Abstract
This paper reviews our work in the development of visualization methods (implemented in R) for understanding and interpreting the effects of predictors in multivariate linear models (MLMs) of the form Y = XB + U, and some of their recent extensions. We begin with a description of and examples from the Hypothesis-error (HE) plots framework (utilizing the heplots package), wherein multivariate tests can be visualized via ellipsoids in 2D, 3D or all pairwise views for the Hypothesis and Error Sum of Squares and Products (SSP) matrices used in hypothesis tests. Such HE plots provide visual tests of significance: a term is significant by Roy’s test if and only if its H ellipsoid projects somewhere outside the E ellipsoid. These ideas extend naturally to repeated measures designs in the multivariate context. When the rank of the hypothesis matrix for a term exceeds 2, these effects can also be visualized in a reduced-rank canonical space via the candisc package, which also provides new data plots for canonical correlation problems. Finally, we discuss some recent work-in-progress: the extension of these methods to robust MLMs, and the development of generalizations of influence measures and diagnostic plots for MLMs (in the mvinfluence package).
Highlights
Multivariate response data are very common in applied research
The aim of this paper is to present a few methods that are currently employed for the visualization of high-dimensional data, and review a series of methods we have worked on to apply these methods to multivariate linear models (MLMs)
The classical univariate general linear model is the cornerstone for the development of much of modern statistical theory and practice
Summary
A research outcome (e.g., depression, job satisfaction, academic achievement, childhood attention deficit hypheractivily disorders-ADHD) may have several observed measurement scales or related aspects. In this framework, the primary concern of the researcher is to ascertain the impact of potential predictors on two or more response variables. The results of such studies are often discussed solely in terms of coefficients and significance, and visualizations of relationships are presented for one response variable at a time This is unfortunate, because visualization affords us a window to truly see what is happening in our data, and can aid in interpretation, yet the univariate graphical methods cannot show the important relations among the multivariate responses.
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