height-diameter relationship. Journal of Forest Science, 61, 235-243
Akaike H. (1973): Information theory and an extension of the maximum likelihood principle. In: Petrov B.N., Csaki F. (eds): Proceedings of the 2nd International symposium on information theory, Budapest, Sept 2–8, 1973: 268–281.
Calama Rafael, Montero Gregorio (2004): Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain. Canadian Journal of Forest Research, 34, 150-163
Calama Rafael, Montero Gregorio (2005): Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fennica, 39, -
Castedo Dorado Fernando, Barrio Anta Marcos, Parresol Bernard R., Álvarez González Juan Gabriel (2005): A stochastic height-diameter model for maritime pine ecoregions in Galicia (northwestern Spain). Annals of Forest Science, 62, 455-465
Crecente-Campo Felipe, Tomé Margarida, Soares Paula, Diéguez-Aranda Ulises (2010): A generalized nonlinear mixed-effects height–diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management, 259, 943-952
Curtis R.O. (1967): Height-diameter and height-diameter-age equations for second-growth douglas-fir. Forest Science, 13: 365–375.
Drápela K. (2011): Regresní modely a možnosti jejich využití v lesnictví. [Habilitation Thesis.] Brno, Mendel University in Brno: 235.
Eerikäinen Kalle (2003): Predicting the height–diameter pattern of planted Pinus kesiya stands in Zambia and Zimbabwe. Forest Ecology and Management, 175, 355-366
Fabrika M., Pretzsch H. (2013): Forest Ecosystem Analysis and Modelling. Zvolen, Technická univerzita vo Zvolene: 620.
Fang Zixing, Bailey R.L. (1998): Height–diameter models for tropical forests on Hainan Island in southern China. Forest Ecology and Management, 110, 315-327
Halaj J. (1955): Tabuľky na určovanie hmoty a prírastku porastov. Bratislava, SVPL: 328.
Huang Shongming, Price Daryl, J. Titus Stephen (2000): Development of ecoregion-based height–diameter models for white spruce in boreal forests. Forest Ecology and Management, 129, 125-141
Huang Shongming, Titus Stephen J., Wiens Douglas P. (1992): Comparison of nonlinear height–diameter functions for major Alberta tree species. Canadian Journal of Forest Research, 22, 1297-1304
Husch B., Beers T.W., Kershaw J. A. (2003): Forest Mensuration. 4th Ed. Hoboken, New Jersey, John Wiley & Sons: 443.
Kangas Annika, Haara Arto (2012): Comparison of nonspatial and spatial approaches with parametric and nonparametric methods in prediction of tree height. European Journal of Forest Research, 131, 1771-1782
Lu J., Zhang L. (2013): Evaluation of structure specification in linear mixed models for modeling the spatial effects in tree height-diameter relationships. Annals of Forest Research, 56: 137–148.
Martin F., Flewelling J. (1998): Evaluation of tree height prediction models for stand inventory. Western Journal of Applied Forestry, 13: 109–119.
Mehtätalo Lauri (2004): A longitudinal height–diameter model for Norway spruce in Finland. Canadian Journal of Forest Research, 34, 131-140
Michailoff I. (1943): Zahlenmäßiges Verfahren für die Ausführung der Bestandeshöhenkurven. Forstwissenschaftliches Centralblatt und Tharandter Forstliches Jahrbuch, 6: 273–279.
Özçelik Ramazan, Diamantopoulou Maria J., Crecente-Campo Felipe, Eler Unal (2013): Estimating Crimean juniper tree height using nonlinear regression and artificial neural network models. Forest Ecology and Management, 306, 52-60
Petterson H. (1955): Barrskogens volymproduktion. Meddelanden från Statens skogsforskningsinstitut, 45: 1–391.
Prodan M. (1951): Messung der Waldbestände. Frankfurt a. M., J.D. Sauerländer's Verlag: 260.
R Development Core Team (2015): R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. Available at (accessed March 1, 2015).
Robinson G. K. (1991): That BLUP is a Good Thing: The Estimation of Random Effects. Statistical Science, 6, 15-32
Schmidt Matthias, Kiviste Andres, von Gadow Klaus (2011): A spatially explicit height–diameter model for Scots pine in Estonia. European Journal of Forest Research, 130, 303-315
Schröder Jörg, Álvarez González Juan Gabriel (2001): Comparing the performance of generalized diameter-height equations for Maritime pine in Northwestern Spain. Forstwissenschaftliches Centralblatt, 120, 18-23
Sharma Mahadev, Parton John (2007): Height–diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management, 249, 187-198
Sharma Mahadev, Yin Zhang Shu (2004): Height–Diameter Models Using Stand Characteristics for Pinus banksiana and Picea mariana. Scandinavian Journal of Forest Research, 19, 442-451
Soares Paula, Tomé Margarida (2002): Height–diameter equation for first rotation eucalypt plantations in Portugal. Forest Ecology and Management, 166, 99-109
Šmelko Š. (2007): Dendrometria. Zvolen, Technická univerzita vo Zvolene: 400.
Šmelko Š., Pánek F., Zanvit B. (1987): Matematická formulácia systému jednotných výškových kriviek rovnovekých porastov SSR. Acta Facultatis Forestalis Zvolen, 19: 151–174.
Temesgen H., v. Gadow K. (2004): Generalized height–diameter models—an application for major tree species in complex stands of interior British Columbia. European Journal of Forest Research, 123, 45-51
Temesgen H., Zhang C.H., Zhao X.H. (2014): Modelling tree height–diameter relationships in multi-species and multi-layered forests: A large observational study from Northeast China. Forest Ecology and Management, 316, 78-89
Trincado Guillermo, VanderSchaaf Curtis L., Burkhart Harold E. (2007): Regional mixed-effects height–diameter models for loblolly pine (Pinus taeda L.) plantations. European Journal of Forest Research, 126, 253-262
Van Laar A., Akça A. (2007): Forest Mensuration. Managing Forest Ecosystems. Volume 13. Dordrecht, Springer: 383.
Vargas-Larreta B., Castedo-Dorado F., Alvarez-Gonzalez J. G., Barrio-Anta M., Cruz-Cobos F. (): A generalized height-diameter model with random coefficients for uneven-aged stands in El Salto, Durango (Mexico). Forestry, 82, 445-462
Vonesh E.F., Chiinchilli V.M. (1997): Linear and nonlinear models for the analysis of repeated measurements. Boca Raton, Chapman & Hall/CRC: 560.
Wolf J. (1978): Systém standardizovaných výškových křivek stejnověkých smrkových porostů. Acta Universtitatis Agriculturae Brno. Series C, Facultas silviculturae, 47: 93–102.
Yang Yuqing, Huang Shongming (2011): Comparison of different methods for fitting nonlinear mixed forest models and for making predictions. Canadian Journal of Forest Research, 41, 1671-1686
ZHANG L (): Cross-validation of Non-linear Growth Functions for Modelling Tree Height–Diameter Relationships. Annals of Botany, 79, 251-257
Zhang Lianjun, Bi Huiquan, Cheng Pengfei, Davis Craig J (2004): Modeling spatial variation in tree diameter–height relationships. Forest Ecology and Management, 189, 317-329
Zhang L., Ma Z., Guo L. (): Spatially assessing model errors of four regression techniques for three types of forest stands. Forestry, 81, 209-225
Zhao Lifang, Li Chunming, Tang Shouzheng (2013): Individual-tree diameter growth model for fir plantations based on multi-level linear mixed effects models across southeast China. Journal of Forest Research, 18, 305-315
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