Derivative-based spatial mediation with INLA-SPDE

In many applied fields, it may be of interest to evaluate mediational mechanisms occurring in spatial domains. The approaches proposed so far in the literature to address this issue deal with areal data and often consider linear models. In this paper, we propose an approach to assess mediation in the presence of geostatistical data by combining the integrated nested Laplace approximation (INLA) with a derivative-based approach for mediation analysis, which allows one to estimate indirect effects also in the case of nonlinear models. We investigate the effect of ignoring spatial processes in the mediator and the outcome models through a simulation study, focusing also on the case of correlated processes. To show the usefulness of our approach, we also provided an ecological application.