Covariates impacts in spatial autoregressive models for compositional data

Abstract

Spatial simultaneous autoregressive models have been adapted to model data with both a geographic and a compositional nature. Interpretation of parameters in such a model is intricate. Indeed, when the model involves a spatial lag of the dependent variable, this interpretation must focus on the so-called impacts rather than on parameters and when moreover the dependent variable of this model is of a compositional nature, this interpretation should be based on elasticities or semi-elasticities. Combining the two difficulties, we provide exact formulas for the evaluation of these elasticity-based impact measures which have been only approximated so far in some applications. We also discuss their decomposition into direct and indirect impacts taking into account the compositional nature of the dependent variable. Finally, we also propose more local summary measures as exploratory tools that we illustrate on a toy data set and a case study.

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Reference

Thibault Laurent, Christine Thomas-Agnan, and Anne Ruiz-Gazen, “Covariates impacts in spatial autoregressive models for compositional data”, TSE Working Paper, n. 20-1162, November 2020, revised October 2021.