Description Usage Arguments Details Value References See Also Examples
This function plots ellipses representing the hypothesis and error sums-of-squares-and-products matrices for terms and linear hypotheses in a multivariate linear model. These include MANOVA models (all explanatory variables are factors), multivariate regression (all quantitative predictors), MANCOVA models, homogeneity of regression, as well as repeated measures designs treated from a multivariate perspective.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | heplot(mod, ...)
## S3 method for class 'mlm'
heplot(mod, terms, hypotheses, term.labels = TRUE,
hyp.labels = TRUE, err.label="Error", label.pos=NULL,
variables = 1:2, error.ellipse = !add,
factor.means = !add, grand.mean = !add, remove.intercept = TRUE,
type = c("II", "III", "2", "3"), idata=NULL, idesign=NULL,
icontrasts=c("contr.sum", "contr.poly"),
imatrix=NULL, iterm=NULL, markH0=!is.null(iterm),
manova, size = c("evidence", "effect.size"),
level = 0.68, alpha = 0.05, segments = 60,
center.pch = "+", center.cex=2,
col = getOption("heplot.colors",
c("red", "blue", "black", "darkgreen",
"darkcyan","magenta", "brown","darkgray")),
lty = 2:1, lwd = 1:2,
fill=FALSE, fill.alpha=0.3,
xlab, ylab, main = "", xlim, ylim, axes=TRUE, offset.axes,
add = FALSE, verbose = FALSE, warn.rank = FALSE, ...)
|
mod |
a model object of class |
terms |
a logical value or character vector of terms in the model
for which to plot
hypothesis matrices; if missing or |
hypotheses |
optional list of linear hypotheses for which to plot hypothesis
matrices; hypotheses are specified as for the
|
term.labels |
logical value or character vector of names for the terms to be
plotted. If |
hyp.labels |
logical value or character vector of names for the hypotheses to
be plotted. If |
err.label |
Label for the error ellipse |
label.pos |
Label position, a vector of integers (in |
variables |
indices or names of the two response variables to be plotted;
defaults to |
error.ellipse |
if |
factor.means |
logical value or character vector of names of
factors for which the means
are to be plotted, or |
grand.mean |
if |
remove.intercept |
if |
type |
“type” of sum-of-squares-and-products matrices to compute; one of
|
idata |
an optional data frame giving a factor or factors defining the
intra-subject model for multivariate repeated-measures data.
See Friendly (2010) and Details of |
idesign |
a one-sided model formula using the “data” in idata and specifying the intra-subject design for repeated measure models. |
icontrasts |
names of contrast-generating functions to be applied by default to factors and ordered factors, respectively, in the within-subject “data”; the contrasts must produce an intra-subject model matrix in which different terms are orthogonal. The default is c("contr.sum", "contr.poly"). |
imatrix |
In lieu of |
iterm |
For repeated measures designs, you must specify one intra-subject term
(a character string) to select the SSPE (E) matrix used in the HE plot.
Hypothesis terms plotted include the |
markH0 |
A logical value (or else a list of arguments to |
manova |
optional |
size |
how to scale the hypothesis ellipse relative to the error
ellipse; if |
level |
equivalent coverage of ellipse for normally-distributed
errors, defaults to |
alpha |
signficance level for Roy's greatest-root test statistic; if
|
segments |
number of line segments composing each ellipse; defaults to
|
center.pch |
character to use in plotting the centroid of the data;
defaults to |
center.cex |
size of character to use in plotting the centroid of the data;
defaults to |
col |
a color or vector of colors to use in plotting ellipses; the first
color is used for the error ellipse; the remaining colors — recycled
as necessary — are used for the hypothesis ellipses.
A single color can be given, in which case it is used for all ellipses.
