iForest - Biogeosciences and Forestry


Comparison of parametric and nonparametric methods for modeling height-diameter relationships

Zdenek Adamec   , Karel Drápela

iForest - Biogeosciences and Forestry, Volume 10, Issue 1, Pages 1-8 (2016)
doi: https://doi.org/10.3832/ifor1928-009
Published: Oct 19, 2016 - Copyright © 2016 SISEF

Research Articles

This paper focuses on the problem of regionalization of the height-diameter model at the stand level. To this purpose, we selected two different modeling techniques. As a parametric method, we chose a linear mixed effects model (LME) with calibrated conditional prediction, whose calibration was carried out on randomly selected trees either close to mean diameter or within three diameter intervals throughout the diameter range. As a nonparametric method, the technique of classification and regression trees (CART) was chosen. These two methods were also compared with the local model created by ordinary least squares regression. The results show that LME with calibrated conditional prediction based on measurements of height at three diameter intervals provided results very close to the local model, especially when six to nine trees are measured. We recommend this technique for the regionalization of the global model. The CART method provided worse results than LME, with the exception of parameters of the residual distribution. Nevertheless, the latter approach is very user-friendly, as the regression tree creation and especially its interpretation are relatively simple, and could be recommended when larger deviations are allowed.


Calibration, Classification and Regression Trees, Hierarchical Structure, Linear Mixed Effects Model, Spatial Heterogeneity

Authors’ address

Zdenek Adamec
Karel Drápela
Department of Forest Management and Applied Geoinformatics, Faculty of Forestry and Wood Technology, Mendel University in Brno, Brno, 613 00 (Czech Republic)

Corresponding author

Zdenek Adamec


Adamec Z, Drápela K (2016). Comparison of parametric and nonparametric methods for modeling height-diameter relationships. iForest 10: 1-8. - doi: 10.3832/ifor1928-009

Academic Editor

Piermaria Corona

Paper history

Received: Nov 24, 2015
Accepted: Jul 07, 2016

First online: Oct 19, 2016
Publication Date: Feb 28, 2017
Publication Time: 3.47 months

