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Open AccessArticle

Improving the Modeling of the Height–Diameter Relationship of Tree Species with High Growth Variability: Robust Regression Analysis of Ochroma pyramidale (Balsa-Tree)

Department of Forest Sciences, Federal University of Parana, Campus III, 3400 Lothário Meissner Av., Curitiba 80000-000, Paraná State, Brazil
School of Natural Resources and the Environmental, The University of Arizona, 1064 E. Lowell St., Tucson, AZ 85721, USA
PLANTABAL S.A.—3ACOREMATERIALS, Ofic. 102 Mz. CC3 SL. 120, Complejo Industrial Quevedo, Km 4 ½ vía a Valencia, Quevedo 120501, Ecuador
Author to whom correspondence should be addressed.
Forests 2020, 11(3), 313;
Received: 23 January 2020 / Revised: 4 March 2020 / Accepted: 9 March 2020 / Published: 12 March 2020
(This article belongs to the Special Issue Forest Resources Assessments: Mensuration, Inventory and Planning)
Ochroma pyramidale (Cav. ex. Lam.) Urb. (balsa-tree) is a commercially important tree species that ranges from Mexico to northern Brazil. Due to its low weight and mechanical endurance, the wood is particularly well-suited for wind turbine blades, sporting equipment, boats and aircrafts; as such, it is in high market demand and plays an important role in many regional economies. This tree species is also well-known to exhibit a high degree of variation in growth. Researchers interested in modeling the height–diameter relationship typically resort to using ordinary least squares (OLS) to fit linear models; however, this method is known to suffer from sensitivity to outliers. Given the latter, the application of these models may yield potentially biased tree height estimates. The use of robust regression with iteratively reweighted least squares (IRLS) has been proposed as an alternative to mitigate the influence of outliers. This study aims to improve the modeling of height–diameter relationships of tree species with high growth variation, by using robust regressions with IRLS for data-sets stratified by site-index and age-classes. We implement a split sample approach to assess the model performance using data from Ecuador’s continuous forest inventory (n = 32,279 trees). A sensitivity analysis of six outlier scenarios is also conducted using a subsample of the former (n = 26). Our results indicate that IRLS regression methods can give unbiased height predictions. At face value, the sensitivity analysis indicates that OLS performs better in terms of standard error of estimate. However, we found that OLS suffers from skewed residual distributions (i.e., unreliable estimations); conversely, IRLS seems to be less affected by this source of bias and the fitted parameters indicate lower standard errors. Overall, we recommend using robust regression methods with IRLS to produce consistent height predictions for O. pyramidale and other tree species showing high growth variation. View Full-Text
Keywords: statistical regression; robust methods; M-estimators; site-index curves; balsa-wood statistical regression; robust methods; M-estimators; site-index curves; balsa-wood
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Zea-Camaño, J.D.; Soto, J.R.; Arce, J.E.; Pelissari, A.L.; Behling, A.; Orso, G.A.; Guachambala, M.S.; Eisfeld, R.L. Improving the Modeling of the Height–Diameter Relationship of Tree Species with High Growth Variability: Robust Regression Analysis of Ochroma pyramidale (Balsa-Tree). Forests 2020, 11, 313.

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