Spread-location and spread-level plots

The eda_sl function generates William Cleveland's spread-location plot for univariate and bivariate data. The function will also generate Tukeys' spread-level plot.

Usage

eda_sl(
  dat,
  x = NULL,
  fac = NULL,
  type = "location",
  p = 1,
  tukey = FALSE,
  sprd = "frth",
  jitter = 0.01,
  robust = TRUE,
  loess.d = list(family = "symmetric", degree = 1, span = 1),
  loe.col = rgb(0.3, 0.3, 1, 1),
  label = TRUE,
  label.col = "lightsalmon",
  plot = TRUE,
  equal = TRUE,
  grey = 0.6,
  pch = 21,
  p.col = "grey50",
  p.fill = "grey80",
  size = 0.8,
  alpha = 0.8,
  xlab = NULL,
  ylab = NULL,
  labelxbuff = 0.05,
  labelybuff = 0.05,
  show.par = TRUE
)

Arguments

dat: Dataframe of univariate data or a linear model.
x: Continuous variable column (ignored if dat is a linear model).
fac: Categorical variable column (ignored if dat is a linear model).
type: s-l plot type. "location" = spread-location, "level" = spread-level (only for univariate data). "dependence" = spread-dependence (only for bivariate model input).
p: Power transformation to apply to variable. Ignored if input is a linear model.
tukey: Boolean determining if a Tukey transformation should be adopted (FALSE adopts a Box-Cox transformation).
sprd: Choice of spreads used in the spread-versus-level plot (i.e. when type = "level"). Either interquartile, sprd = "IQR" or fourth-spread, sprd = "frth" (default).
jitter: Jittering parameter for the spread-location plot. A fraction of the range of location values.
robust: Boolean indicating if robust regression should be used on the spread-level plot.
loess.d: Arguments passed to the internal loess function. Applies only to the bivariate model s-l plots and the spread-level plot.
loe.col: LOESS curve color.
label: Boolean determining if group labels are to be added to the spread-location plot.
label.col: Color assigned to group labels (only applicable if type = location).
plot: Boolean determining if plot should be generated.
equal: Boolean determining if axes lengths should match (i.e. square plot).
grey: Grey level to apply to plot elements (0 to 1 with 1 = black).
pch: Point symbol type.
p.col: Color for point symbol.
p.fill: Point fill color passed to bg (Only used for pch ranging from 21-25).
size: Point size (0-1).
alpha: Point transparency (0 = transparent, 1 = opaque). Only applicable if rgb() is not used to define point colors.
xlab: X label for output plot.
ylab: Y label for output plot.
labelxbuff: Buffer to add to the edges of the plot to make room for the labels in a spread-location plot. Value is a fraction of the plot width.
labelybuff: Buffer to add to the top of the plot to make room for the labels in a spread-location plot. Value is a fraction of the plot width.
show.par: Boolean determining if the power transformation applied to the data should be displayed.

Value

Returns a dataframe of level and spread values.

Details

The function generates a few variations of the spread-location/spread-level plots depending on the data input type and parameter passed to the type argument. The residual spreads are mapped to the y-axis and the levels are mapped to the x-axis. Their values are computed as follows:

type = "location" (univariate data):

William Cleveland's spread-location plot applied to univariate data.
\(\ spread = \sqrt{|residuals|}\)
\(\ location = medians\)
type = "level" (univariate data):

Tukey's spread-level plot (aka spread-versus-level plot, Hoaglin et al., p 260). If the pattern is close to linear, the plot can help find a power transformation that will help stabilize the spread in the data by subtracting one from the fitted slope. This option outputs the slope of the fitted line in the console. A loess is added to assess linearity. By default, the fourth spread is used to define the spread. Alternatively, the IQR can be used by setting spread = "IQR". The output will be nearly identical except for small datasets where the two methods may diverge slightly in output.
\(\ spread = log(fourth\ spread(residuals))\)
\(\ location = log(medians)\)
type = "location" if input is a model of class lm, eda_lm or eda_rline:

William Cleveland's spread-location plot (aka scale-location plot) applied to residuals of a linear model.
\(\ spread = \sqrt{|residuals|}\)
\(\ location = fitted\ values\)
type = "dependence" if input is a model of class lm, eda_lm or eda_rline:

William Cleveland's spread-location plot applied to residuals of a linear model.
\(\ spread = \sqrt{|residuals|}\)
\(\ dependence = x\ variable\)

References

Understanding Robust and Exploratory Data Analysis, Hoaglin, David C., Frederick Mosteller, and John W. Tukey, 1983.
William S. Cleveland. Visualizing Data. Hobart Press (1993)

Examples

cars <- MASS::Cars93
# Cleveland's spread-location plot applied to univariate data
eda_sl(cars, MPG.city, Type)


# You can specify the exact form of the spread on the y-axis
# via the ylab argument
eda_sl(cars, MPG.city, Type, ylab = expression(sqrt(abs(residuals))) )


# The function can also generate Tukey's spread-level plot to identify a
# power transformation that can stabilize spread across fitted values
# following power = 1 - slope
eda_sl(cars, MPG.city, Type, type = "level")

#> Slope =  3.013843

# A slope of around 3 is computed from the s-l plot, therefore, a suggested
# power is 1 - 3 = -2. We can apply a power transformation within the
# function via the p argument. By default, a Box-Cox transformation method
# is adopted.
eda_sl(cars, MPG.city, Type, p = -2)


# Spread-location plot can also be generated from residuals of a linear model
M1 <- lm(mpg ~ hp, mtcars)
eda_sl(M1)


# Spread can be compared to X instead of fitted value
eda_sl(M1, type = "dependence")