Local influence for spatial analysis of soil physical properties and soybean yield using student's t-distribution

Assumpção, Rosangela Aparecida Botinha; Uribe-Opazo, Miguel Ángel; Galea, Manuel

doi:10.1590/s0100-06832011000600008

Cited by 7 publications

(6 citation statements)

References 12 publications

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“…In a similar manner, influence analysis was performed on the Q-function (Equation 3), which was considered the reference measure |h [Q]max |. For more details, see Zhu and Lee (2001) and Assumpção et al (2011Assumpção et al ( , 2014.…”

Section: Local Influence Analysismentioning

confidence: 99%

“…To evaluate the influence on the linear predictor, we considered the methodology presented by Assumpção et al (2011) applied to the SSLM (Equation 1). In this case, maximum influence directions were denoted by L p and Q p .…”

Section: Local Influence Analysismentioning

confidence: 99%

“…Regarding georeferenced data, Uribe-Opazo et al (2012) evaluated the sensitivity of covariance function estimators and linear predictors under small dataset perturbations and/or a spatial linear model with a normal distribution. Assumpção et al (2011) presented techniques for local influence for spatial analysis of soil physical properties and soybean yield using Student's t-distribution. Grzegozewski et al (2013) considered a Gaussian spatial linear model (GSLM) and information about soil macro-and micronutrients in evaluating the effects of influential observations on spatial model selection, parameter estimation by maximum likelihood, and characterization of spatial continuity of soybean yield.…”

Section: Introductionmentioning

confidence: 99%

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Slash Spatial Linear Modeling: Soybean Yield Variability as a Function of Soil Chemical Properties

Fagundes

Uribe-Opazo

Guedes

et al. 2018

Rev. Bras. Ciênc. Solo

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In geostatistical modeling of soil chemical properties, one or more influential observations in a dataset may impair the construction of interpolation maps and their accuracy. An alternative to avoid the problem would be to use most robust models, based on distributions that have heavier tails. Therefore, this study proposes a spatial linear model based on the slash distribution (SSLM) in order to characterize the spatial variability of soybean yields as a function of soil chemical properties. The likelihood ratio statistic (LR) was applied to verify the significance of parameters associated with the model. We evaluated the sensitivity of the maximum likelihood estimators by means of local influence analysis for both the soybean response and the linear predictor. In the proposed model, we analyzed data gathered from a commercial grain production area (127.18 ha) located in the western part of the state of Paraná (Brazil). The results showed that the slash distribution allowed us to adjust the high kurtosis of the data set distribution and the LR test confirmed that the soil chemical properties of phosphorus, potassium, pH, and organic matter were significant for the SSLM. Diagnostic analysis indicated that the atypical value of the sample set was not influential in the parameter estimation process. Construction of the interpolation map based on the proposed model is not affected when considering the atypical and/or influential observations. Thus, SSLM becomes a robust alternative in the study of soybean yield variability as a function of soil chemical properties, making it possible to investigate the productive potential of the areas.

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Section: Local Influence Analysismentioning

confidence: 99%

Section: Local Influence Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Slash Spatial Linear Modeling: Soybean Yield Variability as a Function of Soil Chemical Properties

Fagundes

Uribe-Opazo

Guedes

et al. 2018

Rev. Bras. Ciênc. Solo

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“…According to Manghi et al (2016), class models of symmetric distributions allow reducing the influence of discrepant data, incorporating additional parameters that adjust the kurtosis of data distribution. The t-Student distribution belongs to the class of symmetric distributions and exhibits symmetry properties, greater flexibility regarding the degree of kurtosis, and has as additional shape parameter 0 v  , which defines the degrees of freedom of distribution (Assumpção et al, 2011;2014). Lange et al (1989) propose a reparametrization of the t-Student distribution from a transformation in the shape parameter v , allowing us to assume the existence of the second finite moment and thus a more direct comparison with the normal distribution.…”

Section: Introductionmentioning

confidence: 99%

Spatial Variability of Soybean Yield Through a Reparameterized T-Student Model

et al. 2017

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ABSTRACT:The t-Student distribution has been used to the spatial dependence modelling of soybean yield as an alternative to the normal distribution, being used for data with heavier tails or discrepant values. However, a usual Student t-distribution does not allow direct comparisons of geostatistical methods with a normal distribution. The aim of this study was to assess the soybean yield spatial variability through a reparameterized t-Student linear model, comparing the results with those of a Gaussian linear model. For parameter estimation, a complete maximum likelihood (CML) method was used through an expectation-maximization (EM) algorithm. The maps constructed with both reparameterized t-Student and normal distributions are dissimilar and present a kappa index (K) equivalent to 0.64. The reparameterized t-Student distribution is an alternative in studying data with discrepant values, showing the ability to decrease the influence of these points.

