One objective of human microbiome studies is to identify differentially abundant microbes across biological conditions. Previous statistical methods focus on detecting the shift in the abundance and/or prevalence of the microbes and treat the dispersion (spread of the data) as a nuisance. These methods also assume that the dispersion is the same across conditions, an assumption which may not hold in presence of sample heterogeneity. Moreover, the widespread outliers in the microbiome sequencing data make existing parametric models not overly robust. Therefore, a robust and powerful method that allows covariate-dependent dispersion and addresses outliers is still needed for differential abundance analysis.