One-Dimensional HE Plots
This function plots a 1-dimensional representation of the hypothesis (H) and error (E) sums-of-squares-and-products matrices for terms and linear hypotheses in a multivariate linear model.
heplot1d(mod, ...) ## S3 method for class 'mlm' heplot1d( mod, terms, hypotheses, term.labels = TRUE, hyp.labels = TRUE, variables = 1, error.ellipse = !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, center.pch = "|", col = getOption("heplot.colors", c("red", "blue", "black", "darkgreen", "darkcyan", "magenta", "brown", "darkgray")), lty = 2:1, lwd = 1:2, xlab, main = "", xlim, axes = TRUE, offset.axes = 0.1, add = FALSE, verbose = FALSE, ... )
mod: a model object of class "mlm".
...: arguments to pass down to plot, text, and points.
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.
variables: indices or names of the two response variables to be plotted; defaults to 1:2.
error.ellipse: if TRUE, plot the error ellipse; 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 ellipse 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 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 the response variables therefore indicates statistical significance; defaults to 0.05.
center.pch: character to use in plotting the centroid of the data; defaults to "|".
col: a color or vector of colors to use in plotting ellipses; the first color is used for the error ellipse; the remaining colors --- recycled as necessary --- are used for the hypothesis ellipses. A single color can be given, in which case it is used for all ellipses. For convenience, the default colors for all heplots produced in a given session can be changed by assigning a color vector via options(heplot.colors =c(...). Otherwise, the default colors are c("red", "blue", "black", "darkgreen", "darkcyan", "magenta", "brown","darkgray").
lty: vector of line types to use for plotting the ellipses; the first is used for the error ellipse, the rest --- possibly recycled --- for the hypothesis ellipses; a single line type can be given. Defaults to 2:1.
lwd: vector of line widths to use for plotting the ellipses; the first is used for the error ellipse, the rest --- possibly recycled --- for the hypothesis ellipses; a single line width can be given. Defaults to 1:2.
xlab: x-axis label; defaults to name of the x variable.
main: main plot label; defaults to "".
xlim: x-axis limits; if absent, will be computed from the data.
axes: Whether to draw the x, y axes; defaults to TRUE
offset.axes: proportion to extend the axes in each direction if computed from the data; optional.
add: if TRUE, add to the current plot; the default is FALSE. If TRUE, the error ellipse is not plotted.
verbose: if TRUE, print the MANOVA table and details of hypothesis tests; the default is FALSE.
The function invisibly returns an object of class "heplot1d", with coordinates for the various hypothesis ellipses and the error ellipse, and the limits of the horizontal and vertical axes. (No methods for manipulating these objects are currently available.)
The components are: - H: ranges for the hypothesis terms
E: range for E
xlim: x-axis limits
In particular, for a given response, the 1-D representations of H and E matrices correspond to line segments. The E ellipse'' is shown as a filled rectangle whose width equals the mean squared error for that response. The H ellipse'' for each model term is shown as a line segment whose length represents either the size of the effect or the evidence for that effect.
This version is an initial sketch. Details of the implementation aresubject to change.
## Plastics data plastic.mod <- lm(cbind(tear, gloss, opacity) ~ rate*additive, data=Plastic) heplot1d(plastic.mod, col=c("pink","blue")) heplot1d(plastic.mod, col=c("pink","blue"),variables=2) heplot1d(plastic.mod, col=c("pink","blue"),variables=3) ## Bees data bees.mod <- lm(cbind(Iz,Iy) ~ caste*treat*time, data=Bees) heplot1d(bees.mod) heplot1d(bees.mod, variables=2)
Anova, linearHypothesis for hypothesis tests in mlms
heplot, heplot3d, pairs.mlm for other HE plot methods
Michael Friendly
Useful links