For convenience, the default colors for all heplots produced in a given session can be changed
by assigning a color vector via |
lty |
vector of line types to use for plotting the ellipses; the first is
used for the error ellipse, the rest — possibly recycled — for
the hypothesis ellipses; a single line type can be given. Defaults to
|
lwd |
vector of line widths to use for plotting the ellipses; the first is
used for the error ellipse, the rest — possibly recycled — for
the hypothesis ellipses; a single line width can be given. Defaults to
|
fill |
A logical vector indicating whether each ellipse should be filled or not. The first value is used for the error ellipse, the rest — possibly recycled — for the hypothesis ellipses; a single fill value can be given. Defaults to FALSE for backward compatibility. See Details below. |
fill.alpha |
Alpha transparency for filled ellipses, a numeric scalar or vector of values
within |
xlab |
x-axis label; defaults to name of the x variable. |
ylab |
y-axis label; defaults to name of the y variable. |
main |
main plot label; defaults to |
xlim |
x-axis limits; if absent, will be computed from the data. |
ylim |
y-axis limits; if absent, will be computed from the data. |
axes |
Whether to draw the x, y axes; defaults to |
offset.axes |
proportion to extend the axes in each direction if computed from the data; optional. |
add |
if |
verbose |
if |
warn.rank |
if |
... |
arguments to pass down to |
The heplot
function plots a representation of the covariance ellipses
for hypothesized model terms and linear hypotheses (H) and the corresponding
error (E) matrices for two response variables in a multivariate linear model (mlm).
The plot helps to visualize the nature and dimensionality
response variation on the two variables jointly
in relation to error variation that is summarized in the various multivariate
test statistics (Wilks' Lambda, Pillai trace, Hotelling-Lawley trace, Roy maximum
root). Roy's maximum root test has a particularly simple visual interpretation,
exploited in the size="evidence"
version of the plot. See the description of
argument alpha
.
For a 1 df hypothesis term (a quantitative regressor, a single contrast or parameter test), the H matrix has rank 1 (one non-zero latent root of H E^{-1}) and the H "ellipse" collapses to a degenerate line.
Typically, you fit a mlm with mymlm <- lm(cbind(y1, y2, y3, ...) ~ modelterms)
,
and plot some or all of the modelterms
with heplot(mymlm, ...)
.
Arbitrary linear hypotheses related to the terms in the model (e.g., contrasts of
an effect) can be included in the plot using the hypotheses
argument.
See linearHypothesis
for details.
For repeated measure designs, where the response variables correspond to one or
more variates observed under a within-subject design, between-subject effects
and within-subject effects must be plotted separately, because the error terms
(E matrices) differ. When you specify an intra-subject term (iterm
),
the analysis and HE plots
amount to analysis of the matrix Y of responses post-multiplied by a matrix
M determined by the intra-subject design for that term. See Friendly (2010)
or the vignette("repeated")
in this package for an extended discussion and
examples.
The related candisc
package provides functions for
visualizing a multivariate linear model in a low-dimensional view via a
generalized canonical discriminant analyses. heplot.candisc
and heplot3d.candisc
provide a low-rank 2D (or 3D) view of the effects for
a given term in the space of maximum discrimination.
When an element of fill
is TRUE
, the ellipse outline is drawn using the corresponding
color in col
, and the interior is filled with a transparent version of this color specified
in fill.alpha
. To produce filled (non-degenerate) ellipses without the bounding outline, use
a value of lty=0
in the corresponding position.
The function invisibly returns an object of class "heplot"
, with
coordinates for the various hypothesis ellipses and the error ellipse, and
the limits of the horizontal and vertical axes. These may be useful for
adding additional annotations to the plot, using standard plotting functions.
(No methods for manipulating these objects are currently available.)
The components are:
H |
a list containing the coordinates of each ellipse for the hypothesis terms |
E |
a matrix containing the coordinates for the error ellipse |
center |
x,y coordinates of the centroid |
xlim |
x-axis limits |
ylim |
y-axis limits |
radius |
the radius for the unit circles used to generate the ellipses |
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. http://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
Friendly, Michael (2010). HE Plots for Repeated Measures Designs. Journal of Statistical Software, 37(4), 1-40. URL http://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), http://journal.r-project.org/archive/2013-1/fox-friendly-weisberg.pdf.
Friendly, M. & Sigal, M. (2014) Recent Advances in Visualizing Multivariate Linear Models. Revista Colombiana de Estadistica, 37, 261-283, http://ref.scielo.org/6gq33g.
