Recent Advances in Visualizing Multivariate Linear Models

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 = X B + U, and some of their recent extensions. We begin with a description of and examples from the Hypothesis-error (HE) plots framework (utilizing the \Rpackage{heplots}), 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 Roys 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 \Rpackage{candisc}, 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, development of generalizations of influence measures and diagnostic plots for MLMs (in the \Rpackage{mvinfluence}).