Quantile regression predictions and annotations

Statistics stat_quant_line(), stat_quant_band() and stat_quant_eq() fit models by quantile regression. While stat_quant_line() and stat_quant_band() add prediction lines and bands, stat_quant_eq() adds textual labels to a plot.

Usage

stat_quant_band(
  mapping = NULL,
  data = NULL,
  geom = "smooth",
  position = "identity",
  ...,
  orientation = NA,
  quantiles = c(0.25, 0.5, 0.75),
  formula = NULL,
  fit.seed = NA,
  fm.values = FALSE,
  n = 80,
  fullrange = FALSE,
  limit.to = NULL,
  method = "rq",
  method.args = list(),
  n.min = 3L,
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

stat_quant_eq(
  mapping = NULL,
  data = NULL,
  geom = "text_npc",
  position = "identity",
  ...,
  orientation = NA,
  formula = NULL,
  quantiles = c(0.25, 0.5, 0.75),
  method = "rq:br",
  method.args = list(),
  n.min = 10L,
  fit.seed = NA,
  eq.with.lhs = TRUE,
  eq.x.rhs = NULL,
  coef.digits = 3,
  coef.keep.zeros = TRUE,
  decreasing = getOption("ggpmisc.decreasing.poly.eq", FALSE),
  rho.digits = 4,
  label.x = "left",
  label.y = "top",
  hstep = 0,
  vstep = NULL,
  output.type = NULL,
  na.rm = FALSE,
  parse = NULL,
  show.legend = FALSE,
  inherit.aes = TRUE
)

stat_quant_line(
  mapping = NULL,
  data = NULL,
  geom = "smooth",
  position = "identity",
  ...,
  orientation = NA,
  quantiles = c(0.25, 0.5, 0.75),
  formula = NULL,
  se = length(quantiles) == 1L,
  fit.seed = NA,
  fm.values = FALSE,
  n = 80,
  fullrange = FALSE,
  limit.to = NULL,
  method = "rq",
  method.args = list(),
  n.min = 3L,
  level = 0.95,
  type = "direct",
  interval = "confidence",
  na.rm = FALSE,
  show.legend = NA,
  inherit.aes = TRUE
)

Arguments

mapping: The aesthetic mapping, usually constructed with aes(). Only needs to be set at the layer level if you are overriding the plot defaults.
data: A layer specific dataset, only needed if you want to override the plot defaults.
geom: The geometric object to use display the data
position: The position adjustment to use for overlapping points on this layer.
...: other arguments passed on to layer. This can include aesthetics whose values you want to set, not map. See layer for more details.
orientation: character Either "x" or "y" controlling the default for formula. The letter indicates the aesthetic considered the explanatory variable in the model fit.
quantiles: numeric vector Values in 0..1 indicating the quantiles.
formula: a formula object. Using aesthetic names x and y instead of original variable names.
fit.seed: RNG seed argument passed to set.seed(). Defaults to NA, indicating that set.seed() should not be called.
fm.values: logical Add metadata and parameter estimates extracted from the fitted model object; FALSE by default.
n: Number of points at which to predict with the fitted model.
fullrange: logical Should the fit prediction span the full range of the plot, or just the range of the explanatory variable?
limit.to: character or numeric If character one of "", "x", "y" or "xy". Should the fit prediction be constrained to the range of the variables mapped to x and/or y in each data group? If numeric, the new data values to use for the explanatory variable when computing the predicted line and confidence band. When set, limit.to silently overrides fullrange!
method: function or character If character, "rq", "rqss" or the name of a model fit function are accepted, possibly followed by the fit function's method argument separated by a colon (e.g. "rq:br"). If a function different to rq(), it must accept arguments named formula, data, weights, tau and method and return a model fit object of class rq, rqs or rqss.
method.args: named list with additional arguments passed to rq(), rqss() or to another function passed as argument to method.
n.min: integer Minimum number of distinct values in the explanatory variable (on the rhs of formula) for fitting to the attempted.
na.rm: a logical indicating whether NA values should be stripped before the computation proceeds.
show.legend: logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes.
inherit.aes: If FALSE, overrides the default aesthetics, rather than combining with them. This is most useful for helper functions that define both data and aesthetics and shouldn't inherit behaviour from the default plot specification, e.g. borders.
eq.with.lhs: If character the string is pasted to the front of the equation label before parsing or a logical (see note).
eq.x.rhs: character this string will be used as replacement for "x" in the model equation when generating the label before parsing it.
coef.digits, rho.digits: integer Number of significant digits to use for the fitted coefficients and rho in labels.
coef.keep.zeros: logical Keep or drop trailing zeros when formatting the fitted coefficients and F-value.
decreasing: logical It specifies the order of the terms in the returned character string; in increasing (default) or decreasing powers.
label.x, label.y: numeric with range 0..1 "normalized parent coordinates" (npc units) or character if using geom_text_npc() or geom_label_npc(). If using geom_text() or geom_label() numeric in native data units. If too short they will be recycled.
hstep, vstep: numeric in npc units, the horizontal and vertical step used between labels for different groups.
output.type: character One of "expression", "text", "markdown", "marquee", "latex", "latex.eqn", "latex.deqn" or "numeric".
parse: logical Passed to the geom. If TRUE, the labels will be parsed into expressions and displayed as described in plotmath. Default is TRUE if output.type = "expression" and FALSE otherwise.
se: logical Passed to quantreg::predict.rq().
level: numeric in range [0..1] Passed to quantreg::predict.rq().
type: character Passed to quantreg::predict.rq().
interval: character Passed to quantreg::predict.rq().

