car (version 3.1-5)

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=carPalette()[2], lwd=2, fill=FALSE, fill.alpha=0.3, grid=TRUE, ...)
dataEllipse(x, ...)
# S3 method for formula
dataEllipse(formula, data, subset, weights, xlab, ylab, id=FALSE, ...)
# S3 method for default
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, 
  label.pos=NULL, label.cex=1.25, label.xpd=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,
  grid=TRUE, ...)
  
# S3 method for glm
confidenceEllipse(model, chisq, ...)
# S3 method for mlm
confidenceEllipse(model, xlab, ylab, which.coef=1:2, ...)
# 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, 
  grid=TRUE, ...)
  
confidenceEllipses(model, ...)
# S3 method for default
confidenceEllipses(model, coefnames,  main, grid=TRUE, ...)
# S3 method for mlm
confidenceEllipses(model, coefnames, main, ...)

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; confidenceEllipses invisibly returns NULL.

Details

The ellipse is computed by suitably transforming a unit circle.

dataEllipse superimposes the normal-probability contours over a scatterplot of the data.

confidenceEllipses plots a matrix of all pairwise confidence ellipses; each panel of the matrix is created by confidenceEllipse.

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

cov.trob, cov.wt, linearHypothesis.

Examples

dataEllipse(Duncan$income, Duncan$education, levels=0.1*1:9, 
    ellipse.label=0.1*1:9, lty=2, fill=TRUE, fill.alpha=0.1)

# formula method
dataEllipse(education ~ income | type, data=Duncan,
            levels = 0.68)

dataEllipse(education ~ income | type, data=Duncan, 
            levels=0.68, label.xpd=TRUE)

# vary label positions
dataEllipse(education ~ income | type, data=Duncan,
            levels = 0.68,
            fill = TRUE, fill.alpha = 0.1,
            label.pos = c(3, 2, 4),
            xlim = c(0, 100),
            ylim = c(2, 120))

    
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"))
	
confidenceEllipses(lm(prestige ~ income + education + type, data=Duncan),
  fill=TRUE)
cov2cor(vcov(lm(prestige ~ income + education + type, 
  data=Duncan))) # correlations among coefficients

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))