Three-Dimensional HE Plots

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 mlm
heplot3d(
  mod,
  terms,
  hypotheses,
  term.labels = TRUE,
  hyp.labels = TRUE,
  err.label = "Error",
  variables = 1:3,
  error.ellipsoid = !add,
  factor.means = !add,
  grand.mean = !add,
  remove.intercept = TRUE,
  type = c("II", "III", "2", "3"),
  idata = NULL,
  idesign = NULL,
  icontrasts = c("contr.sum", "contr.poly"),
  imatrix = NULL,
  iterm = NULL,
  manova,
  size = c("evidence", "effect.size"),
  level = 0.68,
  alpha = 0.05,
  segments = 40,
  col = getOption("heplot3d.colors", c("red", "blue", "black", "darkgreen", "darkcyan",
    "magenta", "brown", "darkgray")),
  lwd = c(1, 4),
  shade = TRUE,
  shade.alpha = 0.2,
  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,
  cex.label = 1.5,
  add = FALSE,
  verbose = FALSE,
  warn.rank = FALSE,
  ...
)

Arguments

mod: a model object of class "mlm".
...: arguments passed from generic.
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 linearHypothesis 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.
err.label: Label for the error ellipse
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 synonym).
idata: an optional data frame giving a factor or factors defining the intra-subject model for multivariate repeated-measures data. See Details of Anova for an explanation of the intra-subject design and for further explanation of the other arguments relating to intra-subject factors.
idesign: a one-sided model formula using the ``data'' in idata and specifying the intra-subject design for repeated measure models.
icontrasts: names of contrast-generating functions to be applied by default to factors and ordered factors, respectively, in the within-subject ``data''; the contrasts must produce an intra-subject model matrix in which different terms are orthogonal. The default is c("contr.sum", "contr.poly").
imatrix: In lieu of idata and idesign, you can specify the intra-subject design matrix directly via imatrix, in the form of list of named elements. Each element gives the columns of the within-subject model matrix for an intra-subject term to be tested, and must have as many rows as there are responses; the columns of the within-subject model matrix for different terms must be mutually orthogonal.
iterm: For repeated measures designs, you must specify one intra-subject term (a character string) to select the SSPE (E) matrix used in the HE plot. Hypothesis terms plotted include the iterm effect as well as all interactions of iterm with terms.
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 ellipsoid 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: significance 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 ellipsoid therefore indicates statistical significance; defaults to 0.05.
segments: number of segments composing each ellipsoid; defaults to 40.
col: a color or vector of colors to use in plotting ellipsoids; the first color is used for the error ellipsoid; the remaining colors --- recycled as necessary --- are used for the hypothesis ellipsoid. A single color can be given, in which case it is used for all ellipsoid. For convenience, the default colors for all heplots produced in a given session can be changed by assigning a color vector via options(heplot3d.colors=c(...). Otherwise, the default colors are c("pink", "blue", "black", "darkgreen", "darkcyan", "magenta", "brown", "darkgray").
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.
cex.label: text size for ellipse labels
add: if TRUE, add to the current plot; the default is FALSE. If TRUE, the error ellipsoid is neither plotted nor returned in the output object.
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.

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. An additional component, center, contains the coordinates of the centroid in the plot.

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.

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. See play3d and movie3d for details on creating animations.

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

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. https://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://datavis.ca/papers/jcgs-heplots.pdf

Examples


# Soils data, from carData package
data(Soils, package = "carData")
soils.mod <- lm(cbind(pH,N,Dens,P,Ca,Mg,K,Na,Conduc) ~ Block + Contour*Depth, data=Soils)
car::Anova(soils.mod)
#> 
#> Type II MANOVA Tests: Pillai test statistic
#>               Df test stat approx F num Df den Df    Pr(>F)    
#> Block          3    1.6758   3.7965     27     81 1.777e-06 ***
#> Contour        2    1.3386   5.8468     18     52 2.730e-07 ***
#> Depth          3    1.7951   4.4697     27     81 8.777e-08 ***
#> Contour:Depth  6    1.2351   0.8640     54    180    0.7311    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

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"), wire=FALSE)

# Plastic data
plastic.mod <- lm(cbind(tear, gloss, opacity) ~ rate*additive, data=Plastic)
if (FALSE) {
heplot3d(plastic.mod, col=c("red", "blue", "brown", "green3"), wire=FALSE)
}