OneDimensional HE Plots
Description
This function plots a 1dimensional representation of the hypothesis (H) and error (E) sumsofsquaresandproducts matrices for terms and linear hypotheses in a multivariate linear model.
In particular, for a given response, the 1D representations of H and E matrices correspond to line segments. The E “ellipse” is shown as a filled rectangle whose width equals the mean squared error for that response. The H “ellipse” for each model term is shown as a line segment whose length represents either the size of the effect or the evidence for that effect.
This version is an initial sketch. Details of the implementation are subject to change.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  heplot1d(mod, ...)
## S3 method for class 'mlm'
heplot1d(mod, terms, hypotheses,
term.labels = TRUE, hyp.labels = TRUE,
variables = 1, 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, manova,
size = c("evidence", "effect.size"), level = 0.68, alpha = 0.05,
center.pch = "",
col = getOption("heplot.colors",
c("red", "blue", "black", "darkgreen",
"darkcyan","magenta", "brown","darkgray")),
lty = 2:1, lwd = 1:2, xlab, main = "",
xlim, axes = TRUE, offset.axes, add = FALSE, verbose = FALSE, ...)

Arguments
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 
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 sumofsquaresandproducts matrices to compute; one of

idata 
an optional data frame giving a factor or factors defining the
intrasubject model for multivariate repeatedmeasures data.
See Details of 
idesign 
a onesided model formula using the “data” in idata and specifying the intrasubject design for repeated measure models. 
icontrasts 
names of contrastgenerating functions to be applied by default to factors and ordered factors, respectively, in the withinsubject “data”; the contrasts must produce an intrasubject 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 intrasubject term
(a character string) to select the SSPE (E) matrix used in the HE plot.
Hypothesis terms plotted include the 
manova 
optional 
size 
how to scale the hypothesis ellipse relative to the error
ellipse; if 
level 
equivalent coverage of ellipse for normallydistributed
errors, defaults to 
alpha 
signficance level for Roy's greatestroot test statistic; if

center.pch 
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

xlab 
xaxis label; defaults to name of the x variable. 
main 
main plot label; defaults to 
xlim 
xaxis 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 
... 
arguments to pass down to 
Value
The function invisibly returns an object of class "heplot1d"
, with
coordinates for the various hypothesis ellipses and the error ellipse, and
the limits of the horizontal and vertical axes.
(No methods for manipulating these objects are currently available.)
The components are:
H 
ranges for the hypothesis terms 
E 
range for E 
xlim 
xaxis limits 
Author(s)
Michael Friendly
See Also
Anova
, linearHypothesis
for hypothesis tests in mlm
s
heplot
, heplot3d
, pairs.mlm
for other HE plot methods
Examples
1 2 3 4 5 6 7 8 9 10  ## Plastics data
plastic.mod < lm(cbind(tear, gloss, opacity) ~ rate*additive, data=Plastic)
heplot1d(plastic.mod, col=c("pink","blue"))
heplot1d(plastic.mod, col=c("pink","blue"),variables=2)
heplot1d(plastic.mod, col=c("pink","blue"),variables=3)
## Bees data
bees.mod < lm(cbind(Iz,Iy) ~ caste*treat*time, data=Bees)
heplot1d(bees.mod)
heplot1d(bees.mod, variables=2)
