This function provides a convenient interface to the `pairs`

function to produce
enhanced scatterplot matrices, including univariate displays on the diagonal and a variety of fitted lines, smoothers, variance functions, and concentration ellipsoids.
`spm`

is an abbreviation for `scatterplotMatrix`

.

`scatterplotMatrix(x, ...)`# S3 method for formula
scatterplotMatrix(formula, data=NULL, subset, ...)

# S3 method for default
scatterplotMatrix(x, smooth = TRUE,
id = FALSE, legend = TRUE, regLine = TRUE,
ellipse = FALSE, var.labels = colnames(x), diagonal = TRUE,
plot.points = TRUE, groups = NULL, by.groups = TRUE,
use = c("complete.obs", "pairwise.complete.obs"), col =
carPalette()[-1], pch = 1:n.groups, cex = par("cex"),
cex.axis = par("cex.axis"), cex.labels = NULL,
cex.main = par("cex.main"), row1attop = TRUE, ...)

spm(x, ...)

`NULL`

, returned invisibly. This function is used for its side effect: producing
a plot. If point identification is used, a vector of identified points is returned.

- x
a data matrix or a numeric data frame.

- formula
a one-sided “model” formula, of the form

`~ x1 + x2 + ... + xk`

or`~ x1 + x2 + ... + xk | z`

where`z`

evaluates to a factor or other variable to divide the data into groups.- data
for

`scatterplotMatrix.formula`

, a data frame within which to evaluate the formula.- subset
expression defining a subset of observations.

- smooth
specifies a nonparametric estimate of the mean or median function of the vertical axis variable given the horizontal axis variable and optionally a nonparametric estimate of the spread or variance function. If

`smooth=FALSE`

neither function is drawn. If`smooth=TRUE`

, then both the mean function and variance funtions are drawn for ungrouped data, and the mean function only is drawn for grouped data. The default smoother is`loessLine`

, which uses the`loess`

function from the`stats`

package. This smoother is fast and reliable. See the details below for changing the smoother, line type, width and color, of the added lines, and adding arguments for the smoother.- id
controls point identification; if

`FALSE`

(the default), no points are identified; can be a list of named arguments to the`showLabels`

function;`TRUE`

is equivalent to`list(method="mahal", n=2, cex=1, location="lr")`

, which identifies the 2 points (in each group, if`by.groups=TRUE`

) with the largest Mahalanobis distances from the center of the data;`list(method="identify")`

for interactive point identification is not allowed.- legend
controls placement, point size, and text size of a legend if the plot is drawn by groups; if

`FALSE`

, the legend is suppressed. Can be a list with the named element`coords`

specifying the position of the legend in any form acceptable to the`legend`

function, and elements`pt.cex`

and`cex`

corresponding respectively to the`pt.cex`

and`cex`

arguments of the`legend`

function;`TRUE`

(the default) is equivalent to`list(coords=NULL, pt.cex=cex, cex=cex)`

, for which placement will vary by the the value of the`diagonal`

argument---e.g.,`"topright"`

for`diagonal=TRUE`

.- regLine
controls adding a fitted regression line to each plot, or to each group of points if

`by.groups=TRUE`

. If`regLine=FALSE`

, no line is drawn. This argument can also be a list with named list, with default`regLine=TRUE`

equivalent to`regLine = list(method=lm, lty=1, lwd=2, col=col[1])`

specifying the name of the function that computes the line, with line type 1 (solid) of relative line width 2 and the color equal to the first value in the argument`col`

. Setting`method=MASS::rlm`

would fit using a robust regression.- ellipse
controls plotting data-concentration ellipses. If

`FALSE`

(the default), no ellipses are plotted. Can be a list of named values giving`levels`

, a vector of one or more bivariate-normal probability-contour levels at which to plot the ellipses;`robust`

, a logical value determing whether to use the`cov.trob`

function in the MASS package to calculate the center and covariance matrix for the data ellipses; and`fill`

and`fill.alpha`

, which control whether the ellipse is filled and the transparency of the fill.`TRUE`

is equivalent to`list(levels=c(.5, .95), robust=TRUE, fill=TRUE, fill.alpha=0.2)`

.- var.labels
variable labels (for the diagonal of the plot).

- diagonal
contents of the diagonal panels of the plot. If

`diagonal=TRUE`

adaptive kernel density estimates are plotted, separately for each group if grouping is present.`diagonal=FALSE`

suppresses the diagonal entries. See details below for other choices for the diagonal.- plot.points
if

`TRUE`

the points are plotted in each off-diagonal panel.- groups
a factor or other variable dividing the data into groups; groups are plotted with different colors and plotting characters.