Value

stat_quant_eq() returns a data frame, with one row per quantile and columns as described below, while stat_quant_line() and stat_quant_band() return a data frame, with n rows per quantile and columns as described below. If the number of observations is less than n.min or if the model fit method returns NA or NULL, a data frame with no rows or columns is returned, resulting in an empty/invisible plot layer.

Details

While stat_poly_line() and stat_poly_eq() fit a single model per plot layer, stat_quant_line(), stat_quant_band() and stat_quant_eq() can fit multiple models sharing the same method and formula but differing in their probability. These probabilities are passed a vector argument to parameter quantiles.

stat_quant_line fits one or more quantile regressions and obtains predictions similarly to stat_quantile() from 'ggplot2', but in addition it computes confidence regions for the prediction lines. By default each quantile is plotted as a line, with a confidence band when se = TRUE.

stat_quant_band() fits quantile regressions and obtains predictions identically to stat_quant_line(). stat_quant_band() fits 2 or 3 quantiles in the same plot layer and displays the area between the predicted regression lines for the extreme quantiles as a band.

stat_quant_eq() fits quantile regressions and generates a set of labels for each regression line fitted. By default the labels are formatted as R's plotmath expressions, LaTeX and markdown are also supported.

stat_quant_eq(), stat_quant_line() and stat_quant_band() support both "rq" and "rqss" as method. In the case of "rqss" the model formula makes normally use of qss() to formulate the spline and its constraints. User defined functions are supported as method as long as they accept arguments named formula, data, weights, tau and method and return a model fit object of class rq, rqs or rqss. Such user-defined functions can implement model selection and/or method selection, or conditionally skip model fitting on a per data group basis.

The minimum number of observations with distinct values in the explanatory variable can be set through parameter n.min. The default n.min = 10L is a bare minimum for quantile regression. Model fits with such a small number of observations are of little interest and using larger values of n.min than the default is wise.

There are interesting uses for double quantile regression, i.e., a pair of quantile regressions on x and y on the same data. For example, when two variables are subject to mutual constrains, it is useful to consider both of them as explanatory and interpret the relationship based on them considered as limiting. 'ggpmisc' (>= 0.4.1) supports orientation making it easy implement the approach described by Cardoso (2019) under the name of "Double quantile regression".

Variables returned by `stat_quant_eq()`

If output.type is "numeric" the returned tibble contains columns in addition to a modified version of the original group:

x,npcx: x position
y,npcy: y position
coef.ls: list containing the "coefficients" matrix from the summary of the fit object
rho, AIC, n: numeric values extracted or computed from fit object
rq.method: character, method used.
hjust, vjust: Set to "inward" to override the default of the "text" geom.
quantile: Indicating the quantile used for the fit
quantile.f: Factor with a level for each quantile
b_0.constant: TRUE is polynomial is forced through the origin
b_i: One or columns with the coefficient estimates

If output.type different from "numeric" the returned tibble contains columns below in addition to a modified version of the original group:

x,npcx: x position
y,npcy: y position
eq.label: equation for the fitted polynomial as a character string to be parsed
r.label, and one of cor.label, rho.label, or tau.label: $rho$ of the fitted model as a character string to be parsed
AIC.label: AIC for the fitted model.
n.label: Number of observations used in the fit.
method.label: Set according method used.
rq.method: character, method used.
rho, n: numeric values extracted or computed from fit object.
hjust, vjust: Set to "inward" to override the default of the "text" geom.
quantile: Numeric value of the quantile used for the fit
quantile.f: Factor with a level for each quantile

To explore the computed values returned for a given input we suggest the use of geom_debug as shown in the example below.

