Global and local diagnostic analytics for a geostatistical model based on a new approach to quantile regression

Data with spatial dependence are often modeled by geoestatistical tools. In spatial regression, the mean response is described using explanatory variables with georeferenced data. This modeling frequently considers Gaussianity assuming the response follows a symmetric distribution. However, when this assumption is not satisfied, it is useful to suppose distributions with the same asymmetric behavior of the data. This is the case of the Birnbaum–Saunders (BS) distribution, which has been considered in different areas and particularly in environmental sciences due to its theoretical arguments. We propose a geostatistical model based on a new approach to quantile regression considering the BS distribution. Global and local diagnostic analytics are derived for this model. The estimation of model parameters and its local influence are conducted by the maximum likelihood method. Global influence is based on the Cook distance and it is compared to local influence, in both cases to detect influential observations, whose detection and removal can modify the conclusions of a study. We illustrate the proposed methodology applying it to environmental data, which shows this situation changing the conclusions after removing potentially influential observations. A comparison with Gaussian spatial regression is conducted.