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Microbiomes, populations of microscopic organisms, have been found to be related to human health and it is expected further investigations will lead to novel perspectives of disease. The data used to analyze microbiomes is one of the newest types (the result of high-throughput technology) and the means to analyze these data is still rapidly evolving. One of the distributions that have been introduced into the microbiome literature, the Dirichlet-Multinomial, has received considerable attention. We extend this distribution's use uncover compositional relationships between organisms at a taxonomic level. We apply our new method in two real microbiome data sets: one from human nasal passages and another from human stool samples.