Anova
, linearHypothesis
for details on
testing MLMs.
heplot1d
, heplot3d
, pairs.mlm
, mark.H0
for other
HE plot functions. coefplot.mlm
for plotting confidence ellipses for parameters
in MLMs.
trans.colors
for calculation of transparent colors.
label.ellipse
for labeling positions in plotting H and E ellipses.
candisc
, heplot.candisc
for reduced-rank views of mlm
s
in canonical space.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | ## iris data
contrasts(iris$Species)<-matrix(c(0,-1,1, 2, -1, -1), 3,2)
contrasts(iris$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)
# compare with effect-size scaling
heplot(iris.mod, hypotheses=hyp, size="effect", add=TRUE)
# try filled ellipses
heplot(iris.mod, hypotheses=hyp, fill=TRUE, fill.alpha=0.2, col=c("red", "blue"))
heplot(iris.mod, hypotheses=hyp, fill=TRUE, col=c("red", "blue"), lty=c(0,0,1,1))
# vary label position and fill.alpha
heplot(iris.mod, hypotheses=hyp, fill=TRUE, fill.alpha=c(0.3,0.1), col=c("red", "blue"),
lty=c(0,0,1,1), label.pos=0:3)
hep <-heplot(iris.mod, variables=c(1,3), hypotheses=hyp)
str(hep)
# all pairs
pairs(iris.mod, hypotheses=hyp, hyp.labels=FALSE)
## Pottery data, from car package
data(Pottery)
pottery.mod <- lm(cbind(Al, Fe, Mg, Ca, Na) ~ Site, data=Pottery)
heplot(pottery.mod)
heplot(pottery.mod, terms=FALSE, add=TRUE, col="blue",
hypotheses=list(c("SiteCaldicot = 0", "SiteIsleThorns=0")),
hyp.labels="Sites Caldicot and Isle Thorns")
## Rohwer data, multivariate multiple regression/ANCOVA
#-- ANCOVA, assuming equal slopes
rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ SES + n + s + ns + na + ss, data=Rohwer)
Anova(rohwer.mod)
col <- c("red", "black", "blue", "cyan", "magenta", "brown", "gray")
heplot(rohwer.mod, col=col)
# Add ellipse to test all 5 regressors
heplot(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")), col=col, fill=TRUE)
# View all pairs
pairs(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")))
# or 3D plot
col <- c("pink", "black", "blue", "cyan", "magenta", "brown", "gray")
heplot3d(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")), col=col)
|
Loading required package: car
Loading required package: carData
[,1] [,2]
setosa 0 2
versicolor -1 -1
virginica 1 -1
List of 6
$ H :List of 3
..$ Species: num [1:61, 1:2] 9.66 9.68 9.66 9.6 9.5 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
.. .. ..$ : chr [1:2] "Sepal.Length" "Petal.Length"
..$ V:V : num [1:61, 1:2] 7.41 7.4 7.38 7.33 7.27 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
.. .. ..$ : chr [1:2] "Sepal.Length" "Petal.Length"
..$ S:VV : num [1:61, 1:2] 9.33 9.31 9.25 9.16 9.03 ...
.. ..- attr(*, "dimnames")=List of 2
.. .. ..$ : NULL
.. .. ..$ : chr [1:2] "Sepal.Length" "Petal.Length"
$ E : num [1:61, 1:2] 6.62 6.62 6.61 6.59 6.56 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:2] "Sepal.Length" "Petal.Length"
$ center: Named num [1:2] 5.84 3.76
..- attr(*, "names")= chr [1:2] "Sepal.Length" "Petal.Length"
$ xlim : Named num [1:2] 2.01 9.68
..- attr(*, "names")= chr [1:2] "Sepal.Length" "Sepal.Length"
$ ylim : Named num [1:2] -6.33 13.84
..- attr(*, "names")= chr [1:2] "Petal.Length" "Petal.Length"
$ radius: num 1.52
- attr(*, "class")= chr "heplot"
Type II MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
SES 1 0.37853 12.1818 3 60 2.507e-06 ***
n 1 0.04030 0.8400 3 60 0.477330
s 1 0.09271 2.0437 3 60 0.117307
ns 1 0.19283 4.7779 3 60 0.004729 **
na 1 0.23134 6.0194 3 60 0.001181 **
ss 1 0.04990 1.0504 3 60 0.376988
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Loading required namespace: rgl
Warning messages:
1: In rgl.init(initValue, onlyNULL) : RGL: unable to open X11 display
2: 'rgl.init' failed, running with 'rgl.useNULL = TRUE'.
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.