Birnbaum-Saunders spatial modelling and diagnostics applied to agricultural engineering data

Applications of statistical models to describe spatial dependence in geo-referenced data are widespread across many disciplines including the environmental sciences. Most of these application assume that the data follow a Gaussian distributions. However, in many of them the normality assumption, and even a more general assumption of symmetry, are not appropriate. In non-spatial applications, where the data are uni-modal and positively skewed, the Birnbaum-Saunders distribution has excelled. This paper proposes a spatial log-linear model based in the Birnbaum-Saunders distribution. Model parameters are estimated using the maximum likelihood method. Local influence diagnostics are derived to assess the sensitivity of the estimators to perturbations in the response variable. As illustration, the proposed model and its diagnostics are used to analyse a real-world agricultural data-set, where the spatial variability of phosphorus concentration in the soil is considered- which is extremely important for agricultural management.