Sufficient dimension reduction for compositional data
- Tomassi, Diego Rodolfo
- Forzani, Liliana Maria
- Duarte, Sabrina Lorena
- Pfeiffer, Ruth M.
DOIAbstract
Recent efforts to characterize the human microbiome and its relation to chronic diseases have led to a surge in statistical development for compositional data. We develop likelihood-based sufficient dimension reduction methods (SDR) to find linear combinations that contain all the information in the compositional data on an outcome variable, i.e., are sufficient for modeling and prediction of the outcome. We consider several models for the inverse regression of the compositional vector or transformations of it, as a function of outcome. They include normal, multinomial, and Poisson graphical models that allow for complex dependencies among observed counts. These methods yield efficient estimators of the reduction and can be applied to conti...
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