Three-Dimensional Scatterplots and Point Identification

The scatter3d function uses the rgl package to draw 3D scatterplots with various regression surfaces. The function Identify3d allows you to label points interactively with the mouse: Press the right mouse button (on a two-button mouse) or the centre button (on a three-button mouse), drag a rectangle around the points to be identified, and release the button. Repeat this procedure for each point or set of “nearby” points to be identified. To exit from point-identification mode, click the right (or centre) button in an empty region of the plot.

Usage

scatter3d(x, ...)

# S3 method for class 'formula'
scatter3d(formula, data, subset, radius, xlab, ylab, zlab, id=FALSE, ...)

# Default S3 method
scatter3d(x, y, z,
    xlab=deparse(substitute(x)), ylab=deparse(substitute(y)),
    zlab=deparse(substitute(z)), axis.scales=TRUE, axis.ticks=FALSE,
    revolutions=0,
    bg.col=c("white", "black"),
    axis.col=if (bg.col == "white") c("darkmagenta", "black", "darkcyan")
                else c("darkmagenta", "white", "darkcyan"),
    surface.col=carPalette()[-1], surface.alpha=0.5,
    neg.res.col="magenta", pos.res.col="cyan",
    square.col=if (bg.col == "white") "black" else "gray",
    point.col="yellow", text.col=axis.col,
    grid.col=if (bg.col == "white") "black" else "gray",
    fogtype=c("exp2", "linear", "exp", "none"),
    residuals=(length(fit) == 1),
    surface=TRUE, fill=TRUE,
    grid=TRUE, grid.lines=26, df.smooth=NULL, df.additive=NULL,
    sphere.size=1, radius=1, threshold=0.01, speed=1, fov=60,
    fit="linear", groups=NULL, parallel=TRUE,
    ellipsoid=FALSE, level=0.5, ellipsoid.alpha=0.1, id=FALSE,
    model.summary=FALSE, 
    reg.function, reg.function.col=surface.col[length(surface.col)], 
    mouseMode=c(none="none", left="polar", right="zoom", middle="fov", 
                 wheel="pull"),
    ...)

Identify3d(x, y, z, axis.scales=TRUE, groups = NULL, labels = 1:length(x),
  col = c("blue", "green", "orange", "magenta", "cyan", "red", "yellow", "gray"),
  offset = ((100/length(x))^(1/3)) * 0.02)

Note

You have to install the rgl package to produce 3D plots. On a Macintosh (but not on Windows or Linux), you may also need to install the X11 windowing system. Go to https://www.xquartz.org/ and click on the link for XQuartz. Double-click on the downloaded disk-image file, and then double-click on XQuartz.pkg to start the installer. You may take all of the defaults in the installation. After XQuartz is installed, you should restart your Macintosh.

Arguments

formula: “model” formula, of the form y ~ x + z or to plot by groups y ~ x + z | g, where g evaluates to a factor or other variable dividing the data into groups.
data: data frame within which to evaluate the formula.
subset: expression defining a subset of observations.
x: variable for horizontal axis.
y: variable for vertical axis (response).
z: variable for out-of-screen axis.
xlab, ylab, zlab: axis labels.
axis.scales: if TRUE, label the values of the ends of the axes. Note: For Identify3d to work properly, the value of this argument must be the same as in scatter3d.
axis.ticks: if TRUE, print interior axis-“tick” labels; the default is FALSE. (The code for this option was provided by David Winsemius.)
revolutions: number of full revolutions of the display.
bg.col: background colour; one of "white", "black".
axis.col: colours for axes; if axis.scales is FALSE, then the second colour is used for all three axes.
surface.col: vector of colours for regression planes, used in the order specified by fit; for multi-group plots, the colours are used for the regression surfaces and points in the several groups.
surface.alpha: transparency of regression surfaces, from 0.0 (fully transparent) to 1.0 (opaque); default is 0.5.
neg.res.col, pos.res.col: colours for lines representing negative and positive residuals.
square.col: colour to use to plot squared residuals.
point.col: colour of points.
text.col: colour of axis labels.
grid.col: colour of grid lines on the regression surface(s).
fogtype: type of fog effect; one of "exp2", "linear", "exp", "none".
residuals: plot residuals if TRUE; if residuals="squares", then the squared residuals are shown as squares (using code adapted from Richard Heiberger). Residuals are available only when there is one surface plotted.
surface: plot surface(s) (TRUE or FALSE).
fill: fill the plotted surface(s) with colour (TRUE or FALSE).
grid: plot grid lines on the regression surface(s) (TRUE or FALSE).
grid.lines: number of lines (default, 26) forming the grid, in each of the x and z directions.
df.smooth: degrees of freedom for the two-dimensional smooth regression surface; if NULL (the default), the gam function will select the degrees of freedom for a smoothing spline by generalized cross-validation; if a positive number, a fixed regression spline will be fit with the specified degrees of freedom.
df.additive: degrees of freedom for each explanatory variable in an additive regression; if NULL (the default), the gam function will select degrees of freedom for the smoothing splines by generalized cross-validation; if a positive number or a vector of two positive numbers, fixed regression splines will be fit with the specified degrees of freedom for each term.
sphere.size: general size of spheres representing points; the actual size is dependent on the number of observations.
radius: relative radii of the spheres representing the points. This is normally a vector of the same length as the variables giving the coordinates of the points, and for the formula method, that must be the case or the argument may be omitted, in which case spheres are the same size; for the default method, the default for the argument, 1, produces spheres all of the same size. The radii are scaled so that their median is 1.
threshold: if the actual size of the spheres is less than the threshold, points are plotted instead.
speed: relative speed of revolution of the plot.
fov: field of view (in degrees); controls degree of perspective.
fit: one or more of "linear" (linear least squares regression), "quadratic" (quadratic least squares regression), "smooth" (nonparametric regression), "additive" (nonparametric additive regression), "robust" (robust linear regression); to display fitted surface(s); partial matching is supported – e.g., c("lin", "quad").
groups: if NULL (the default), no groups are defined; if a factor, a different surface or set of surfaces is plotted for each level of the factor; in this event, the colours in surface.col are used successively for the points, surfaces, and residuals corresponding to each level of the factor.
parallel: when plotting surfaces by groups, should the surfaces be constrained to be parallel? A logical value, with default TRUE.
ellipsoid: plot concentration ellipsoid(s) (TRUE or FALSE).
level: expected proportion of bivariate-normal observations included in the concentration ellipsoid(s); default is 0.5.
ellipsoid.alpha: transparency of ellipsoids, from 0.0 (fully transparent) to 1.0 (opaque); default is 0.1.
id: FALSE, TRUE, or a list controlling point identification, similar to showLabels for 2D plots (see Details).
model.summary: print summary or summaries of the model(s) fit (TRUE or FALSE). scatter3d rescales the three variables internally to fit in the unit cube; this rescaling will affect regression coefficients.
labels: text labels for the points, one for each point; defaults to the observation indices.
col: colours for the point labels, given by group. There must be at least as many colours as groups; if there are no groups, the first colour is used. Normally, the colours would correspond to the surface.col argument to scatter3d.
offset: vertical displacement for point labels (to avoid overplotting the points).
reg.function: an arithmetic expression that is a function of x and z (respectively, the horizontal and out-of-screen explanatory variables), representing an arbitrary regression function to plot.
reg.function.col: color to use for the surface produced by reg.function; defaults to the last color in surface.col.
mouseMode: defines what the mouse buttons, etc., do; passed to par3d in the rgl package; the default in scatter3d is the same as in the rgl package, except for the left mouse button.
...: arguments to be passed down.

