  Within the statistical literature, there is a lack of methods that allow for
asymmetric multivariate spatial effects to model relations underlying complex
spatial phenomena. Intercropping is one such phenomenon. In this ancient
agricultural practice multiple crop species or varieties are cultivated
together in close proximity and are subject to mutual competition. To properly
analyse such a system, it is necessary to account for both within- and
between-plot effects, where between-plot effects are asymmetric. Building on
the multivariate spatial autoregressive model and the Gaussian graphical model,
the proposed method takes asymmetric spatial relations into account, thereby
removing some of the limiting factors of spatial analyses and giving
researchers a better indication of the existence and extend of spatial
relationships. Using a Bayesian-estimation framework, the model shows promising
results in the simulation study. The model is applied on intercropping data
consisting of Belgian endive and beetroot, illustrating the usage of the
proposed methodology. An R package containing the proposed methodology can be
found on https:// CRAN.R-project.org/package=SAGM.

Methodology