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Quantile-Quantile and Tukey mean-difference plots

Source: R/eda_qq.R
eda_qq.Rd

eda_qq Generates an empirical QQ plot and a Tukey mean-difference plot

Usage

eda_qq(
  x,
  y = NULL,
  fac = NULL,
  norm = FALSE,
  sym = FALSE,
  md = FALSE,
  p = 1L,
  tukey = FALSE,
  base = exp(1),
  fx = NULL,
  fy = NULL,
  show.par = TRUE,
  grey = 0.6,
  pch = 21,
  p.col = "grey50",
  p.fill = "grey80",
  size = 1,
  alpha = 0.8,
  med = TRUE,
  inner = 0.75,
  q = TRUE,
  q.type = 5,
  qcol = rgb(0, 0, 0, 0.05),
  tails = FALSE,
  tail.pch = 21,
  tail.p.col = "grey70",
  tail.p.fill = NULL,
  switch = FALSE,
  xlab = NULL,
  ylab = NULL,
  title = NULL,
  t.size = 1.2,
  plot = TRUE,
  ...
)

Arguments

x

Vector for first variable, or a dataframe.

y

Vector for second variable, or column defining the continuous variable if x is a dataframe.

fac

Column defining the categorical variable if x is a dataframe. The categorical column must be limited to two levels (groups). dataframe. Ignored if x and y are vectors.

norm

Defunct. Use eda_theo instead.

sym

Defunct. Use eda_sym instead.

md

Boolean determining if a Tukey mean-difference plot should be generated.

p

Power transformation to apply to continuous variable(s).

tukey

Boolean determining if a Tukey transformation should be adopted (FALSE adopts a Box-Cox transformation).

base

Base used with the log() function if p = 0.

fx

Formula to apply to x variable before pairing up with y. This is computed after any transformation is applied to the x variable.

fy

Formula to apply to y variable before pairing up with x. This is computed after any transformation is applied to the y variable.

show.par

Boolean determining if parameters such as power transformation and formula should be displayed.

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 color.

med

Boolean determining if median lines should be drawn.

inner

Fraction of the data considered as "mid values". Defaults to 75\ which of the tail-end points are to be symbolized differently, tails=TRUE.

q

Boolean determining if inner data region should be shaded.

q.type

An integer between 1 and 9 selecting one of the nine quantile algorithms. (See quantile function).

qcol

Fill color of inner quantile box.

tails

Boolean determining if points outside of the inner region should be symbolized differently. Tail-end points are symbolized via the tail.pch, tail.p.col and tail.p.fill arguments.

tail.pch

Tail-end point symbol type (See tails).

tail.p.col

Tail-end color for point symbol (See tails).

tail.p.fill

Tail-end point fill color passed to bg (Only used for tail.pch ranging from 21-25).

switch

Boolean determining if the axes should be swapped in an empirical QQ plot. Only applies to dataframe input. Ignored if vectors are passed to the function.

xlab

X label for output plot. Ignored if x is a dataframe.

ylab

Y label for output plot. Ignored if x is a dataframe.

title

Title to add to plot.

t.size

Title size.

plot

Boolean determining if plot should be generated.

...

Arguments passed on to .eda_plot_xy

dat

Optional data frame containing x and y.

px

Power transformation used in the input data to display if show.par = TRUE.

py

Power transformation used in the input data to display if show.par = TRUE.

raw_tick

Logical. If TRUE, original (untransformed) equally spaced tick values are displayed on the re-expressed axes.

xlim

X-axis range.

ylim

Y-axis range.

reg

Logical; whether to fit and display a regression line.

poly

Integer; regression model polynomial degree (defaults to 1 for linear model).

robust

Logical; if TRUE, uses robust regression (MASS::rlm).

rlm.d

List; parameters for MASS::rlm, (e.g., list(psi = "psi.bisquare")).

w

Optional numeric vector of weights for regression.

lm.col

Regression line color.

lm.lw

Numeric; Regression line width.

lm.lty

Numeric; Regression line type.

sd

Logical; whether to show ±1 SD lines.

mean.l

Logical; whether to show x and y mean reference lines.

asp

Logical; whether to preserve the aspect ratio (ignored if square = FALSE).

square

Logical; whether to create a square plotting window.

loe

Logical; whether to plot loess smooth line.

loe.lw

Numeric; Loess smooth line width.

loe.col

Loess smooth color.

loe.lty

Numeric; Loess smooth line type.

loess.d

List; parameters for loess.smooth, e.g., list(span = 0.7, degree = 1).

stats

Logical; if TRUE, displays model statistics (R², β, p-value).

stat.size

Text size for stats plot display.

hline

Numeric; location(s) of additional horizontal reference lines. Can be passed via the c() function.

vline

Numeric; location(s) of additional vertical reference lines. Can be passed via the c() function.

