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.

Reduction of Sample Size in the Soil Physical-Chemical Attributes Using the Multivariate Effective Sample Size

“…The increase in the standard error of the parameters after sample resizing indicates that the reduction in the number of sample points influenced the spatial dependence structure of the physical-chemical attributes of the soil (Table 2). Moreover, regarding the standard error values following the magnitude of the estimated parameter, this characteristic is also perceived in the results of Schemmer et al (2017) and Fagundes et al (2018), who used in their studies both the Gaussian linear spatial model (as well as this study), and the Slash and t-Student linear spatial models, applied to variables related to soil and plants.…”