car (version 2.0-15)

Ellipses: Ellipses, Data Ellipses, and Confidence Ellipses

Description

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=palette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, grid=TRUE, ...)

dataEllipse(x, y, 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 = palette()[1:2], lwd = 2,
    fill = FALSE, fill.alpha = 0.3, grid = TRUE, labels, id.method = "mahal",
    id.n = if (id.method[1] == "identify") Inf else 0, id.cex = 1,
    id.col = palette()[1], ...)

confidenceEllipse(model, ...)

## S3 method for class 'lm':
confidenceEllipse(model, which.coef, L, levels=0.95, Scheffe=FALSE, dfn,
  center.pch=19, center.cex=1.5, segments=51, xlab, ylab, 
  col=palette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, draw=TRUE, add=!draw, ...)
  
## S3 method for class 'glm':
confidenceEllipse(model, chisq, ...)

## S3 method for class 'default':
confidenceEllipse(model, which.coef, L, levels=0.95, Scheffe=FALSE,  dfn,
  center.pch=19, center.cex=1.5, segments=51, xlab, ylab, 
  col=palette()[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"

center.pch

character for plotting ellipse center; if FALSE or NULL 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; if FALSE, 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.

weights

a numeric vector of weights, of the same length as x and y to be used by cov.wt or cov.trob in computing a weighted

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 the cov.trob function in the MASS package to calculate the center and covariance matrix for the data ellipse.

model

a model object produced by lm or glm.

which.coef

2-element vector giving indices of coefficients to plot; if missing, the first two coefficients (disregarding the regression constant) will be selected.

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 the which.coef arg

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 is TRUE, or to

chisq

if TRUE, the confidence ellipse for the coefficients in a generalized linear model are based on the chisquare statistic, if FALSE on the $F$-statistic. This corresponds to using the default and linear-model methods resp

col

color for lines and ellipse center; the default is the second entry in the current color palette (see palette and par). For <

lwd

line width; default is 2 (see par).

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 and line.

labels,id.method,id.n,id.cex,id.col

Arguments for the labelling of points. The default is id.n=0 for labeling no points. See showLabels for details of these arguments.

grid

If TRUE, the default, a light-gray background grid is put on the graph

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.

Details

The ellipse is computed by suitably transforming a unit circle. dataEllipse superimposes the normal-probability contours over a scatterplot of the data.

References

Fox, J. (2008) Applied Regression Analysis and Generalized Linear Models, Second Edition. Sage. Fox, J. and Weisberg, S. (2011) An R Companion to Applied Regression, Second 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

cov.trob, cov.wt, linearHypothesis.

Examples

dataEllipse(Duncan$income, Duncan$education, levels=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), 
	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")
	})