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Abstract:
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High-dimensional count data from metagenomic studies display several characteristics, such as zero-inflation, skewness, and overdispersion, that cause difficulty for standard probability models such as the Poisson and Negative Binomial distributions. The Dirichlet-Multinomial distribution has been suggested as a more appropriate way to model data with these characteristics and can be extended, in a straight-forward way, to a regression framework via log-linear models. In the microbiome setting this extension allows the integration of taxonomic count data with other information taken on the same samples, e.g. demographics, diet logs, etc. However, the number of variables can quickly exceed the number of samples and, assuming that many of the parameters are superfluous, variable selection methods may be used to determine which variables represent important associations between the two data types. We propose a Bayesian approach to variable selection using spike-and-slab priors which simultaneously estimates variable inclusion/exclusion and the log-linear regression parameters. Our method compares favorably in simulations to other recently proposed models. We also present data analysis
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