Mixed-effect non-linear modelling for diameter estimation along the stem of<i>Tectona grandis</i>in mid-western Brazil

Lanssanova, Luciano Rodrigo; Machado, Sebastião do Amaral; Garrett, Alexandre Techy de Almeida; Bonete, Izabel Passos; Pelissari, Allan Libanio; Filho, Afonso Figueiredo; Silva, Franciele Alba da; Ciarnoschi, Lucas Dalmolin

doi:10.2989/20702620.2018.1531279

Cited by 7 publications

(2 citation statements)

References 25 publications

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“…Kozak [1] model had the highest adjusted determination coefficient among the four optimal variable-exponent taper equations while considering tree-level effect and nested two-level effect. The inclusion of an intra-group variance-covariance matrix in the mixed effect model can eliminate the autocorrelation, which is consistent with the results of previous studies [16,44,51,52]. It can be found that the fitting residual scatterplot of taper model based on common least square method and plot-level effect shows significant positive correlation, while the residual diagram of mixed model based on tree-level effect and nested two-level effect both have removed this trend in a large part.…”

Section: Discussionsupporting

confidence: 90%

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Zhang

Sun

Duan

et al. 2021

Forests

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A variable-exponent taper equation was developed for Chinese fir (Cunninghamia lanceolate (Lamb.) Hook.) trees grown in southern China. Thirty taper equations from different groups of models (single, segmented, or variable-exponent taper equation) were compared to find the excellent basic model with S-plus software. The lowest Akaike information criteria (AIC), Bayesian information criteria (BIC), and -2loglikelihood (-2LL) was chosen to determine the best combination of random parameters. Single taper models were found having the lowest precision, and the variable-exponent taper equations had higher precision than the segmented taper equations. Four variable-exponent taper models that developed by Zeng and Liao, Bi, Kozak, Sharma, and Zhang respectively, were selected as basic model and had no difference in fit statistics between them. Compared with the model without seldom parameter, the nonlinear mixed-effects (NLME) model improves the fitting performance. The plot-level NLME model was found not to remove the residual autocorrelation. The tree-level and two-level NLME model had better simulation accuracy than the plot-level NLME model, and there were no significant differences between the tree-level and two-level NLME model. Variable-exponent taper model developed by Kozak showed the best performance while considering two-level or tree-level NLME model, and produced better predictions for medium stems compared to lower and upper stems.

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Section: Discussionsupporting

confidence: 90%

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Zhang

Sun

Duan

et al. 2021

Forests

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“…In modelling the stem taper of Betula pubescens in north-west Spain, the function received recommendations [25]; it also became the option of choice for Quercus glauca in South Korea [50]. It was recommended for modelling stem taper of several tropical species in the area of the Philippines [51], as well as for estimating stem diameter of Tectona grandis in mid-western Brazil [52]. The range of species for which the Kozak function has been recommended, as well as the number of regions for which it has been used, both make it possible to deduce that the taper function is a species-specific function.…”

Section: Discussionmentioning

confidence: 99%

Evaluation of Different Calibration Approaches for Merchantable Volume Predictions of Norway Spruce Using Nonlinear Mixed Effects Model

Adamec

Adolt

Drápela

et al. 2019

Forests

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Research Highlights: Determination of merchantable wood volume is one of the key preconditions for sustainable forest management. This study explores accuracy of calibrated predictions of merchantable wood volume of Norway spruce (Picea abies (L.) H. Karst.) using stem taper curves (STC) in a form of a mixed model. Background and Objectives: The study is devoted to the determination of merchantable wood volume (over bark) of individual standing stems based on the integration of an STC model calibrated using upper diameter measurements. Various options of upper diameter measurement were tested and their impact on the accuracy of merchantable wood volume prediction was evaluated. Materials and Methods: To model stem taper curves, a Kozak 02 function was applied in a form of a nonlinear, mixed effects model. Accuracies of calibrated merchantable wood volume predictions obtained through remote (optical) upper diameter measurements were compared to accuracies corresponding to contact measurements by a caliper. The performance of two alternative methods used in the Czech National Forest Inventory (NFI) and forestry practice, involving diameter at breast height and total tree height as the only predictors, were also tested. The contact measurements were performed at identical stem positions after felling the respective sample tree. The calibration was done in order to account for factors inherent in particular location, and, optionally, also in a particular sample stem (within the respective location). Input data was sourced as part of a dedicated survey involving the entire territory of the Czech Republic. In total, 716 individual spruce trees were measured, felled and analysed at 169 locations. Results: In general, the best merchantable volume predictions were obtained by integrating the STC fitted (and calibrated) by minimising errors of stem cross-sectional areas instead of diameters. In terms of calibrated predictions, using single-directional, caliper measurement of upper diameter at 7 m (after felling) led to the best accuracy. In this case, the observed mean bias of merchantable volume prediction was only 0.63%, indicating underestimation. The best optical calibration strategy involved upper diameter measurements at two heights (5 and 7 m) simultaneously. Bias of this volume prediction approach was estimated at 2.1%, indicating underestimation. Conclusions: Concerning the prediction of merchantable stem volume of standing Norway spruce trees, STC calibration using two optical upper diameter measurements (at 5 and 7 m) was found to be practically applicable, provided a bias up to 3.7% can be accepted. This method was found to be more accurate than the existing national alternatives using diameter at breast height and the total tree height as the only predictors.

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Volumetric model estimation using regression and geostatistical application for the Tectona grandis stands in Sabah

Kiram

Yunus

Japarudin³

et al. 2023

The 5TH ISM INTERNATIONAL STATISTICAL CONFERENCE 2021 (ISM-V): Statistics in the Spotlight: Navigating the New Norm

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Mixed-effect non-linear modelling for diameter estimation along the stem ofTectona grandisin mid-western Brazil

Cited by 7 publications

References 25 publications

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Variable-Exponent Taper Equation Based on Multilevel Nonlinear Mixed Effect for Chinese Fir in China

Evaluation of Different Calibration Approaches for Merchantable Volume Predictions of Norway Spruce Using Nonlinear Mixed Effects Model

Volumetric model estimation using regression and geostatistical application for the Tectona grandis stands in Sabah

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