# spreadLevelPlot

##### Spread-Level Plots

Creates plots for examining the possible dependence of spread on level, or an extension of these plots to the studentized residuals from linear models.

- Keywords
- hplot, regression

##### Usage

`spreadLevelPlot(x, ...)`slp(...)

# S3 method for formula
spreadLevelPlot(x, data=NULL, subset, na.action,
main=paste("Spread-Level Plot for", varnames[response],
"by", varnames[-response]), ...)

# S3 method for default
spreadLevelPlot(x, by, robust.line=TRUE,
start=0, xlab="Median", ylab="Hinge-Spread",
point.labels=TRUE, las=par("las"),
main=paste("Spread-Level Plot for", deparse(substitute(x)),
"by", deparse(substitute(by))),
col=carPalette()[1], col.lines=carPalette()[2],
pch=1, lwd=2, grid=TRUE, ...)

# S3 method for lm
spreadLevelPlot(x, robust.line=TRUE,
xlab="Fitted Values", ylab="Absolute Studentized Residuals", las=par("las"),
main=paste("Spread-Level Plot for\n", deparse(substitute(x))),
pch=1, col=carPalette()[1], col.lines=carPalette()[2:3], lwd=2, grid=TRUE,
id=FALSE, smooth=TRUE, ...)
# S3 method for spreadLevelPlot
print(x, ...)

##### Arguments

- x
a formula of the form

`y ~ x`

, where`y`

is a numeric vector and`x`

is a factor, or an`lm`

object to be plotted; alternatively a numeric vector.- data
an optional data frame containing the variables to be plotted. By default the variables are taken from the environment from which

`spreadLevelPlot`

is called.- subset
an optional vector specifying a subset of observations to be used.

- na.action
a function that indicates what should happen when the data contain

`NA`

s. The default is set by the`na.action`

setting of`options`

.- by
a factor, numeric vector, or character vector defining groups.

- robust.line
if

`TRUE`

a robust line is fit using the`rlm`

function in the`MASS`

package; if`FALSE`

a line is fit using`lm`

.- start
add the constant

`start`

to each data value.- main
title for the plot.

- xlab
label for horizontal axis.

- ylab
label for vertical axis.

- point.labels
if

`TRUE`

label the points in the plot with group names.- las
if

`0`

, ticks labels are drawn parallel to the axis; set to`1`

for horizontal labels (see`par`

).- col
color for points; the default is the first entry in the current car palette (see

`carPalette`

and`par`

).- col.lines
for the default method, the line color, defaulting to the second entry in the car color palette; for the

`"lm"`

method, a vector of two colors for, respectively, the fitted straight line and a nonparametric regression smooth line, default to the second and third entries in the car color palette.- pch
plotting character for points; default is

`1`

(a circle, see`par`

).- lwd
line width; default is

`2`

(see`par`

).- grid
If TRUE, the default, a light-gray background grid is put on the graph

- 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=list("x", "y"), n=2, cex=1, col=carPalette()[1], location="lr")`

, which identifies the 2 points the most extreme horizontal ("X", absolute studentized residual) values and the 2 points with the most extreme horizontal ("Y", fitted values) values.- smooth
specifies the smoother to be used along with its arguments; if

`FALSE`

, no smoother is shown; can be a list giving the smoother function and its named arguments;`TRUE`

, the default, is equivalent to`list(smoother=loessLine)`

. See`ScatterplotSmoothers`

for the smoothers supplied by the car package and their arguments.- …
arguments passed to plotting functions.

##### Details

Except for linear models, computes the statistics for, and plots, a Tukey spread-level plot of log(hinge-spread) vs. log(median) for the groups; fits a line to the plot; and calculates a spread-stabilizing transformation from the slope of the line.

For linear models, plots log(abs(studentized residuals) vs. log(fitted values). Point labeling was added in November, 2016.

The function `slp`

is an abbreviation for `spreadLevelPlot`

.

##### Value

An object of class `spreadLevelPlot`

containing:

a matrix with the lower-hinge, median, upper-hinge, and hinge-spread
for each group. (Not for an `lm`

object.)

spread-stabilizing power transformation, calculated as \(1 - slope\) of the line fit to the plot.

##### References

Fox, J. (2016)
*Applied Regression Analysis and Generalized Linear Models*,
Third Edition. Sage.

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

Hoaglin, D. C., Mosteller, F. and Tukey, J. W. (Eds.) (1983)
*Understanding Robust and Exploratory Data Analysis.* Wiley.

##### See Also

##### Examples

```
# NOT RUN {
spreadLevelPlot(interlocks + 1 ~ nation, data=Ornstein)
slp(lm(interlocks + 1 ~ assets + sector + nation, data=Ornstein))
# }
```

*Documentation reproduced from package car, version 3.0-3, License: GPL (>= 2)*