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

ABSTRACT: 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.

摘要：在土壤化学属性的地质统计建模中，数据集内的一个或多个强影响观测值可能会损害插值地图的构建精度与质量。规避该问题的可行方案之一是采用基于重尾分布的高鲁棒性模型。据此，本研究提出一种基于斜线分布（slash distribution）的空间线性模型（SSLM），用于表征大豆产量作为土壤化学属性函数的空间变异性。本研究采用似然比统计量（likelihood ratio statistic, LR）对模型关联参数的显著性进行验证；针对大豆产量响应变量与线性预测项，通过局部影响分析评估了极大似然估计量的敏感性。基于所提模型，本研究分析了采集自巴西巴拉那州西部一处商用谷物生产区域（面积127.18公顷）的实测数据。结果表明，斜线分布可适配数据集分布的高峰度特征，且似然比检验证实，磷、钾、pH值与有机质这几项土壤化学属性对SSLM均具有显著影响。诊断分析显示，样本集中的异常值并未对参数估计过程产生影响。在纳入异常值和/或强影响观测值的场景下，基于本模型构建的插值地图未受显著影响。综上，SSLM可作为研究土壤化学属性驱动下大豆产量变异性的高鲁棒性备选方案，为探究区域农业生产潜力提供了可行路径。