A spatial autoregressive graphical model

Abstract

Within the statistical literature, a significant gap exists in methods capable of modelling asymmetric multivariate spatial effects that elucidate the relationships underlying complex spatial phenomena. For such a phenomenon, observations at any location are expected to arise from a combination of within- and between-location effects, where the latter exhibit asymmetry. This asymmetry is represented by heterogeneous spatial effects between locations pertaining to two different categories, that is, a feature inherent to each location in the data, such that based on the feature label, asymmetric spatial relations are postulated between neighbouring locations with different labels. Our novel approach synergises the principles of multivariate spatial autoregressive models and the Gaussian graphical model. This synergy enables us to effectively address the gap by accommodating asymmetric spatial relations, overcoming the usual constraints in spatial analyses. However, the resulting flexibility comes at a cost: the spatial effects are not identifiable without either prior knowledge of the underlying phenomenon or additional parameter restrictions. Using a Bayesian-estimation framework, the model performance is assessed in a simulation study. We apply the model on intercropping data, where spatial effects between different crops are unlikely to be symmetric, in order to illustrate the usage of the proposed methodology. An R package containing the proposed methodology can be found on https://CRAN.R-project.org/package=SAGM.