HE Plots for Repeated Measures Designs

Hypothesis error (HE) plots, introduced in Friendly (2007), provide graphical methods to visualize hypothesis tests in multivariate linear models, by displaying hypothesis and error covariation as ellipsoids and providing visual representations of effect size and significance. These methods are implemented in the heplots for R (Fox, Friendly, and Monette 2009a) and SAS (Friendly 2006), and apply generally to designs with fixed-effect factors (MANOVA), quantitative regressors (multivariate multiple regression) and combined cases (MANCOVA). This paper describes the extension of these methods to repeated measures designs in which the multivariate responses represent the outcomes on one or more “within-subject” factors. This extension is illustrated using the heplots for R. Examples describe one- sample profile analysis, designs with multiple between-S and within-S factors, and doubly- multivariate designs, with multivariate responses observed on multiple occasions.