- by.groups
if

`TRUE`

, the default, regression lines and smooths are fit by groups.- use
if

`"complete.obs"`

(the default), cases with missing data are omitted; if`"pairwise.complete.obs"), all valid cases are used in each panel of the plot.`

- pch
plotting characters for points; default is the plotting characters in order (see

`par`

).- col
colors for points; the default is

`carPalette`

starting at the second color. The color of the`regLine`

and`smooth`

are the same as for points but can be changed using the the`regLine`

and`smooth`

arguments.- cex
relative size of plotted points. You can use

`cex = 0.001`

to suppress the plotting of points if all you want to show are other graphical features, such as data ellipses, regression lines, smooths, etc.- cex.axis
relative size of axis labels

- cex.labels
relative size of labels on the diagonal

- cex.main
relative size of the main title, if any

- row1attop
If

`TRUE`

(the default) the first row is at the top, as in a matrix, as opposed to at the bottom, as in graph (argument suggested by Richard Heiberger).- ...
arguments to pass down.

John Fox jfox@mcmaster.ca

Many arguments to `scatterplotMatrix`

were changed in version 3 of car, to simplify use of
this function.

The `smooth`

argument is usually either set to `TRUE`

or `FALSE`

to draw, or omit,
the smoother. Alternatively `smooth`

can be set to a list of arguments. The default behavior of
`smooth=TRUE`

is equivalent to `smooth=list(smoother=loessLine, spread=TRUE, lty.smooth=1, lwd.smooth=1.5, lty.spread=3, lwd.spread=1)`

, specifying the smoother to be used, including the spread or variance smooth,
and the line widths and types for the curves. You can also specify the colors you want to use for the mean and variance smooths with the arguments `col.smooth`

and `col.spread`

. Alternative smoothers are `gamline`

which uses the
`gam`

function from the mgcv package, and `quantregLine`

which uses quantile regression to
estimate the median and quartile functions using `rqss`

from the quantreg package. All of these
smoothers have one or more arguments described on their help pages, and these arguments can be added to the
`smooth`

argument; for example, `smooth = list(span=1/2)`

would use the default
`loessLine`

smoother,
include the variance smooth, and change the value of the smoothing parameter to 1/2. For `loessLine`

and `gamLine`

the variance smooth is estimated by separately
smoothing the squared positive and negative
residuals from the mean smooth, using the same type of smoother. The displayed curves are equal to
the mean smooth plus the square root of the fit to the positive squared residuals, and the mean fit minus
the square root of the smooth of the negative squared residuals. The lines therefore represent the
comnditional variabiliity at each value on the horizontal axis. Because smoothing is done separately for
positive and negative residuals, the variation shown will generally not be symmetric about the fitted mean
function. For the `quantregLine`

method, the center estimates the median for each value on the
horizontal axis, and the spread estimates the lower and upper quartiles of the estimated conditional
distribution for each value of the horizontal axis.

The sub-arguments `spread`

, `lty.spread`

and `col.spread`

of the `smooth`

argument are equivalent to the newer `var`

, `col.var`

and `lty.var`

, respectively, recognizing that the spread is a measuure of conditional variability.

By default the diagonal argument is used to draw kernel density estimates of the
variables by setting `diagonal=TRUE`

, which is equivalent to setting ```
diagonal =
list(method="adaptiveDensity", bw=bw.nrd0, adjust=1, kernel=dnorm, na.rm=TRUE)
```

. The additional arguments
shown are descibed at `adaptiveKernel`

. The other methods avaliable, with their default
arguments, are `diagonal=list(method="density", bw="nrd0", adjust=1, kernel="gaussian", na.rm=TRUE)`

which uses `density`

for nonadaptive kernel density estimation; ```
diagonal=list(method
="histogram", breaks="FD")
```

which uses `hist`

for drawing a histogram that ignores grouping, if present;
`diagonal=list(method="boxplot")`

with no additional arguments which draws (parallel) boxplots;
`diagonal=list(method="qqplot")`

with no additional arguments which draws a normal QQ plot; and
`diagonal=list(method="oned")`

with no additional arguments which draws a rug plot tilted to the
diagonal, as suggested by Richard Heiberger.

Earlier versions of `scatterplotMatrix`

included arguments `transform`

and `family`

to estimate power transformations using the `powerTransform`

function before drawing the plot. The same functionality can be achieved by calling `powerTransform`

directly to estimate a transformation, saving the transformed variables, and then plotting.

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

```
scatterplotMatrix(~ income + education + prestige | type, data=Duncan)
scatterplotMatrix(~ income + education + prestige | type, data=Duncan,
regLine=FALSE, smooth=list(span=1))
scatterplotMatrix(~ income + education + prestige,
data=Duncan, id=TRUE, smooth=list(method=gamLine))
```

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