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. We discuss parameters interpretation taking into account the non linear structure as well as the spatial dimension. We compute and interpret the semi-elasticities of the shares with respect to the explanatory variables and the spatial impact summary measures.