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Aakala T, Fraver S, Amato AW, Palik BJ (2013)
Influence of competition and age on tree growth in structurally complex old-growth forests in Northern Minnesota, USA. Forest Ecology and Management 308: 128-135.
CrossRef | Gscholar
Adame P, Del Rio M, Cañellas I (2008)
A mixed nonlinear height-diameter model for Pyrenean oak (Quercus pyrenaica Willd.). Forest Ecology and Management 256: 88-98.
CrossRef | Gscholar
Aertsen W, Kint V, Van Orshoven J, Ozkan K, Muys B (2010)
Comparison and ranking of different modelling techniques for prediction of site index in Mediterranean mountain forests. Ecological Modelling 221: 1119-1130.
CrossRef | Gscholar
Akaike H (1973)
Information theory and an extension of the maximum likelihood principle. In: Proceedings of the “2nd International Symposium on Information Theory” (Petrov BN, Csáki F eds). Budapest (Hungary) 2-8 September 1973. Akademiai Kiado, Budapest, Hungary, pp. 268-281.
Anderson MG, Ferree CE, Olivero AP, Zhao F (2010)
Assessing floodplain forests: using flow modeling and remote sensing to determine the best places for conservation. Natural Areas Journal 30: 39-52.
CrossRef | Gscholar
Breiman L, Friedman JH, Olshen RA, Stone CJ (1984)
Classification and regression trees. Chapman and Hall/CRC, Boca Raton, FL, USA, pp. 368.
Budhathoki CB, Lynch TB, Guldin JM (2008)
Nonlinear mixed modeling of basal area growth for shortleaf pine. Forest Ecology and Management 255: 3440-3446.
CrossRef | Gscholar
Calama R, Montero G (2005)
Multilevel linear mixed model for tree diameter increment in stone pine (Pinus pinea): a calibrating approach. Silva Fennica 39: 37-54.
CrossRef | Gscholar
Castaño-Santamaría J, Crecente-Campo F, Fernández-Martínez JL, Barrio-Anta M, Obeso JR (2013)
Tree height prediction approaches for uneven-aged beech forests in northwestern Spain. Forest Ecology and Management 307: 63-73.
CrossRef | Gscholar
Crecente-Campo F, Tomé M, Soares P, Diéguez-Aranda U (2010)
A generalized nonlinear mixed-effects height-diameter model for Eucalyptus globulus L. in northwestern Spain. Forest Ecology and Management 259: 943-952.
CrossRef | Gscholar
De’ath G, Fabricius KE (2000)
Classification and regression trees: a powerful yet simple technique for ecological data analysis. Ecology 81: 3178-3192.
CrossRef | Gscholar
Dobbertin M, Biging GS (1998)
Using the non-parametric classifier CART to model forest tree mortality. Forest Science 44: 507-516.
Online | Gscholar
Drápela K (2011)
Regresní modely a možnosti jejich využití v lesnictví [The regression models and options of their utilization in the forestry]. Mendel University in Brno, Brno, Czech Republic, pp. 236. [in Czech]
Eerikäinen K (2003)
Predicting the height-diameter pattern of planted Pinus kesiya stands in Zambia and Zimbabwe. Forest Ecology and Management 175: 355-366.
CrossRef | Gscholar
Fan Z, Kabrick JM, Shifley SR (2006)
Classification and regression tree based survival analysis in oak-dominated forests of Missouri’s Ozark highlands. Canadian Journal of Forest Research 36: 1740-1748.
CrossRef | Gscholar
Ferguson IS, Leech JW (1978)
Generalized least squares estimation of yield functions. Forest Science 24: 27-42.
Online | Gscholar
Fox JC, Ades PK, Bi H (2001)
Stochastic structure and individual-tree growth models. Forest Ecology and Management 154: 261-276.
CrossRef | Gscholar
Gómez C, Wulder MA, Montes F, Delgado JA (2012)
Modeling forest structural parameters in the Mediterranean pines of central Spain using QuickBird-2 imagery and classification and regression tree analysis (CART). Remote Sensing 4: 135-159.
CrossRef | Gscholar
Gregoire TG, Schabenberger O, Barrett JP (1995)
Linear modelling of irregularly spaced, unbalanced, longitudinal data from permanent plot measurements. Canadian Journal of Forest Research 25: 137-156.
CrossRef | Gscholar
Huang S, Price D, Titus SJ (2000)
Development of ecoregion-based height-diameter models for white spruce in boreal forest. Forest Ecology and Management 129: 125-141.
CrossRef | Gscholar
Kangas A, Haara A (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.
CrossRef | Gscholar
Legendre P (1993)
Spatial autocorrelation: trouble or new paradigm? Ecology 74: 1659-1673.
CrossRef | Gscholar
Levakovic A (1935)
Analytical form of growth laws. Glasnik za sumske pokuse 4: 189-282.
Lu J, Zhang L (2012)
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.
