heplot3d: Three-Dimensional HE Plots
In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

heplot3d

R Documentation

Three-Dimensional HE Plots

Description

This function plots ellipsoids in 3D representing the hypothesis (\mathbf{H}) and error (\mathbf{E}) sums-of-squares-and-products matrices for terms and linear hypotheses in a multivariate linear model. It allow you to visualize model effects on three response variables together, as opposed to the 2D views offered by heplot() and pairs.mlm().

Usage

heplot3d(mod, ...)

## S3 method for class '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", "significance"),
  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 `car::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 `car::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 (`\mathbf{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 ellipse relative to the error ellipse; if `"evidence"`, the default, the scaling is done so that a “significant” hypothesis ellipse at level `alpha` extends outside of the error ellipse. 'size = "significance"' is a synonym and does the same thing. If '"effect.size"', the hypothesis ellipse is on the same scale as the error ellipse.
`level`	equivalent coverage of ellipse (assuming normally-distributed errors). This defaults to `0.68`, giving a standard 1 SD bivariate ellipse.
`alpha`	significance level for Roy's greatest-root test statistic; if `size="evidence"` or `size="significance"`, then the hypothesis ellipse is scaled so that it just touches the error ellipse at the specified alpha level. A larger hypothesis ellipse somewhere in the space of all the response variables therefore indicates statistical significance. With more than three responses, an H ellipsoid inside E in this 3D view does not mean "not significant": the effect may lie in directions not shown (see Details in `heplot()`). 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 `rgl::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 `rgl::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 `rgl::bg3d()`.
`fov`	field of view angle; controls perspective. See `rgl::view3d()`.
`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`.

Details

It uses the rgl package for rendering, so it adds some arguments (e.g., fogtype) to those used in heplot(), but is otherwise the same.

Rotating the plot can be particularly revealing, showing views in which \mathbf{H} variation is particularly large or small in relation to \mathbf{E} variation. If you find a view making \mathbf{H} as large as possible, this corresponds closely to the canonical view chosen by the candisc.

See rgl::play3d() and rgl::movie3d() for details on creating animations, rotating the 3D scene around on or more coordinate axes, or zooming in/out to highlight some feature.

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

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

Use in documents

For use in an R Markdown, Quarto, or pkgdown document, follow the call to heplot3d() with rgl::rglwidget() to embed the plot as an interactive, rotatable widget instead of a static image.

In a knitted document, call rgl::setupKnitr() with autoprint = TRUE once, near the top of the document, so that low-level rgl calls are captured automatically;
On a pkgdown reference page like this, the trailing rgl::rglwidget() call in the example is enough by itself, and no setupKnitr() call is needed.

Note that the widget capture depends on rglwidget() itself being the visibly-printed value – heplot3d() returns its ellipsoid bounding boxes invisibly (for compatibility with heplot()), so calling it alone does not trigger a plot in either context.

For a bookdown-based vignette with pkgdown: as_is: true in its YAML header (needed for ⁠\@ref()⁠ figure/table numbering), calling rglwidget() directly renders fine in the standalone vignette (⁠R CMD build⁠/devtools::build_vignettes()) but shows as a blank box on the pkgdown site: pkgdown replaces the document's own ⁠<head>⁠ when assembling the article page, silently dropping the ⁠<script>⁠ tags the widget needs to render, even though its scene data is still present in the page. The fix is to pre-render the widget to a self-contained file and embed that with an ⁠<iframe>⁠ instead, since body content (unlike the ⁠<head>⁠) survives pkgdown's page assembly:

w <- rgl::rglwidget()
htmlwidgets::saveWidget(w, "vignettes/images/myplot.html", selfcontained = TRUE)

and in the vignette text, in place of the live call:

htmltools::tags$iframe(src = "images/myplot.html", width = "100%", height = "500",
                       style = "border: none;")

pkgdown copies the referenced file into the built site automatically, the same way it already copies images referenced via knitr::include_graphics().

Value

heplot3d invisibly returns a list containing the bounding boxes of the error (\mathbf{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.

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)

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)
rgl::rglwidget()

# Plastic data
plastic.mod <- lm(cbind(tear, gloss, opacity) ~ rate*additive, data=Plastic)
## Not run: 
heplot3d(plastic.mod, col=c("red", "blue", "brown", "green3"), wire=FALSE)

## End(Not run)

heplots documentation built on Oct. 4, 2026, 5:06 p.m.