On the effects of spatial relationships in spatial compositional multivariate models

Spatial compositional multivariate models have recently been developed in environmental and ecological research. However, little attention has been paid to how the results of these models are affected by different settings of spatial relationships, which are generally formulated using the so-called “spatial weight matrix.” Many studies set their models to first order contiguity, which is analogous to the moves of a rook in chess, without examining the effects of this choice of spatial relationship type. In this study, we examine the formulation of spatial relationship in spatial compositional multivariate models. We investigate the question of prediction accuracy through an empirical illustration that uses land use compositional data and compositional multivariate conditionally autoregressive models with different spatial relationship formulations. The results indicate that the wide range and smoothed setting of spatial relationship is preferable for prediction accuracy in our empirical case. The results for each variate suggest that the preferable relationships vary: the preferable setting on the total is not always preferable for each variate. Improving prediction accuracy requires that we consider a different spatial weight for each variate in multivariate cases.