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.

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

# S3 method for default
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, ...)

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)

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"`

, `"quadratic"`

, `"smooth"`

,
`"additive"`

; 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).

…

arguments to be passed down.

`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.

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).

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

```
# NOT RUN {
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)
}
# }
# NOT RUN {
# 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"))
# }
```

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