The `heplots`

package provides functions for visualizing hypothesis tests
in multivariate linear models (MANOVA, multivariate multiple regression, MANCOVA, and repeated measures designs).
HE plots represent sums-of-squares-and-products matrices for linear hypotheses and for
error using ellipses (in two dimensions), ellipsoids (in three dimensions),
or by line segments in one dimension.
See Fox, Friendly and Monette (2007) for a brief introduction
and Friendly, Monette and Fox (2013) for a general discussion of the role of
elliptical geometry in statistical understanding.

Other topics now addressed here include robust MLMs, tests for equality of covariance matrices in MLMs, and chi square Q-Q plots for MLMs.

The package also provides a collection of data sets illustrating a variety of multivariate linear models of the types listed above, together with graphical displays.

Several tutorial vignettes are also included. See `vignette(package="heplots")`

.

Package: | heplots |

Type: | Package |

Version: | 1.3-8 |

Date: | 2021-01-20 |

License: | GPL (>= 2), GPL version 2 or newer |

The graphical functions contained here all display multivariate model effects in variable (data) space, for one or more response variables (or contrasts among response variables in repeated measures designs).

`heplot`

constructs two-dimensional HE plots for model terms and linear hypotheses for pairs of response variables in multivariate linear models.

`heplot3d`

constructs analogous 3D plots for triples of response variables.

`pairs.mlm`

constructs a ``matrix'' of pairwise HE plots.

`heplot1d`

constructs 1-dimensional analogs of HE plots for model terms and linear hypotheses for single response variables.

For repeated measure designs, between-subject effects and within-subject
effects must be plotted separately, because the error terms (E matrices)
differ. For terms involving within-subject effects,
these functions carry out a linear
transformation of the matrix **Y** of responses to a matrix **Y M**, where
**M** is the model matrix for a term in
the intra-subject design and produce plots of
the H and E matrices in this transformed space. The vignette `repeated`

describes
these graphical methods for repeated measures designs.

The related car package calculates Type II and Type III tests
of multivariate
linear hypotheses using the `Anova`

and `linearHypothesis`

functions.

The `candisc-package`

package provides functions for
visualizing effects for MLM model terms in a low-dimensional canonical space
that shows the largest hypothesis relative to error variation.
The candisc package now also includes related methods for
canonical correlation analysis.

The `heplots`

package also contains a large number of multivariate data sets with examples
of analyses and graphic displays. Use `data(package="heplots")`

to see
the current list.

Friendly, M. (2006).
Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear
Models: SAS Software and Examples.
*Journal of Statistical Software*, 17(6), 1-42.
https://www.jstatsoft.org/v17/i06/

Friendly, M. (2007).
HE plots for Multivariate General Linear Models.
*Journal of Computational and Graphical Statistics*, 16(2) 421-444.
http://datavis.ca/papers/jcgs-heplots.pdf

Fox, J., Friendly, M. & Monette, G. (2007).
Visual hypothesis tests in multivariate linear models: The heplots package for R.
*DSC 2007: Directions in Statistical Computing*.
https://socialsciences.mcmaster.ca/jfox/heplots-dsc-paper.pdf

Friendly, M. (2010). HE Plots for Repeated Measures Designs. *Journal of Statistical Software*,
37(4), 1-40. URL https://www.jstatsoft.org/v37/i04/.

Fox, J., Friendly, M. & Weisberg, S. (2013).
Hypothesis Tests for Multivariate Linear Models Using the car Package.
*The R Journal*, **5**(1),
https://journal.r-project.org/archive/2013-1/fox-friendly-weisberg.pdf.

Friendly, M., Monette, G. & Fox, J. (2013).
Elliptical Insights: Understanding Statistical Methods Through Elliptical Geometry.
*Statistical Science*, 2013, **28** (1), 1-39,
http://datavis.ca/papers/ellipses.pdf.

Friendly, M. & Sigal, M. (2014).
Recent Advances in Visualizing Multivariate Linear Models.
*Revista Colombiana de Estadistica*, **37**, 261-283

Friendly, M. & Sigal, M. (2016). Graphical Methods for Multivariate Linear Models in Psychological Research: An R Tutorial. Submitted for publication.

`Anova`

, `linearHypothesis`

for Anova.mlm computations and tests

`candisc-package`

for reduced-rank views in canonical space

`manova`

for a different approach to testing effects in MANOVA designs