Ellipses
Ellipses, Data Ellipses, and Confidence Ellipses
These functions draw ellipses, including data ellipses, and confidence ellipses for linear, generalized linear, and possibly other models.
Usage
ellipse(center, shape, radius, log="", center.pch=19, center.cex=1.5,
segments=51, draw=TRUE, add=draw, xlab="", ylab="",
col=carPalette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, grid=TRUE, ...)dataEllipse(x, y, groups, group.labels=group.levels, ellipse.label,
weights, log="", levels=c(0.5, 0.95), center.pch=19,
center.cex=1.5, draw=TRUE, plot.points=draw, add=!plot.points, segments=51,
robust=FALSE, xlab=deparse(substitute(x)), ylab=deparse(substitute(y)),
col=if (missing(groups)) carPalette()[1:2] else carPalette()[1:length(group.levels)],
pch=if (missing(groups)) 1 else seq(group.levels),
lwd=2, fill=FALSE, fill.alpha=0.3, grid=TRUE, id=FALSE, ...)
confidenceEllipse(model, ...)
# S3 method for lm
confidenceEllipse(model, which.coef, vcov.=vcov,
L, levels=0.95, Scheffe=FALSE, dfn,
center.pch=19, center.cex=1.5, segments=51, xlab, ylab,
col=carPalette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, draw=TRUE, add=!draw, ...)
# S3 method for glm
confidenceEllipse(model, chisq, ...)
# S3 method for default
confidenceEllipse(model, which.coef, vcov.=vcov,
L, levels=0.95, Scheffe=FALSE, dfn,
center.pch=19, center.cex=1.5, segments=51, xlab, ylab,
col=carPalette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, draw=TRUE, add=!draw, ...)
Arguments
- center
2-element vector with coordinates of center of ellipse.
- shape
\(2\times 2\) shape (or covariance) matrix.
- radius
radius of circle generating the ellipse.
- log
when an ellipse is to be added to an existing plot, indicates whether computations were on logged values and to be plotted on logged axes;
"x"
if the x-axis is logged,"y"
if the y-axis is logged, and"xy"
or"yx"
if both axes are logged. The default is""
, indicating that neither axis is logged.- center.pch
character for plotting ellipse center; if
FALSE
orNULL
the center point isn't plotted.- center.cex
relative size of character for plotting ellipse center.
- segments
number of line-segments used to draw ellipse.
- draw
if
TRUE
produce graphical output; ifFALSE
, only invisibly return coordinates of ellipse(s).- add
if
TRUE
add ellipse(s) to current plot.- xlab
label for horizontal axis.
- ylab
label for vertical axis.
- x
a numeric vector, or (if
y
is missing) a 2-column numeric matrix.- y
a numeric vector, of the same length as
x
.- groups
optional: a factor to divide the data into groups; a separate ellipse will be plotted for each group (level of the factor).
- group.labels
labels to be plotted for the groups; by default, the levels of the
groups
factor.- ellipse.label
a label for the ellipse(s) or a vector of labels; if several ellipses are drawn and just one label is given, then that label will be repeated. The default is not to label the ellipses.
- weights
a numeric vector of weights, of the same length as
x
andy
to be used bycov.wt
orcov.trob
in computing a weighted covariance matrix; if absent, weights of1
are used.- plot.points
if
FALSE
data ellipses are drawn, but points are not plotted.- levels
draw elliptical contours at these (normal) probability or confidence levels.
- robust
if
TRUE
use thecov.trob
function in the MASS package to calculate the center and covariance matrix for the data ellipse.- model
a model object produced by
lm
orglm
.- which.coef
2-element vector giving indices of coefficients to plot; if missing, the first two coefficients (disregarding the regression constant) will be selected.
