Open AccessSufficient dimension reduction for compositional data
Author(s) -
Diego Tomassi,
Liliana Forzani,
Sabrina Duarte,
Ruth M. Pfeiffer
Publication year - 2019
Publication title -
biostatistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.493
H-Index - 82
eISSN - 1468-4357
pISSN - 1465-4644
DOI - 10.1093/biostatistics/kxz060
Subject(s) - categorical variable , dimensionality reduction , sufficient dimension reduction , computer science , sliced inverse regression , estimator , reduction (mathematics) , data mining , feature selection , outcome (game theory) , dimension (graph theory) , multinomial distribution , statistics , machine learning , mathematics , geometry , mathematical economics , pure mathematics
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 continuous or categorical outcomes. We incorporate variable selection into the estimation via penalties and address important invariance issues arising from the compositional nature of the data. We illustrate and compare our methods and some established methods for analyzing microbiome data in simulations and using data from the Human Microbiome Project. Displaying the data in the coordinate system of the SDR linear combinations allows visual inspection and facilitates comparisons across studies.