Michael Friendly's

# HE plots for Multivariate General Linear Models • HE plots for Multivariate General Linear Models.
• Journal of Computational and Graphical Statistics, vol. 16, no. 2, pp. 421–444, 2007.

Multivariate analysis of variance (MANOVA) extends the ideas and methods of univariate ANOVA in simple and straight-forward ways. But the familiar graphical methods typically used for univariate ANOVA are inadequate for showing how measures in a multivariate response vary with each other, and how their means vary with explanatory factors. Similarly, the graphical methods commonly used in multiple regression are not widely available or used in multivariate multiple regression (MMRA). We describe a variety of graphical methods for multiple-response (MANOVA and MMRA) data aimed at understanding what is being tested in a multivariate test, and how factor/predictor effects are expressed across multiple response measures. In particular, we describe and illustrate: (a) Data ellipses and biplots for multivariate data, (b) HE plots, showing the hypothesis and error covariance matrices for a given pair of responses, and a given effect, (c) HE plot matrices, showing all pairwise HE plots, and (d) reduced-rank analogs of HE plots, showing all observations, group means, and their relations to the response variables. All of these methods are implemented in a collection of easily used SAS macro programs.

Keywords: biplot; canonical discriminant plot, data ellipse, HE plot, HE plot matrix, MANOVA, multivariate multiple regression, MMRA, scatterplot matrix

```@Article{Friendly07manova,
author = {Michael Friendly},
title = {HE plots for Multivariate General Linear Models},
journal = {Journal of Computational and Graphical Statistics},
year = {2007},
volume = {16},
pages = {421–444},
number = {2},
doi = {10.1198/106186007X208407},
url = {http://datavis.ca/papers/jcgs-heplots.pdf},
}```