Value

scatter3d does not return a useful value; it is used for its side-effect of creating a 3D scatterplot. Identify3d returns the labels of the identified points.

Details

The id argument to scatter3d can be FALSE, TRUE (in which case 2 points will be identified according to their Mahalanobis distances from the center of the data), or a list containing any or all of the following elements:

method: if "mahal" (the default), relatively extreme points are identified automatically according to their Mahalanobis distances from the centroid (point of means); if "identify", points are identified interactively by right-clicking and dragging a box around them; right-click in an empty area to exit from interactive-point-identification mode; if "xz", identify extreme points in the predictor plane; if "y", identify unusual values of the response; if "xyz" identify unusual values of an variable; if "none", no point identification. See showLabels for more information.
n: Number of relatively extreme points to identify automatically (default, 2, unless method="identify", in which case identification continues until the user exits).
labels: text labels for the points, one for each point; in the default method defaults to the observation indices, in the formula method to the row names of the data.
offset: vertical displacement for point labels (to avoid overplotting the points).

Author

John Fox jfox@mcmaster.ca

References

Fox, J. and Weisberg, S. (2019) An R Companion to Applied Regression, Third Edition, Sage.

Examples

    if(interactive() && require(rgl) && require(mgcv)){
scatter3d(prestige ~ income + education, data=Duncan, id=list(n=3))
Sys.sleep(5) # wait 5 seconds
scatter3d(prestige ~ income + education | type, data=Duncan)
Sys.sleep(5)
scatter3d(prestige ~ income + education | type, surface=FALSE,
  ellipsoid=TRUE, revolutions=3, data=Duncan)
scatter3d(prestige ~ income + education, fit=c("linear", "additive"),
  data=Prestige)
Sys.sleep(5)
scatter3d(prestige ~ income + education | type,
    radius=(1 + women)^(1/3), data=Prestige)
Sys.sleep(5)
if (require(mvtnorm)){
  local({
    set.seed(123)
    Sigma <- matrix(c(
      1, 0.5,
      0.5, 1),
      2, 2
    )
    X <- rmvnorm(200, sigma=Sigma)
    D <- data.frame(
      x1 = X[, 1],
      x2 = X[, 2]
    )
    D$y <- with(D, 10 + 1*x1 + 2*x2 + 3*x1*x2 + rnorm(200, sd=3))
    # plot true regression function
    scatter3d(y ~ x1 + x2, D, 
              reg.function=10 + 1*x + 2*z + 3*x*z,
              fit="quadratic", revolutions=2)
  })
}
  }
  if (FALSE)  # requires user interaction to identify points
# drag right mouse button to identify points, click right button in open area to exit
scatter3d(prestige ~ income + education, data=Duncan, id=list(method="identify"))
scatter3d(prestige ~ income + education | type, data=Duncan, id=list(method="identify"))
#> Error in if (llx > urx) {    temp <- llx    llx <- urx    urx <- temp}: argument is of length zero
     # \dontrun{}