Graphical methods for multivariate data analysis

点击翻译按钮获取中文摘要

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.