Sparse Logistic Normal Multinomial Regression for Modeling Over-dispersed Count Data with an Application to Microbiome Data Analysis(Session 2B(IASC-ARS))

Abstract

Changes in human microbiome are associated with many human diseases. One important problem of microbiome data analysis is to identify the environmental/biological covariates that are associated with different bacterial taxa. Taxa count data in microbiome studies are often over-dispersed and include many zeros. To account for such an over-dispersion, we propose to use an additive logistic normal multinomial regression model to associate the covariates to bacterial compositions. The model can naturally account for sampling variabilities and zero observations and also allow for a flexible covariance structure among the bacterial taxa. In order to select the relevant covariates and to estimate the corresponding regression coefficients, we propose a group l_1 penalized likelihood estimation method for variable selection and estimation. A Monte Carlo expectation-maximization (MCEM) algorithm is developed to implement the penalized likelihood estimation. We demonstrate the method using a data set that associates human gut microbiome to diet intake in order to identify the micro-nutrients that are associated with the human gut microbiome.