Online | Gscholar
Meyer HA (1940)
A mathematical expression for height curves. Journal of Forestry 38: 415-420.
Online | Gscholar
Mehtätalo L (2004)
A longitudinal height-diameter model for Norway spruce in Finland. Canadian Journal of Forest Research 34: 131-140.
CrossRef | Gscholar
Michailov I (1943)
Zahlenmäßiges Verfahren für die Ausführung der Bestandeshöhenkurven [Numerical estimation of stand height curves]. Forstwissenschaftliches Centralblatt und Tharandter Forstliches Jahrbuch 6: 273-279. [in German]
Miguel S, Guzmán G, Pukkala T (2013)
A comparison of fixed- and mixed-effects modelling in tree growth and yield prediction of an indigenous Neotropical species (Centrolobium tomentosum) in a plantation system. Forest Ecology and Management 291: 249-258.
CrossRef | Gscholar
Moisen GG, Frescino TS (2002)
Comparing five modelling techniques for predicting forest characteristics. Ecological Modelling 157: 209-225.
CrossRef | Gscholar
Näslund M (1947)
Functions and tables for computing the cubic volume of standing trees: pine, spruce and birch in Southern Sweden and in the whole of Sweden. Reports of the Forest Research Institute of Sweden 36, Stockholm, Sweden, pp. 81.
Petterson H (1955)
Barrskogens volymproduktion [Volume production of coniferous forests]. Meddelanden från Statens skogsforskningsinstitut, Stockholm, Sweden, pp. 391. [in Swedish]
Petráš R, Pajtík J (1991)
Sústava česko-slovenských objemových tabuliek drevín [Volume tables for the Czech and Slovak Republic]. Lesnický časopis - Forestry Journal 37: 49-56. [in Slovak]
Räty M, Kangas A (2008)
Localizing general models with classification and regression trees. Scandinavian Journal of Forest Research 23: 419-430.
CrossRef | Gscholar
R Core Team (2015)
R: a language and environment for statistical computing. R foundation for Statistical Computing, Vienna, Austria.
Online | Gscholar
Rejwan C, Collins LJ, Brunner LJ, Shuter BJ, Ridgway MS (1999)
Tree regression analysis on the nesting habitat of smallmouth bass. Ecology 80: 341-348.
CrossRef | Gscholar
Robinson GK (1991)
That BLUP is a good thing: the estimation of random effects. Statistical Science 6: 15-32.
CrossRef | Gscholar
Schmidt M, Kiviste A, Von Gadow K (2011)
A spatially explicit height-diameter model for Scots pine in Estonia. European Journal of Forest Research 130: 303-315.
CrossRef | Gscholar
Sharma M, Parton J (2007)
Height-diameter equations for boreal tree species in Ontario using a mixed-effects modeling approach. Forest Ecology and Management 249: 187-198.
CrossRef | Gscholar
Shifley SR, Fan Z, Kabrick JM, Jensen RG (2006)
Oak mortality risk factors and mortality estimation. Forest Ecology and Management 229: 16-26.
CrossRef | Gscholar
Sironen S, Kangas A, Maltamo M, Kangas J (2003)
Estimating individual tree growth with nonparametric methods. Canadian Journal of Forest Research 33: 444-449.
CrossRef | Gscholar
Soares P, Tomé M (2002)
Height-diameter equation for first rotation eucalypt plantations in Portugal. Forest Ecology and Management 166: 99-109.
CrossRef | Gscholar
Trincado G, VanderSchaaf CL, Burkhart HE (2007)
Regional mixed-effects height-diameter models for loblolly pine (Pinus taeda L.) plantations. European Journal of Forest Research 126: 253-262.
CrossRef | Gscholar
Van Laar A, Akça A (2007)
Forest mensuration. Springer, Dordrecht, Netherlands, pp. 389.
Online | Gscholar
Vonesh EF, Chiinchilli VM (1997)
Linear and nonlinear models for the analysis of repeated measurements. Marcel Dekker, New York, NY, USA, pp. 560.
Weiss J (2007)
Environmental studies 562: Statistics for Environmental Science. Lecture notes, web site.
Online | Gscholar
Yang Y, Huang S (2011)
Comparison of different methods for fitting nonlinear mixed forest models and for making predictions. Canadian Journal of Forest Research 41: 1671-1686.
CrossRef | Gscholar
Zhang L, Bi H, Cheng P, Davis CJ (2004)
Modeling spatial variation in tree diameter-height relationships. Forest Ecology and Management 189: 317-329.
CrossRef | Gscholar
Zhang L, Gove JH, Heath LS (2005)
Spatial residual analysis of six modeling techniques. Ecological Modelling 186: 154-177.
CrossRef | Gscholar
Zhang L, Ma Z, Guo L (2008)
Spatially assessing model errors of four regression techniques for three types of forest stands. Forestry 81: 209-225.
CrossRef | Gscholar

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