heplot3d {heplots}R Documentation

Three-Dimensional HE Plots

Description

This function plots ellipsoids in 3D representing the hypothesis and error sums-of-squares-and-products matrices for terms and linear hypotheses in a multivariate linear model.

Usage

heplot3d(mod, ...)

## S3 method for class 'mlm':
heplot3d(mod, terms, hypotheses, term.labels = TRUE, 
    hyp.labels = TRUE, variables = 1:3, error.ellipsoid = !add,
    factor.means = !add, grand.mean = !add, remove.intercept = TRUE, 
    type = c("II", "III", "2", "3"), manova, size = c("evidence", "effect.size"),
    level = 0.68, alpha = 0.05,  segments = 40, col = palette()[-1], lwd=c(1, 4),
    shade=TRUE, shade.alpha=0.1, wire=c(TRUE,FALSE),
    bg.col = c("white", "black"), fogtype = c("none", "exp2", "linear", "exp"), 
    fov = 30, offset = 0.01, xlab, ylab, zlab, xlim, ylim, zlim, add = FALSE, verbose = FALSE, 
    warn.rank = FALSE, ...)

Arguments

mod a model object of class "mlm".
terms a logical value or character vector of terms in the model for which to plot hypothesis matrices; if missing or TRUE, defaults to all terms; if FALSE, no terms are plotted.
hypotheses optional list of linear hypotheses for which to plot hypothesis matrices; hypotheses are specified as for the linear.hypothesis function in the car package; the list elements can be named, in which case the names are used.
term.labels logical value or character vector of names for the terms to be plotted. If TRUE (the default) the names of the terms are used; if FALSE, term labels are not plotted.
hyp.labels logical value or character vector of names for the hypotheses to be plotted. If TRUE (the default) the names of components of the list of hypotheses are used; if FALSE, hypothesis labels are not plotted.
variables indices or names of the three response variables to be plotted; defaults to 1:3.
error.ellipsoid if TRUE, plot the error ellipsoid; defaults to TRUE, if the argument add is FALSE (see below).
factor.means logical value or character vector of names of factors for which the means are to be plotted, or TRUE or FALSE; defaults to TRUE, if the argument add is FALSE (see below).
grand.mean if TRUE, plot the centroid for all of the data; defaults to TRUE, if the argument add is FALSE (see below).
remove.intercept if TRUE (the default), do not plot the ellipsoid for the intercept even if it is in the MANOVA table.
type ``type'' of sum-of-squares-and-products matrices to compute; one of "II", "III", "2", or "3", where "II" is the default (and "2" is a synomym).
manova optional Anova.mlm object for the model; if absent a MANOVA is computed. Specifying the argument can therefore save computation in repeated calls.
size how to scale the hypothesis ellipsoid relative to the error ellipsoid; if "evidence", the default, the scaling is done so that a ``significant'' hypothesis elliposid extends outside of the error ellipsoid; if "effect.size", the hypothesis ellipsoid is on the same scale as the error ellipsoid.
level equivalent coverage of ellipsoid for normally-distributed errors, defaults to 0.68.
alpha signficance level for Roy's greatest-root test statistic; if size="evidence", then the hypothesis ellipsoid is scaled so that it just touches the error ellipsoid at the specified alpha level; a larger hypothesis elllipsoid therefore indicates statistical significance; defaults to 0.05.
segments number of segments composing each elliposid; defaults to 40.
col a colour or vector of colours to use in plotting ellipsoids; the first colour is used for the error ellipsoid; the remaining colours — recycled as necessary — are used for the hypothesis ellipsoids; a single colour can be given, in which case it is used for all ellipsoids. Defaults to the current colour palette, less its first element.
lwd a two-element vector giving the line width for drawing ellipsoids (including those that degenerate to an ellipse) and for drawing ellipsoids that degenerate to a line segment. The default is c(1, 4).
shade a logical scalar or vector, indicating whether the ellipsoids should be rendered with shade3d. Works like col, except that FALSE is used for any 1 df degenerate ellipsoid.
shade.alpha a numeric value in the range [0,1], or a vector of such values, giving the alpha transparency for ellipsoids rendered with shade=TRUE.
wire a logical scalar or vector, indicating whether the ellipsoids should be rendered with wire3d. Works like col, except that TRUE is used for any 1 df degenerate ellipsoid.
bg.col background colour, "white" or "black", defaulting to "white".
fogtype type of ``fog'' to use for depth-cueing; the default is "none". See bg.
fov field of view angle; controls perspective. See viewpoint.
offset proportion of axes to off set labels; defaults to 0.01.
xlab x-axis label; defaults to name of the x variable.
ylab y-axis label; defaults to name of the y variable.
zlab z-axis label; defaults to name of the z variable.
xlim x-axis limits; if absent, will be computed from the data.
ylim y-axis limits; if absent, will be computed from the data.
zlim z-axis limits; if absent, will be computed from the data.
add if TRUE, add to the current plot; the default is FALSE. If TRUE, the error ellipsoid is not plotted
verbose if TRUE, print the MANOVA table and details of hypothesis tests; the default is FALSE.
warn.rank if TRUE, do not suppress warnings about the rank of the hypothesis matrix when the ellipsoid collapses to an ellipse or line; the default is FALSE.
... arguments passed from generic.

Details

When the H matrix for a term has rank < 3, the ellipsoid collapses to an ellipse (rank(H)=2) or a line (rank(H)=1).

Rotating the plot can be particularly revealing, showing views in which H variation is particularly large or small in relation to E variation.

The arguments xlim, ylim, and zlim can be used to expand the bounding box of the axes, but cannot decrease it.

Value

heplot3d invisibly returns a list containing the bounding boxes of the error (E) ellipsoid and for each term or linear hypothesis specified in the call. Each of these is a 2 x 3 matrix with rownames "min" and "max" and colnames corresponding to the variables plotted.
The function also leaves an object named .frame in the global environment, containing the rgl object IDs for the axes, axis labels, and bounding box; these are deleted and the axes, etc. redrawn if the plot is added to.

References

Friendly, M. (2006). Data Ellipses, HE Plots and Reduced-Rank Displays for Multivariate Linear Models: SAS Software and Examples Journal of Statistical Software, 17(6), 1-42. http://www.jstatsoft.org/v17/i06/

Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421-444. http://www.math.yorku.ca/SCS/Papers/jcgs-heplots.pdf

See Also

Anova, linear.hypothesis, heplot, pairs.mlm, rgl-package, heplot3d.candisc.

Examples

# Soils data, from car package
soils.mod <- lm(cbind(pH,N,Dens,P,Ca,Mg,K,Na,Conduc) ~ Block + Contour*Depth, data=Soils)
Anova(soils.mod)

heplot(soils.mod, variables=c("Ca", "Mg"))
pairs(soils.mod, terms="Depth", variables=c("pH", "N", "P", "Ca", "Mg"))

heplot3d(soils.mod, variables=c("Mg", "Ca", "Na"))

# Plastic data
plastic.mod <- lm(cbind(tear, gloss, opacity) ~ rate*additive, data=Plastic)
heplot3d(plastic.mod)

[Package heplots version 0.8-4 Index]