Spatial simultaneous autoregressive models for compositional data: application to land use

Econometric land use models study determinants of land use shares of different classes: “agriculture”, “forest”, “urban” and “other” for example. Land use shares have a compositional nature as well as an important spatial dimension. We compare two compositional regression models with a spatial autoregressive nature in the framework of land use. We study the impact of the choice of coordinate space and prove that a choice of coordinate representation does not have any impact on the parameters in the simplex as long as we do not impose further restrictions. We discuss parameters interpretation taking into account the non-linear structure as well as the spatial dimension. In order to assess the explanatory variables impact, we compute and interpret the semi-elasticities of the shares with respect to the explanatory variables and the spatial impact summary measures