We present global diagnostics techniques to assess the influence of observations on spatial linear mixed models. We review concepts of Cook's distance based on the likelihood and Q-function in the framework of geostatistical models. The main novelty in spatial statistics, is that we obtain more details to evaluate the sensitivity of the model by splitting the information we have related to the covariance matrix, identifying if the influential observation affects variance error or if it also affects the parameters that determine the spatial dependence structure, i.e. if it changes the geostatistical model selected. A simulation study shows the behavior of this methodology and an application to real data illustrates the methodology developed. (C) 2018 Elsevier B.V. All rights reserved.