2020/04/16 by Jacob Fiksel, Scott L. Zeger, Fiksel, Jacob +3 · 1 citation
Computer Science · #FOS: Computer and information sciences #Geochemistry and Geologic Mapping #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.2004.07881
openalex publication_date 2020/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Compositional data are common in many fields, both as outcomes and predictor\nvariables. The inventory of models for the case when both the outcome and\npredictor variables are compositional is limited and the existing models are\ndifficult to interpret, due to their use of complex log-ratio transformations.\nWe develop a transformation-free linear regression model where the expected\nvalue of the compositional outcome is expressed as a single Markov transition\nfrom the compositional predictor. Our approach is based on generalized method\nof moments thereby not requiring complete specification of data likelihood and\nis robust to different data generating mechanism. Our model is simple to\ninterpret, allows for 0s and 1s in both the compositional outcome and\ncovariates, and subsumes several interesting subcases of interest. We also\ndevelop a permutation test for linear independence. Finally, we show that\ndespite its simplicity, our model accurately captures the relationship between\ncompositional data from education and medical research.\n