Visualizing Hypothesis Tests in Multivariate Linear Models

Version 1.8.3; documentation built for pkgdown 2026-08-11

Description

The heplots package provides functions for visualizing hypothesis tests in multivariate linear models (“MLM” = {MANOVA, multivariate multiple regression, MANCOVA, and repeated measures designs}). It also provides other tools for analysis and graphical display of MLMs.

HE plots represent sums-of-squares-and-products matrices for linear hypotheses (H) and for error (E) using ellipses (in two dimensions), ellipsoids (in three dimensions), or by line segments in one dimension. For the theory and applications, see:

• Friendly (2007) for the basic theory on which this is based.
• Fox, Friendly and Monette (2009) for a brief introduction,
• Friendly (2010) for the application of these ideas to repeated measure designs,
• Friendly, Monette and Fox (2013) for a general discussion of the role of elliptical geometry in statistical understanding,
• Friendly & Sigal (2017) for an applied R tutorial,
• Friendly & Sigal (2018) for theory and examples of visualizing equality of covariance matrices.

If you use this work in teaching or research, please cite it as given by citation("heplots") or see Citation.

Other topics now addressed here include:

• robust MLMs, using iteratively re-weighted least squared to down-weight observations with large multivariate residuals, robmlm().
• Mahalanobis() calculates classical and robust Mahalanobis squared distances using MCD and MVE estimators of center and covariance.
• visualizing tests for equality of covariance matrices in MLMs (Box’s M test), boxM() and plot.boxM(). Also: bartlettTests() and LeveneTests() for homogeneity of variance for each response in a MLM.