References -- Part II Exploratory Analyses of Microbial Communities -- Statistical Methods for Pairwise Comparison of Metagenomic Samples -- 1 Introduction -- 2 Microbial Community Comparison Methods Based on OTU Abundance Data -- 3 Microbial Community Comparison Measures Based on a Phylogenetic Tree -- 3.1 The Fst Statistic and Phylogenetic Test for Comparing Communities -- 3.2 UniFrac, W-UniFrac, VAW-UniFrac, and Generalized UniFrac for Comparing Microbial Communities -- 3.3 VAW-UniFrac for Comparing Communities -- 4 Alignment-Free Methods for the Comparison of Microbial Communities -- 5 A Tutorial on the Use of UniFrac Type and Alignment-Free Dissimilarity Measures for the Comparison of Metagenomic Samples -- 5.1 Analysis Steps for UniFrac, W-UniFrac, Generalized UniFrac, and VAW-UniFrac -- 5.2 Analysis Steps for the Comparison of Microbial Communities Based on Alignment-Free Methods -- 6 Discussion -- References -- Beta Diversity and Distance-Based Analysis of Microbiome Data -- 1 Introduction -- 2 Quantifying Dissimilarity: Common Beta Diversity Metrics -- 3 Ordination and Dimension Reduction -- 3.1 Principal Coordinates Analysis -- 3.2 Double Principal Coordinate Analysis -- 3.3 Biplots -- 3.4 Accounting for Compositionality -- 3.5 Model-Based Ordination Using Latent Variables -- 4 Distance-Based Hypothesis Testing -- 4.1 Permutation Tests -- 4.2 Kernel Machine Regression Tests -- 4.3 Sum of Powered Score Tests -- 4.4 Adaptive Tests -- 4.5 Comparison of Distance-Based Tests -- 5 Strengths, Weaknesses, and Future Directions -- References -- Part III Statistical Models and Inference -- Joint Models for Repeatedly Measured Compositional and Normally Distributed Outcomes -- 1 Introduction -- 2 Motivating Data -- 3 Statistical Models -- 3.1 The Multinomial Logistic Mixed Model (MLMM) -- 3.2 Dirichlet-Multinomial Mixed Model (DMMM). |