Variables returned by `stat_quant_line()`

y or x: predicted value
ymin or xmin: lower confidence limit around the fitted line
ymax or xmax: upper confidence limit around the fitted line

If fm.values = TRUE is passed then one column with the number of observations n used for each fit is also included, with the same value in each row within a group. This is wasteful and disabled by default, but provides a simple and robust approach to achieve effects like colouring or hiding of the model fit line based on the number of observations.

Variables returned by `stat_quant_band()`

y or x: Regression prediction for the middle quantile, if three quantiles are passed as argument
ymin or xmin: Regression prediction for the smallest quantile
ymax or xmax: Regression prediction for the largest quantile

Output types

The formatting of character strings to be displayed in plots are marked as mathematical equations. Depending on the geom used, the mark-up needs to be encoded differently, or in some cases mark-up not applied.

"expression": The labels are encoded as character strings to be parsed into R's plotmath expressions.
"LaTeX", "TeX", "tikz", "latex": The labels are encoded as 'LaTeX' maths equations, without the "fences" for switching in math mode.
"latex.eqn": Same as "latex" but enclosed in single $, i.e., as in-line maths.
"latex.deqn": Same as "latex" but enclosed in double $$, i.e., as display maths.
"markdown": The labels are encoded as character strings using markdown syntax, with some embedded HTML.
"marquee": The labels are encoded as character strings using markdown syntax, with 'marquee' supported spans.
"text": The labels are plain ASCII character strings.
"numeric": No labels are generated. This value is accepted by the statistics, but not by the label formatting functions.
NULL: The value used depends on the argument passed to geom.

If geom = "latex" (package 'xdvir') the output type used is "latex.eqn". If geom = "richtext" (package 'ggtext') or geom = "textbox" (package 'ggtext') the output type used is "markdown". If geom = "marquee" (package 'marquee') the output type used is "marquee". For all other values of geom the default is "expression". Invalid values as argument trigger an error.

Model equation label

By default the equation label uses as symbols the names of the aesthetics, x and y. However, "x" and "y" can be substituted by providing a replacement character string for the right-hand-side and left-hand-side through eq.x.rhs and eq.with.lhs, respectively. For backward compatibility a logical is also accepted as argument for eq.with.lhs, with FALSE suppressing the left-hand-side.

If the model formula includes a transformation of the explanatory variable in its right-hand-side (rhs), a matching argument should be passed to parameter eq.x.rhs as its default value would result in an equation label that does not reflect the applied transformation. In most cases, a transformation should not be applied within the left hand side (lhs) of the model formula, but instead in the mapping of the response variable within aes. In this case it may be necessary to also pass a matching argument to parameter eq.with.lhs.

Parameter orientation is redundant as the orientation can be set by the formula but is included for consistency with ggplot2::stat_smooth().

Position of labels

When data are grouped by mapping a factor to an aesthetic, e.g., colour, shape and/or linetype the model is fitted separately to each group, and for each group a whole set of labels is generated. If the argument passed to label.y is a vector of length 1, this value determines the position of the equation and/or other labels for the first group, and the positions of the labels for the remaining groups are generated by adding vspace based on the group number. If the argument passed to label.y is a vector of length > 1, it is used unchanged, possibly extended by recycling, ignoring vstep.

If the labels are rotated by 90 degrees then the automatic stepping is best based on hstep with vstep = 0. Similarly as described above, if label.x is a vector of length > 1, it is used unchanged, possibly extended by recycling, ignoring hstep.

When using facets and with a grouping that does not repeat in each panel, the automatic positioning in most cases will not be the desired one. Manual positioning using a vector of length > 1 for label.x and/or label.y is the currently available workaround.

Model formula and model fitting

A ggplot statistic receives as data a data frame that is not the one passed as argument by the user, but instead a data frame with the variables mapped to aesthetics. In stat_poly_eq() the compute function is applied by group, each call "seeing" the subset of data for an individual group. As supported models are for regression lines, variables mapped to x and y should both be continuous, i.e., numeric or date time and model formulas defined using x and y as variable names.

The interpretation of the argument passed to formula is enhanced compared to stat_smooth(). Formulas with x as explanatory variable work as in stat_smooth() but formulas with y as explanatory variable are also accepted. orientation is set automatically based on which explanatory variable appears in the formula. Spline-based smoothers are only partially supported.

