Compositional data can be analyzed by either Dirichlet regression or using log-ratio analysis as pioneered by John Aitchison.
My questions are
- What are the main differences in assumptions between these two models? When should you prefer one above the other?
- Are there any "methods" that one topic allows which the other doesn't? My current data set has multiple independent variables (both factors and continuous), and I would like to model both fixed and random effects, and then do parameter estimation, test hypotheses, find confidence intervals, etc.
- What are the best resources to learn these two topics from? The log-ratio analysis seems to be the topic of many books, but on the other hand, Dirichlet regression seems to be mainly covered in small lecture notes (20-30 pages).