Birnbaum-Saunders spatial regression models: Diagnostics and application to chemical data

Geostatistical modelling is widely used to describe data with spatial dependence structure. Such modelling often assumes a Gaussian distribution, an assumption which is frequently violated due to the asymmetric nature of variables in diverse applications. The Birnbaum-Saunders distribution is asymmetrical and has several appealing properties, including theoretical arguments for describing chemical data. This work examines a Birnbaum-Saunders spatial regression model and derives global and local diagnostic methods to assess the influence of atypical observations on the maximum likelihood estimates of its parameters. Modelling and diagnostic methods are then applied to experimental data describing the spatial distribution of magnesium and calcium in the soil in the Parana state of Brazil. This application shows the importance of such a diagnostic analysis in spatial modelling with chemical data.