GAUSSIAN SPATIAL LINEAR MODEL OF SOYBEAN YIELD USING BOOTSTRAP METHODS

Dalposso, Gustavo H.; Uribe-Opazo, Miguel A.; Johann, Jerry A.; Galea, Manuel; Bastiani, Fernanda De

doi:10.1590/1809-4430-Eng.Agric.v38n1p110-116/2018

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Sumário

Scientific Paper, Topography, Photogrammetry and Remote Sensing • Eng. agríc. (Online) 38 (1) • Jan-Feb 2018 • https://doi.org/10.1590/1809-4430-Eng.Agric.v38n1p110-116/2018 copy

GAUSSIAN SPATIAL LINEAR MODEL OF SOYBEAN YIELD USING BOOTSTRAP METHODS

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

This study aims to quantify the uncertainties associated to the parameters of a Gaussian spatial linear model (GSLM) and the assumption of normality residuals in the modeling of the spatial dependence of the soybean yield as a function of soil chemical attributes. The spatial bootstrap methods were used to determine the point and interval estimators associated with the model parameters. Hypothesis tests were carried out on the significance of the model parameters and the quantile-quantile probability plot was elaborated to verify the data normality. The uncertainties associated to the parameters of the spatial dependence structure were quantified and the potassium content, phosphorus content and soil pH covariates were significant to explain the soybean yield mean. These covariates were used in the elaboration of a new model, which provided the elaboration of a contour map of soybean yield. Analysis of the quantile-quantile plot indicated that soybean yield data follow a normal probability distribution.

KEYWORDS
geostatistics; spatial resampling; spatial variability

Statistics	Yield	Ca	Mg	K	P	Mn	pH
Minimum	2.15	2.30	0.85	0.09	5.80	37.00	390
Q₁	2.95	5.49	1.99	0.22	13.40	62.00	4.70
Median	3.23	6.37	2.53	0.31	17.40	71.00	5.00
Average	3.25	6.51	2.64	0.33	18.20	74.50	5.00
Q3	3.53	7.48	3.10	0.40	21.40	84.00	5.25
Maximum	4.51	13.10	5.75	1.11	52.40	140.00	7.10
SD	0.47	1.64	0.90	0.15	7.56	19.36	0.45
CV (%)	14.30	25.20	34.30	47.10	41.50	25.98	9.06

k	$\hat{φ}$	$\hat{φ}$	â	CrV	LML	Tr
0.5	0.1783	37.2544	111.6041	0.2616456	-54.56541	1.298518
1.5	0.1783	23.7864	112.8393	0.2589309	-54.07624	1.285411
2.5	0.1785	18.8569	111.6076	0.2576171	-53.89274	1.277847
4.5	0.1787	14.2486	109.8489	0.2563692	-53.73963	1.270118

${\hat{β}}_{o}$	${\hat{β}}_{C a}$	${\hat{β}}_{M g}$	${\hat{β}}_{K}$	${\hat{β}}_{P}$	${\hat{β}}_{M n}$	${\hat{β}}_{P H}$	${\hat{φ}}_{1}$	${\hat{φ}}_{2}$	${\hat{φ}}_{3}$
4.54	0.06	0.06	0.85	-0.01	0.00	-0.44	0.00	0.18	14.25
(6.8e-1)	(5e-2)	(6e-2)	(3e-1)	(1e-3)	(1e-3)	(1.8e-1)	(8e-2)	(9e-2)	(9.8e-1)

Method	Parameter	Min	Q₁	Median	Average	Q₃	Max	SD	As	L_L	U_L
SB	β ₀	2.50	4.03	4.54	4.53	4.99	7.16	0.71	0.15	3.15	5.94
	β_Ca	-0.12	0.02	0.05	0.05	0.09	0.27	0.06	0.31	-0.04	0.17
	β_Mg	-0.16	0.02	0.07	0.06	0.11	0.28	0.07	-0.11	-0.07	0.20
	β_K	-0.05	0.64	0.84	0.84	1.05	1.83	0.30	0.01	0.25	1.43
	β_P	-0.04	-0.02	-0.01	-0.01	-0.01	0.01	0.01	-0.04	-0.03	-0.00
	β_Mn	-0.00	0.00	0.00	0.00	0.01	0.01	0.00	-0.02	-0.00	0.01
	β_PH	-1.14	-0.56	-0.43	-0.43	-0.31	0.15	0.19	-0.15	-0.80	-0.09
	φ ₁	0.00	0.00	0.00	0.05	0.10	0.24	0.06	0.90	0.00	0.18
	φ ₂	0.00	0.05	0.14	0.12	0.17	0.30	0.07	-0.47	0.00	0.21
	φ ₃	0.00	13.00	16.40	22.30	21.40	283.00	24.80	4.52	11.40	26.20
PSB	β ₀	2.25	4.13	4.55	4.53	4.98	6.37	0.68	-0.09	3.12	5.86
	β_Ca	-0.14	0.02	0.06	0.06	0.10	0.23	0.06	-0.18	-0.05	0.17
	β_Mg	-0.18	0.02	0.06	0.06	0.10	0.26	0.06	0.01	-0.06	0.19
	β_K	-0.08	0.66	0.86	0.86	1.06	2.06	0.31	-0.00	0.23	1.49
	β_P	-0.04	-0.02	-0.01	-0.01	-0.01	0.01	0.01	0.04	-0.03	-0.00
	β_Mn	-0.00	0.00	0.00	0.00	0.01	0.01	0.00	-0.04	-0.00	0.01
	β_PH	-0.97	-0.56	-0.44	-0.44	-0.33	0.13	0.18	0.09	-0.79	-0.07
	φ ₁	0.00	0.00	0.00	0.05	0.10	0.22	0.06	0.94	0.00	0.18
	φ ₂	0.00	0.06	0.14	0.12	0.17	0.28	0.07	-0.50	0.00	0.22
	φ ₃	0.00	13.20	16.70	23.10	21.70	232.20	24.90	3.99	11.70	27.70

Null hypothesis	LR	p-value
β_Ca = 0	1.18	0.2033
β_Mg = 0	0.86	0.2782
β_K = 0	7.68	0.0030 *
β_P =0	4.40	0.0211 *
β_Mn = 0	2.76	0.0604
β_PH = 0	5.66	0.0098 *

${\hat{β}}_{o}$	${\hat{β}}_{K}$	${\hat{β}}_{P}$	${\hat{β}}_{P H}$	${\hat{φ}}_{1}$	${\hat{φ}}_{2}$	${\hat{φ}}_{3}$
3.99	0.84	-0.01	-0.16	0.00	0.19	13.14
(4.9e-1)	(3e-1)	(1e-3)	(1e-1)	(11e-1)	(1.2e-1)	(9.3e-1)

Associação Brasileira de Engenharia Agrícola SBEA - Associação Brasileira de Engenharia Agrícola, Departamento de Engenharia e Ciências Exatas FCAV/UNESP, Prof. Paulo Donato Castellane, km 5, 14884.900 | Jaboticabal - SP, Tel./Fax: +55 16 3209 7619 - Jaboticabal - SP - Brazil
E-mail: revistasbea@sbea.org.br

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[1] *Corresponding author. Universidade Tecnológica Federal do Paraná/ Toledo - PR, Brasil. E-mail: gustavodalposso@utfpr.edu.br