Q-Function-Based Diagnostic and Spatial Dependence in Reparametrized t-Student Linear Model

Characterizingthe spatial variability of agricultural data is a fundamental step in precision agriculture, especially in soil management and the creation of differentiated management units for increasing productivity. Modeling the spatial dependence structure using geostatistical methods is of great importance for efficiency, estimating the parameters that define this structure, and performing kriging-based interpolation. This work presents diagnostic techniques for global and local influence and generalized leverage using the displacement of the conditional expectation of the logarithm of the joint-likelihood, called the Q-function. This method is used to identify the presence of influential observations that can interfere with parameter estimations, geostatistics model selection, map construction, and spatial variability. To study spatially correlated data, we used reparameterized t-Student distribution linear spatial modeling. This distribution has been used as an alternative to the normal distribution when data have outliers, and it has the same form of covariance matrix as the normal distribution, which enables a direct comparison between them. The methodology is illustrated using one real data set, and the results showed that the modeling was more robust in the presence of influential observations. The study of these observations is indispensable for decision-making in precision agriculture.