Estimation of the Basic Wood Density of Native Species Using Mixed Linear Models

Silva, Jeferson Pereira Martins; Fernandes, Márcia Rodrigues de Moura; Gonçalves, Anny Francielly Ataide; Lopes, Isáira Leite e; Silva, Gilson Fernandes da; Cabacinha, Christian Dias

doi:10.1590/2179-8087.038718

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Original Article, Forest Management • Floresta Ambient. 26 (spe1) • 2019 • https://doi.org/10.1590/2179-8087.038718 copy

Estimation of the Basic Wood Density of Native Species Using Mixed Linear Models

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This paper aimed to estimate the basic density (DB) of the wood of Cerrado species using mixed linear models. For performing the DBH measurement, the sampling of 334 individuals was carried out. By keeping the Pilodyn apparatus in the DBH position, two measurements were made on opposite sides. Further, for determining DB, the trees were knocked down, followed by removal of five wood discs at different height of stem positions. For this purpose, two sets of modeling alternatives were proposed, which take into account with and without random effects, employing species as a random effect grouping variable. Thus, it was elucidated that, for the estimation of DB, the mixed model that considered the random effects performed better as compared to the alternative model without random effects. The inclusion of random effects leads to the estimation of DB with high accuracy.

Keywords:
Cerrado stricto sensu; wood quality; regression

Species	Amount	DBH (cm)			H (m)			PIL (mm)
Species	Amount	min	average	max	min	average	max	min	average	max
Luehea paniculata Mart. & Zucc	7	3.50	5.21	10.12	3.4	5.4	8.6	8.0	9.4	11.0
Terminalia fagifolia Mart. & Zucc	29	3.34	5.21	9.33	3.3	4.7	6.7	5.6	9.3	11.5
Copaifera langsdorffii Desf	20	3.02	6.56	13.96	3.2	5.6	8.9	7.5	9.9	15.0
Maytenus sp.	7	3.18	5.79	8.21	3.8	4.9	5.9	6.0	9.1	12.5
Heteropterys byrsonimifolia A. Juss	120	2.93	4.80	14.45	2.7	4.3	6.8	4.8	8.5	12.0
Tocoyena formosa Cham. & Schltdl	19	3.34	4.56	6.94	2.7	4.2	6.5	6.5	8.5	14.0
Machaerium opacum Vog.	55	3.50	6.19	16.39	1.9	4.0	6.3	4.2	7.0	10.5
Machaerium sp	7	3.92	5.45	7.32	3.9	6.8	8.8	6.5	8.0	9.0
Curatela americana L	22	3.72	6.39	13.81	2.0	3.5	5.8	8.5	13.4	18.0
Byrsonima heterophyla	13	3.25	6.43	12.11	3.2	4.7	6.2	5.5	10.3	14.5
Combretum leprosum Mart	12	3.63	5.37	10.82	3.0	4.1	5.5	7.8	11.2	13.5
Dalbergia brasiliensis Vog	20	3.02	5.69	10.89	3.1	5.0	7.3	7.0	10.1	12.5
Magonia pubescens A.St & Hil	7	3.02	4.52	7.00	3.3	4.3	5.9	6.5	7.5	9.0

Statistics	Formulas	Nº
Adjusted coefficient of determination	${\bar{R}}^{2} = 1 - (\frac{n - 1}{n - p}) [1 - (1 - \frac{{\sum_{i = 1}^{n} (Y_{i} - {\hat{Y}}_{i})}^{2}}{{\sum_{i = 1}^{n} (Y_{i} - {\bar{Y}}_{i})}^{2}})]$	(13)
relative bias	$B (%) = \frac{100}{\bar{Y}} \frac{\sum_{i = 1}^{n} Y_{i} - \sum_{i = 1}^{n} {\hat{Y}}_{i}}{n}$	(14)
Root mean square relative error	$R M S E (%) = \frac{100}{\bar{Y}} \sqrt{\frac{{\sum_{i = 1}^{n} (Y_{i} - {\hat{Y}}_{i})}^{2}}{n}}$	(15)

Model	Intercept	PIL	DBH	H
1	0.763422^* * significance level at 5% probability by the student t test.	-0.017727*
2	0.589491*		0.003167^ns
3	0.590297*			0.003671^ns
4	0.736935*	-0.019765*	0.008264*
5	0.734533*	-0.018225*		0.007518*
6	0.730152*	-0.019782*	0.007742*	0.002201^ns

Model	Fitting
Model	RMSE%	${\bar{R}}^{2}_{}$	RMSE%	BIAS	${\bar{R}}^{2}_{}$
1	8.35	0.37	7.35	-0.14	0.47
2	10.40	0.01	10.43	0.93	0.00
3	10.48	0.00	10.34	0.85	0.00
4	7.86	0.44	7.64	-0.12	0.44
5	8.21	0.38	7.49	-0.22	0.45
6	7.85	0.43	7.67	-0.15	0.43

Model	Fitting			Validation
Model	RMSE%	BIAS	${\bar{R}}^{2}_{}$	RMSE%	BIAS	${\bar{R}}^{2}_{}$
7	5.81	0.04	0.69	5.60	0.75	0.70
8	5.96	0.04	0.67	5.90	1.07	0.67
9	5.88	0.03	0.68	5.79	1.04	0.69
10	5.56	0.02	0.72	5.86	0.77	0.68
11	5.48	0.01	0.73	5.66	0.73	0.70
12	5.40	0.02	0.73	5.74	0.72	0.68

	Value	Std.Error	t-value	p-value
(Intercept)	0.6309446	0.026086759	24.186392	0
PIL	-0.0068727	0.002453106	-2.801615	0.0055
H	0.0080633	0.003663857	2.200755	0.0288

Group	$γ_{0 j}$	$γ_{1 j}$	$γ_{2 j}$
Luehea paniculata Mart. & Zucc	-0.00671568	-0.005109	-0.00024296
Terminalia fagifolia Mart. & Zucc	-0.04778732	0.0054803	0.00088041
Copaifera langsdorffii Desf	0.05640130	-0.006009	-0.00249756
Maytenus sp.	0.01573392	0.0022004	-0.00108434
Heteropterys byrsonimifolia A. Juss	-0.02077278	0.0024771	-0.00100297
Tocoyena formosa Cham. & Schltdl	0.00041378	0.0041583	-0.00088258
Machaerium opacum Vog.	0.04630224	0.0041536	-0.00154117
Machaerium sp	0.04079368	0.0031197	-0.01204169
Curatela americana L	-0.07278023	-0.004694	0.01215873
Byrsonima heterophyla	-0.00077800	-0.006311	0.00960528
Combretum leprosum Mart	-0.02528282	-0.002264	0.00252822
Dalbergia brasiliensis Vog	-0.06963246	0.0018974	0.00301561
Magonia pubescens A.St & Hil	0.084104259	0.0009007	-0.00889499

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[1] Jeferson Pereira Martins SilvaDepartamento de Ciências Florestais e da Madeira, Universidade Federal do Espírito Santo – UFES, Av. Governador Carlos Lindemberg, Centro, CEP 29550-000, Jerônimo Monteiro, ES, Brasil e-mail: jefersonsb09@hotmail.com