R: Ellipses, Data Ellipses, and Confidence Ellipses

Ellipses {car}

R Documentation

Ellipses, Data Ellipses, and Confidence Ellipses

Description

These functions draw ellipses, including data ellipses, and confidence ellipses for linear and generalized linear 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, ...)

confidenceEllipse(model, ...)

## S3 method for class 'lm'
confidenceEllipse(model, which.coef, 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, which.coef, 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 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.
`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 covariance matrix; if absent, weights of `1` 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 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.
`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 `2` otherwise; selecting `dfn = 1` will draw the “confidence-interval generating” ellipse, with projections on the axes corresponding to individual confidence intervals with the stated level of coverage.
`col`	color for lines and ellipse center; the default is the second entry in the current color palette (see `palette` and `par`). For `dataEllipse`, two colors can be given, in which case the first is for plotted points and the second for lines and the ellipse center.
`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`.
`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.

Author(s)

Georges Monette, John Fox jfox@mcmaster.ca, and Michael Friendly.

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.

Examples

dataEllipse(Prestige$income, Prestige$education, levels=0.1*1:9, lty=2, 
	fill=TRUE, fill.alpha=0.1)
confidenceEllipse(lm(prestige~income+education, data=Prestige), Scheffe=TRUE)

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")
	})

[Package car version 2.0-12 Index]