微生物資料為從生物體上所收集的細菌、病毒、真菌等微生物的資料，針對微生物資料，本篇論文介紹現有兩種分析該資料的統計方法：假設檢定方法、狄氏多項迴歸。假設檢定方法與狄氏多項迴歸屬於有母數統計方法，皆架構在狄氏多項分配之下，本文應用兩種統計方法比較兩群資料的微生物組成分布是否相同，其中假設檢定方法透過檢定兩群微生物資料的比例參數向量是否相同；而狄氏多項迴歸，在本篇論文將組別當成一個解釋變數，透過檢定迴歸係數，比較兩群微生物組成分布是否相同。除此之外，本篇論文透過模擬的方式，比較多項分配與狄氏多項分配的差異以及比較兩種統計方法在檢定兩群資料組成分布是否相同時的型Ⅰ誤差率(TypeⅠerror rate)及模擬檢定力(Empirical power)。

The collection of microorganisms, including viruses, bacteria, and some unicellular eukaryotes, that live in and on organisms is microbiome. Two statistical methods have been developed to analyze microbiome dataset. This research presents two statistical methods for the analysis of microbiome data based on a fully parametric approach. In particular, the Dirichlet-multinomial distribution is used. One of the methods perform hypothesis testing, the other is considering the Dirichlet-multinomial regression model. The goal of this research is to apply two statistical methods to compare the composition of two microbiome samples. Moreover, we conducted simulation studies to assess the performance of two statistical methods. In addition, those methods are applied to a real microbiome dataset.

[1] Human microbiome project consortium. Structure, function and diversity of the healthy human microbiome. Nature 486, 207-214 (2012).
[2] La Rosa, P. S., Deych, E., Shands, B., and Shannon, W. D. HMP: Hypothesis testing and power calculations for comparing metagenomic samples from HMP. R package version, 1.4.3 (2011).
[3] La Rosa, P. S., Brooks, J. P., Deych, E., Boone, E. L., Edwards, D. J., Wang, Q., and Shannon, W. D. Hypothesis testing and power calculations for taxonomic-based human microbiome data. PloS one, 7(12) (2012).
[4] Mebane Jr, W. R., and Sekhon, J. S. multinomRob: Robust estimation of overdispersed multinomial regression models. R package version, 1.8-6.1 (2009).
[5] Tvedebrink, T. dirmult: Estimation in dirichlet-multinomial distribution. R package version, 0.1.3-4 (2010).
[6] Zhang, Y., and Zhou, H. MGLM: multivariate response generalized linear models. R package version, 0.0.7 (2015).
[7] Zhang, Y., Zhou, H., Zhou, J., and Sun, W. Regression models for multivariate count data. Journal of computational and graphical statistics, 26(1), 1-13 (2017).
[8] 陳安綺 和 陳志洪，結合概念圖與角色扮演遊戲之自然學習系統，科學家村莊。(2013)