- vcov.
a coefficient-covariance matrix or a function (such as
hccm
) to compute the coefficent-covariance matrix frommodel
; the default is thevcov
function.- L
As an alternative to selecting coefficients to plot, a transformation matrix can be specified to compute two linear combinations of the coefficients; if the
L
matrix is given, it takes precedence over thewhich.coef
argument.L
should have two rows and as many columns as there are coefficients. It can be given directly as a numeric matrix, or specified by a pair of character-valued expressions, in the same manner as for thelink{linearHypothesis}
function, but with no right-hand side.- Scheffe
if
TRUE
scale the ellipse so that its projections onto the axes give Scheffe confidence intervals for the coefficients.- dfn
``numerator'' degrees of freedom (or just degrees of freedom for a GLM) for drawing the confidence ellipse. Defaults to the number of coefficients in the model (disregarding the constant) if
Scheffe
isTRUE
, or to2
otherwise; selectingdfn = 1
will draw the ``confidence-interval generating'' ellipse, with projections on the axes corresponding to individual confidence intervals with the stated level of coverage.- chisq
if
TRUE
, the confidence ellipse for the coefficients in a generalized linear model are based on the chisquare statistic, ifFALSE
on the $F$-statistic. This corresponds to using the default and linear-model methods respectively.- col
color for lines and ellipse center; the default is the second entry in the current car palette (see
carPalette
andpar
). FordataEllipse
, two colors can be given, in which case the first is for plotted points and the second for lines and the ellipse center; if ellipses are plotted forgroups
, then this is a vector of colors for the groups.- pch
for
dataEllipse
this is the plotting character (default, symbol1
, a hollow circle) to use for the points; if ellipses are plotted bygroups
, then this a vector of plotting characters, with consecutive symbols starting with1
as the default.- lwd
line width; default is
2
(seepar
).- fill
fill the ellipse with translucent color
col
(default,FALSE
)?- fill.alpha
transparency of fill (default =
0.3
).- …
other plotting parameters to be passed to
plot
andline
.- id
controls point identification; if
FALSE
(the default), no points are identified; can be a list of named arguments to theshowLabels
function;TRUE
is equivalent tolist(method="mahal", n=2, cex=1, col=carPalette()[1], location="lr")
(with the defaultcol
actually dependent on the number of groups), which identifies the 2 points with the largest Mahalanobis distances from the center of the data.- grid
If TRUE, the default, a light-gray background grid is put on the graph
Details
The ellipse is computed by suitably transforming a unit circle.
dataEllipse
superimposes the normal-probability contours over a scatterplot
of the data.
Value
These functions are mainly used for their side effect of producing plots. For
greater flexibility (e.g., adding plot annotations), however, ellipse
returns invisibly the (x, y) coordinates of the calculated ellipse.
dataEllipse
and confidenceEllipse
return invisibly the coordinates of one or more ellipses, in the latter instance a list named by
levels
.
References
Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.
Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.
Monette, G. (1990) Geometry of multiple regression and 3D graphics. In Fox, J. and Long, J. S. (Eds.) Modern Methods of Data Analysis. Sage.
See Also
Examples
# NOT RUN {
dataEllipse(Duncan$income, Duncan$education, levels=0.1*1:9,
ellipse.label=0.1*1:9, lty=2, fill=TRUE, fill.alpha=0.1)
confidenceEllipse(lm(prestige~income+education, data=Duncan), Scheffe=TRUE)
confidenceEllipse(lm(prestige~income+education, data=Duncan), vcov.=hccm)
confidenceEllipse(lm(prestige~income+education, data=Duncan),
L=c("income + education", "income - education"))
wts <- rep(1, nrow(Duncan))
wts[c(6, 16)] <- 0 # delete Minister, Conductor
with(Duncan, {
dataEllipse(income, prestige, levels=0.68)
dataEllipse(income, prestige, levels=0.68, robust=TRUE,
plot.points=FALSE, col="green3")
dataEllipse(income, prestige, weights=wts, levels=0.68,
plot.points=FALSE, col="brown")
dataEllipse(income, prestige, weights=wts, robust=TRUE, levels=0.68,
plot.points=FALSE, col="blue")
})
with(Prestige, dataEllipse(income, education, type,
id=list(n=2, labels=rownames(Prestige)), pch=15:17,
xlim=c(0, 25000), center.pch="+",
group.labels=c("Blue Collar", "Professional", "White Collar"),
ylim=c(5, 20), level=.95, fill=TRUE, fill.alpha=0.1))
# }