knitr::opts_chunk$set( warning = FALSE, # avoid warnings and messages in the output message = FALSE, collapse = TRUE, fig.width = 4, fig.height = 4, dpi = 96, comment = "#>", fig.path = "man/figures/README-" ) par(mar=c(3,3,1,1)+.1)
library(heplots)
Version 1.6.3
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 (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:
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:
robmlm()
.Mahalanobis()
calculates classical and robust Mahalanobis squared
distances using MCD and MVE estimators of center and covariance.boxM()
and plot.boxM()
.cqplot()
) to detect outliers and
assess multivariate normality of residuals.coefplot()
).In this respect, the heplots
package now aims to provide a wide range
of tools for analyzing and visualizing multivariate response linear
models, together with other packages:
candisc
package
provides HE plots in canonical discriminant space, the space of
linear combinations of the responses that show the maximum possible
effects and for canonical correlation in multivariate regression
designs.mvinfluence
, provides
diagnostic measures and plots for influential observations in MLM
designs.Several tutorial vignettes are also included. See
vignette(package="heplots")
.
+-------------------+-------------------------------------------------+
| CRAN version | install.packages("heplots")
|
+-------------------+-------------------------------------------------+
| Development | remotes::install_github("friendly/heplots")
|
| version | |
+-------------------+-------------------------------------------------+
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.
The pairs
method, pairs.mlm()
constructs a scatterplot matrix of
pairwise HE plots.
heplot1d()
constructs 1-dimensional analogs of HE plots for model
terms and linear hypotheses for single response variables.
glance.mlm()
extends broom::glance.lm()
to multivariate response
models, giving a one-line statistical summary for each response
variable.
boxM()
Calculates Box's M test for homogeneity of covariance
matrices in a MANOVA design. A plot
method displays a visual
representation of the components of the test. Associated with this,
bartletTests()
and levineTests()
give the univariate tests of
homogeneity of variance for each response measure in a MLM.
covEllipses()
draw covariance (data) ellipses for one or more
group, optionally including the ellipse for the pooled within-group
covariance.
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. (At present, this
vignette is only available at HE plots for repeated measures
designs.)
The package also provides a large collection of data sets illustrating a
variety of multivariate linear models of the types listed above,
together with graphical displays. The table below classifies these with
method tags. Their names are linked to the documentation on the
pkgdown
website, [http://friendly.github.io/heplots].
library(here) library(DT) library(dplyr) dsets <- read.csv(here::here("extra", "datasets.csv")) dsets <- dsets[,-1] # remove row number # link dataset to pkgdown doc refurl <- "http://friendly.github.io/heplots/reference/" dsets <- dsets |> mutate(dataset = glue::glue("[{dataset}]({refurl}{dataset}.html)")) knitr::kable(dsets) # doesn't work -- can't find phantomJS #DT::datatable(dsets, # options = list(pageLength = 15), # rownames = FALSE, # filter = "none")
This example illustrates HE plots using the classic iris
data set. How
do the means of the flower variables differ by Species
? This dataset
was the imputus for R. A. Fisher (1936) to propose a method of
discriminant analysis using data collected by Edgar Anderson (1928).
Though some may rightly deprecate Fisher for being a supporter of
eugenics, Anderson's iris
dataset should not be blamed.
A basic HE plot shows the H and E ellipses for the first two
response variables (here: Sepal.Length
and Sepal.Width
). The
multivariate test is significant (by Roy's test) iff the H ellipse
projects anywhere outside the E ellipse.
The positions of the group means show how they differ on the two response variables shown, and provide an interpretation of the orientation of the H ellipse: it is long in the directions of differences among the means.
#| echo=-1, #| out.width="70%" par(mar=c(4,4,1,1)+.1) iris.mod <- lm(cbind(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) ~ Species, data=iris) heplot(iris.mod)
Contrasts or other linear hypotheses can be shown as well, and the
ellipses look better if they are filled. We create contrasts to test the
differences between versacolor
and virginca
and also between
setosa
and the average of the other two. Each 1 df contrast plots as
degenerate 1D ellipse-- a line.
Because these contrasts are orthogonal, they add to the total 2 df
effect of Species
. Note how the first contrast, labeled V:V
,
distinguishes the means of versicolor from virginica; the second
contrast, S:VV
distinguishes setosa
from the other two.
par(mar=c(4,4,1,1)+.1) contrasts(iris$Species)<-matrix(c(0, -1, 1, 2, -1, -1), nrow=3, ncol=2) contrasts(iris$Species) iris.mod <- lm(cbind(Sepal.Length, Sepal.Width, Petal.Length, Petal.Width) ~ Species, data=iris) hyp <- list("V:V"="Species1","S:VV"="Species2") heplot(iris.mod, hypotheses=hyp, fill=TRUE, fill.alpha=0.1)
All pairwise HE plots are produced using the pairs()
method for MLM
objects.
pairs(iris.mod, hypotheses=hyp, hyp.labels=FALSE, fill=TRUE, fill.alpha=0.1)
MANOVA relies on the assumption that within-group covariance matrices are all equal.
It is useful to visualize these in the space of some of the predictors.
covEllipses()
provides this both for classical and robust estimates.
The figure below shows these for the three Iris species and the
pooled covariance matrix, which is the same as the E matrix used
in MANOVA tests.
covEllipses(iris[,1:4], iris$Species) covEllipses(iris[,1:4], iris$Species, fill=TRUE, method="mve", add=TRUE, labels="")
Anderson, E. (1928). The Problem of Species in the Northern Blue Flags, Iris versicolor L. and Iris virginica L. Annals of the Missouri Botanical Garden, 13, 241--313.
Fisher, R. A. (1936). The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 8, 379--388.
Friendly, M. (2006). Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples. Journal of Statistical Software, 17, 1-42.
Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421-444. DOI.
Fox, J., Friendly, M. & Monette, G. (2009). Visualizing hypothesis tests in multivariate linear models: The heplots package for R Computational Statistics, 24, 233-246.
Friendly, M. (2010). HE plots for repeated measures designs. Journal of Statistical Software, 37, 1--37.
Friendly, M.; Monette, G. & Fox, J. (2013). Elliptical Insights: Understanding Statistical Methods Through Elliptical Geometry Statistical Science, 28, 1-39.
Friendly, M. & Sigal, M. (2017). Graphical Methods for Multivariate Linear Models in Psychological Research: An R Tutorial. The Quantitative Methods for Psychology, 13, 20-45.
Friendly, M. & Sigal, M. (2018): Visualizing Tests for Equality of Covariance Matrices, The American Statistician, DOI
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