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“…BORSSOI et al (2009) usaram técnicas de diagnósticos de influência local em modelos espaciais gaussianos empregados em geoestatística, buscando avaliar a sensibilidade dos estimadores de máxima verossimilhança. ASSUMPÇÃO et al (2011) estudaram técnicas de influência local para dados com distribuição t-Student, considerando a perturbação aditiva na variável resposta e os graus de liberdade fixos. BORSSOI et al (2011b) usaram técnicas de influência local para avaliar pontos influentes em dados agrícolas.…”

Section: Introductionunclassified

Influência local em um modelo espacial linear da produtividade da soja utilizando distribuição t-Student

et al. 2013

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RESUMO:O uso das ferramentas da geoestatística, aliadas à agricultura de precisão permitem o acompanhamento das áreas agrícolas produtoras de soja, estabelecendo as relações de dependência espacial entre os pontos amostrados. A modelagem da estrutura de variabilidade espacial possibilita a construção de mapas temáticos dos atributos estudados, utilizando como método de interpolação a krigagem. Porém, a presença de valores atípicos entre os elementos amostrais pode influenciar na construção e interpretação desses mapas. A distribuição de probabilidades t-Student tem sido utilizada na tentativa de diminuir a influência dos valores atípicos durante a estimativa dos parâmetros de dependência espacial, por ter caudas mais pesadas que a distribuição normal. A detecção dos valores influentes na área em estudo, por meio da análise de diagnósticos de influência local, confere maior confiabilidade na utilização dos mapas gerados, corroborando a aplicação de insumos. Deste modo, o objetivo deste trabalho foi aplicar as técnicas de influência local em dados espacialmente referenciados, com os modelos de perturbação aditiva e utilizando a matriz escala, considerando a distribuição t-Student n-variada. Foi utilizado um modelo espacial linear para o estudo de dados da produtividade da soja em função da altura média de plantas e do número médio de vagens por planta. As técnicas de influência local foram eficientes para detectar pontos que influenciam na escolha do modelo geoestatístico, nas estimativas dos parâmetros e na construção do mapa temático. PALAVRAS-CHAVE: máxima verossimilhança; variabilidade espacial; diagnósticos. LOCAL INFLUENCE IN A LINEAR MODEL SPACE USING SOYBEAN PRODUCTIVITY WITH T-STUDENT DISTRIBUITIONABSTRACT: The use of geostatistical tools combined with precision agriculture, allow the monitoring of agricultural soybean producing areas, establishing relationships of spatial dependence between the sampled points. The modeling of spatial variability structure enables the construction of thematic maps of the attributes studied, using the kriging as the interpolation method. However, the presence of outliers among the elements sampling can influence the construction and interpretation of these maps. The distribution of t-Student probability has been used in attempts to reduce the influence of atypical points in the estimation of parameters of spatial dependence, having heavier tails than the normal distribution of probabilities. The detection of influential points in the study area, through the analysis of local influence diagnostics, provides greater reliability in the use of maps, providing an efficient use of inputs. Then, the objective was to apply the techniques of local influence on spatially referenced data with models of disturbance and using the matrix additive scale, considering the distribution t-Student n-variate. It was used a linear spatial model for the study of soybean yield data as a function of average plant height and number of pods per plant. The local influence techniques were effective to...

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Local influence for spatial analysis of soil physical properties and soybean yield using student's t-distribution

Cited by 7 publications

References 12 publications

Slash Spatial Linear Modeling: Soybean Yield Variability as a Function of Soil Chemical Properties

Slash Spatial Linear Modeling: Soybean Yield Variability as a Function of Soil Chemical Properties

Spatial Variability of Soybean Yield Through a Reparameterized T-Student Model

Influência local em um modelo espacial linear da produtividade da soja utilizando distribuição t-Student

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