Value

Returns a list with the following components:

  • data: Dataframe with input x and y values. Data will be interpolated to smallest quantile batch if batch sizes differ. Values will reflect power transformation defined in p.

  • p: Re-expression applied to original values.

  • fx: Formula applied to x variable.

  • fy: Formula applied to y variable.

Details

By default, the QQ plot will highlight the inner 75\ for both x and y axes to mitigate the visual influence of extreme values. The inner argument controls the extent of this region. For example inner = 0.5 will highlight the IQR region.

If the shaded regions are too distracting, you can opt to have the tail-end points symbolized differently by setting tails = TRUE and q = FALSE. The tail-end point symbols can be customized via the tail.pch, tail.p.col and tail.p.fill arguments.
The middle dashed line represents each batch's median value. It can be turned off by setting med = FALSE

Console output prints the suggested multiplicative and additive offsets. It adopts a resistant line fitting technique to derive the coefficients. The suggested offsets output applies to the raw or re-expressed data but it ignores any fx or fy transformations applied to the data. Note that the suggested offsets may not always be the most parsimonious fit. Eyeballing the offsets may sometimes result in a more satisfactory characterization of the differences between batches. See the QQ plot article for an introduction on its use and interpretation.

To generate a Tukey mean-difference plot, set med = TRUE.

For more information on this function and on interpreting a QQ plot see the QQ plot article.

References

Examples


# Passing data as a dataframe
 singer <- lattice::singer
 dat <- singer[singer$voice.part  %in% c("Bass 2", "Tenor 1"), ]
 eda_qq(dat, height, voice.part)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

# If the shaded region is too distracting, you can apply a different symbol
# to the tail-end points and different color to the points falling in the
# inner region.
eda_qq(dat, height, voice.part, q = FALSE, tails = TRUE, tail.pch = 3,
       p.fill = "coral", size = 1.2, med = FALSE)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

# For a more traditional look to the QQ plot
eda_qq(dat, height, voice.part, med = FALSE, q = FALSE)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

# Passing data as two separate vector objects
 bass2 <- subset(singer, voice.part == "Bass 2", select = height, drop = TRUE )
 tenor1 <- subset(singer, voice.part == "Tenor 1", select = height, drop = TRUE )

 eda_qq(bass2, tenor1)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # The function suggests an offset of the form y = x * 1.04 - 5.2
 eda_qq(bass2, tenor1, fx = "x * 1.04 - 5.2")

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # The suggested offset helps align the points along the x=y line, but we
 # we might come up with a better characterization of this offset.
 # There seems to be an additive offset of about 2 inches. By subtracting 2
 # from the x variable, we should have points line up with the x=y line
 eda_qq(bass2, tenor1, fx = "x - 2")

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # We can fine-tune by generating the Tukey mean-difference plot
 eda_qq(bass2, tenor1, fx = "x - 2", md = TRUE)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # An offset of another 0.5 inches seems warranted
 # We can say that overall, bass2 singers are 2.5 inches taller than  tenor1.
 # The offset is additive.
 eda_qq(bass2, tenor1, fx = "x - 2.5", md = TRUE)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # Note that the "suggested offset" in the console could have also been
 # applied to the data (though this formula is a bit more difficult to
 # interpret than our simple additive model)
 eda_qq(bass2, tenor1, fx = "x * 1.04 -5.2", md = TRUE)

#> [1] "Suggested offsets:y = x * 1.04 + (-5.2163)"

 # Example 2: Sepal width
 setosa <- subset(iris, Species == "setosa", select = Petal.Width, drop = TRUE)
 virginica <- subset(iris, Species == "virginica", select = Petal.Width, drop = TRUE)

 eda_qq(setosa, virginica)

#> [1] "Suggested offsets:y = x * 1.7143 + (1.6286)"

 # The points are not completely parallel to the  x=y line suggesting a
 # multiplicative offset. The slope may be difficult to eyeball. The function
 # outputs a suggested slope and intercept. We can start with that
 eda_qq(setosa, virginica, fx = "x *  1.7143")

#> [1] "Suggested offsets:y = x * 1.7143 + (1.6286)"

 # Now let's add the suggested additive offset.
 eda_qq(setosa, virginica, fx = "x *  1.7143  + 1.6286")

#> [1] "Suggested offsets:y = x * 1.7143 + (1.6286)"

 # We can confirm this value via the mean-difference plot
 # Overall, we have both a multiplicative and additive offset between the
 # species' petal widths.
 eda_qq(setosa, virginica, fx = "x *  1.7143 + 1.6286", md = TRUE)

#> [1] "Suggested offsets:y = x * 1.7143 + (1.6286)"