There are considerable challenges in analyzing large-scale compositional data. In this paper, we introduce the Spike-and-Slab Lasso linear regression in the presence of compositional covariates for parameter estimation and variable selection. We consider the well-known isometric log-ratio (ilr) coordinates to avoid misleading statistical inference. The separable and non-separable (adaptative) Spike-and-Slab Lasso penalties are compared to verify the advantages of each approach. The proposed method is illustrated on simulated and on real Brazilian child malnutrition data.
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