# Ellipses: Ellipses, Data Ellipses, and Confidence Ellipses In car: Companion to Applied Regression

## Description

These functions draw ellipses, including data ellipses, and confidence ellipses for linear, generalized linear, and possibly other models.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30``` ```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, 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)) palette()[1:2] else palette()[1:length(group.levels)], pch = if (missing(groups)) 1 else seq(group.levels), 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 = if (missing(groups)) palette()[1] else palette()(1:length(groups)), id.location="lr", ...) 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, ...) ## Default S3 method: 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 * 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` 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`. `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` 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. `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` 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 the `link{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` 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. `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 respectively. `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; if ellipses are plotted for `groups`, then this is a vector of colors for the groups. `pch` for `dataEllipse` this is the plotting character (default, symbol `1`, a hollow circle) to use for the points; if ellipses are plotted by `groups`, then this a vector of plotting characters, with consecutive symbols starting with `1` as the default. `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,id.location` 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

## 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 [email protected], 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.

`cov.trob`, `cov.wt`, `linearHypothesis`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```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), 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.n=2, pch=15:17, labels=rownames(Prestige), 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)) ```