多變量變異數分析建模之矩陣視覺化; Matrix Visualization for MANOVA Modeling

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题名:	多變量變異數分析建模之矩陣視覺化;Matrix Visualization for MANOVA Modeling
作者:	田銀錦;Yin-Jing Tien
贡献者:	統計研究所
关键词:	矩陣視覺化;多變量變異數分析;Matrix Visualization;MANOVA
日期:	2010-06-22
上传时间:	2010-12-08 14:23:37 (UTC+8)
出版者:	國立中央大學
摘要:	相較於箱型圖、散佈圖陣列、與平行座標圖等傳統方法，矩陣視覺化相關方法在高維度資料的視覺化與分群上，為更具效率且功能較強大之探索式資料分析工具。Chen (2002)的廣義相關圖是一個全方位的矩陣視覺化環境；許多的廣義相關圖模組與擴充功能已被開發以觀察更多樣的科學資料與更複雜的統計模型。本研究將針對多變量變異數分析之建模過程提出一套完整的矩陣視覺化程序，作為廣義相關圖環境的新成員。現有的矩陣視覺化方法並不適用於多變量變異數分析模型中資料與資訊之群集與觀察，因為這些方法視個別樣本為分析基本單位，並未將統計模型效應納入分析與視覺化過程。為了將多變量變異數分析模型中相關資料與訊息結構做全面的視覺化呈現，必須同時探索模型與殘差兩個層次的資訊。在我們提出的方法中，不僅呈現共變異矩陣分解成模型及殘差，也將資料矩陣相對應的分解一併呈現。我們進一步將各類統計檢定的結果(多變量變異數分析與個別變異數分析之p-值)以矩陣視覺化方式呈現，預期對於多變量變異數分析建模過程，在資料描述上或是統計推論上，都能有更強大且完整的呈現與了解。藉由變數校正的方法，此一矩陣視覺化過程，亦得以延伸應用於多變數共變異數分析模型之矩陣視覺化呈現。 Matrix visualization (MV) related graphical methods are more efficient and powerful exploratory data analysis (EDA) tools for visualizing and clustering high-dimensional data than conventional methods such as box-plots, scatterplot-matrix, or parallel coordinate plots. Generalized association plots (GAP), introduced by Chen (2002), serve as an environment for general-purposes matrix visualization. Many modules and extensions have been developed for GAP for visualizing scientific datasets with more versatile formats and studying statistical models of more complex nature. This study proposes a new member of the GAP family: a comprehensive matrix visualization procedure for analyzing multivariate analysis of variance (MANOVA) models. Existing matrix visualization methods are not suitable for clustering and visualizing data and information structures with a MANOVA setting, because they regard individual samples as the base analysis unit without taking into consideration the model’s effects. In order to comprehensively visualize data and information structures for MANOVA modeling, it is necessary to simultaneously explore related information structures at both the model and the residual levels. In our proposed method, we visualize not only the decomposition of a covariance matrix into model and residual components, but also the decomposition of the data matrix. We further convert statistical testing results (p-values from MANOVA and ANOVA for individual variables) into MV format, in order to obtain a more powerful and complete visualization for understanding MANOVA modeling at both the descriptive and inference levels. With a covariate adjusted MV, adopted before the MANOVA MV procedure, our proposed method can be extended to visualizations of MANCOVA modeling.
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