Graphical methods for multivariate data analysis

多变量数据分析的图形方法

• 批准号: RGPIN-2014-03772
• 负责人: Friendly, Michael
• 金额: $ 0.8万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=636043
• 关键词: Graphical; methods; multivariate; data; analysis

Statistical graphics play a crucial role in data analysis and scientific discovery by revealing unexpected structure, showing features and patterns that might be missed in numerical summaries, and providing for assessment of the assumptions on which statistical tests of scientific hypotheses are based. As examples, some of the most important discoveries in the history of science (e.g., atomic number by Henry Moseley, anti-cyclonic weather patterns by Francis Galton, stellar evolution and classification of stars by Herzsprung and Russell) were largely based on graphical analysis.Multivariate data and complex statistical modeling are now commonplace in much applied research, particularly in psychology. A research outcome (e.g., depression, job satisfaction, academic achievement) may have several observed indicators or methods of measurement, or there may be several distinct but related outcomes of interest (depression, anxiety, interpersonal trust), and these may be assessed on multiple occasions for an individual, or within within multiple strata (schools, patient groups). While statistical analysis for such data has advanced considerably, methods for visualization, interpretation and communicating the results in such studies have not, and often relies on available methods for the univariate case, and therefore is unable to illuminate the relations among multiple outcomes. This proposal seeks to extend my previous work on visualization methods for (possibly large) multivariate data sets consisting of both continuous and categorical variables, with a view to more fully integrate graphics and visualization in statistical practice and applied research.These graphical methods include exploratory tools for understanding relationships among variables, analysis tools used in fitting and testing a variety of statistical models and presentation tools for explicating the results of analysis for scientific presentation. The statistical methods to which these apply include classical multivariate linear models (MANOVA, multivariate regression), robust extensions of these, loglinear models for contingency tables and generalized linear models for non-Gaussian data and mixed models for hierarchical and longitudinal data. A general approach to such data display problems is proposed, comprising both static graphics and dynamic, interactive methods, together with the idea of generalized projection views, comprising 2D and 3D views in data space, parameter space, reduced-rank “optimal” projections and specialized diagnostic functions (e.g., “scagnostics”).This research program is important, and of direct benefit, both to statisticians and applied researchers who will be able to apply these methods to the understanding of complex multivariate data.

统计图表在数据分析和科学发现中发挥着至关重要的作用，它揭示了意想不到的结构，显示了数字总结中可能遗漏的特征和模式，并提供了对科学假设的统计检验所基于的假设的评估。例如，科学史上一些最重要的发现(如Henry Moseley的原子序数、Francis Galton的反气旋天气模式、Herzsprung和Russell的恒星演化和恒星分类)在很大程度上是基于图形分析。多变量数据和复杂的统计建模现在在许多应用研究中很常见，特别是在心理学中。一个研究结果(例如，抑郁、工作满意度、学业成就)可能有几个观察到的指标或衡量方法，或者可能有几个不同但相关的结果(抑郁、焦虑、人际信任)，这些结果可能对个人或在多个层面(学校、患者群体)内进行多次评估。虽然对这类数据的统计分析有了很大进步，但这种研究中的可视化、解释和交流结果的方法并没有，而且往往依赖于单变量情况下的现有方法，因此无法说明多个结果之间的关系。这项建议旨在扩展我之前在包括连续变量和分类变量的多变量数据集(可能是大型)可视化方法方面的工作，以期在统计实践和应用研究中更充分地整合图形和可视化。这些图形方法包括用于理解变量之间关系的探索性工具，用于拟合和测试各种统计模型的分析工具，以及用于解释分析结果以进行科学展示的展示工具。应用这些方法的统计方法包括经典的多元线性模型(Manova，多元回归)，这些模型的稳健扩展，列联表的对数线性模型和非高斯数据的广义线性模型，以及分层和纵向数据的混合模型。提出了一种解决这类数据显示问题的一般方法，包括静态图形和动态交互方法，以及广义投影视图的思想，广义投影视图包括数据空间、参数空间中的2D和3D视图、降阶“最优”投影和专门的诊断函数(例如“Sagnostics”)。这项研究计划对统计学家和应用研究人员都是重要的，而且直接受益，他们将能够将这些方法应用于理解复杂的多变量数据。