Range of the prediction line

The range of the prediction line is controlled by parameters fullrange and limit.to. fullrange is backwards compatible both with earlier versions of 'ggpmisc' and with stat_smooth() from 'ggplot2'; an argument passed to limit.to overrides fullrange making it possible to constrain the range to that of x, y, or both simultaneously, with "x", "y", or "xy", respectively, as argument. limit.to also accepts a numeric vector of values to be used as newdata when computing the prediction. Limiting the range based on both aesthetics is the best approach for major axis regression (MA, SMA, RMA) but can occasionally be useful also with some other methods when slopes are very steep and error variance in the explanatory variable is large. A numeric vector can be used to predict the response at specific values of the explanatory variable. If a single or very few values are predicted, it can be necessary to override the default geom = "smooth" with geom = "pointrange".

Model fit methods supported

Several model fit functions are supported explicitly (see tables), and some of their differences smoothed out. Compatibility is checked late, based on the class of the returned fitted model object. This makes it possible to use wrapper functions that do model selection or other adjustments to the fit procedure on a per panel or per group basis. Moreover, if the value returned as model fit object is NULL or NA, plotting is skipped on a per group within panel basis.

In the case of fitted model objects of classes not explicitly supported, an attempt is made to find the usual accessors and/or fitted object members, and if found, either complete or partial support is frequently achieved. In this case a message is issued encouraging users to check the validity of the values extracted as the structure of fitted model objects belonging to different classes and the values returned by their accessors can vary, potentially resulting in decoding errors leading to the return of wrong values for estimates.

The argument to parameter method can be either the name of a function object, possibly using double colon notation in case its package is not attached, or a character string matching the function name for functions in the search path. This approach makes it possible to support model fit functions that are not dependencies of 'ggpmisc'. Either by attaching the package where the function is defined and passing it by name or as string, or using double colon notation when passing the name of the function.

User-defined functions can be passed as argument to parameter method as long as they have parameters formula, data subset and possibly weights. Additional arguments can be passed to any method as a named list through parameter method.args. As in stat_smooth() prior weights are passed to the model fit functions' weights (plural!) parameter by mapping a numeric variable to plot aesthetic weight (singular!).

Tables 1 lists natively supported model fit functions, with the caveat that only some 'broom' methods' specializations have been actually tested with statistics from 'ggpmisc'. In addition, the statistics based on 'broom' methods require the user to tailor their behaviour by passing additional arguments in the call and occasionally some detective work to find out the names of variables in the returned data frame as these names are set by methods from 'broom'.

Table 1. Model fit methods supported by the different statistics available in package 'ggpmisc'. Column $f$ indicates whether computations are done by group (G) or by plot panel (P).

Statistic	$f$	Supported model fit methods
`stat_poly_line()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with methods `predict()` or `fitted()`
`stat_poly_eq()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with needed accesors
`stat_quant_line()`	G	"rq", "rqss"
`stat_quant_band()`	G	"rq", "rqss"
`stat_quant_eq()`	G	"rq", "rqss"
`stat_ma_line()`	G	"SMA", "MA", "RMA", "OLS"
`stat_ma_eq()`	G	"SMA", "MA", "RMA", "OLS"
`stat_fit_residuals()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", "rq", "rqss" others with method `residuals()`
`stat_fit_fitted()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with method `fitted()`
`stat_fit_deviations()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with methods `fitted()` and `weights()`
`stat_fit_augment()`	G	any with 'broom' method `augment()`
`stat_fit_glance()`	G	any with 'broom' method `glance()`
`stat_fit_tidy()`	G	any with 'broom' method `tidy()`
`stat_fit_tb()`	P	any with 'broom' method `tidy()`

The single colon notation is based on parsing the name and is available when passing the name of the fit method as a character string. In a string such as "head:tail" the "head" gives the name of the model fit function and the "tail" gives the argument to pass it's method parameter. This is only a convenience, as method.args can be also used. In some methods, i.e., splines, the default formula = y ~ x needs to be overridden by the user.

Table 2 lists the correspondence of pre-defined method names to model fit method functions. As mentioned above, these are only a subset of the model fit methods that are expected to work. When using these names there is no need for users to attach additional packages but the packages must be available (installed).

Table 2. Available predefined method names, the model fit functions they call, the packages where the functions reside, the class of the returned fitted model object and the arguments that can be passed to their method parameter using single colon notation.

Predefined method names	Model fit methods	R package	Object class
"lm", "lm:qr"	`lm()`	'stats'	"lm"
"rlm", "rlm:M", "rlm:MM"	`rlm()`	'MASS'	"rlm" ("lm")
"lts", "ltsReg"	`ltsReg()`	'robustbase'	"lts"
"ma", "sma", "sma:SMA", "sma:MA", "sma:OLS"	`sma()`	'smatr'	"ma" or "sma"
"gls", "gls:REML", "gls:ML"	`gls()`	'nlme'	"gls"
"rq", "rq:sfn", "rq:sfnc", "rq:lasso"	`rq()`	'quantreg'	"rq"
"rqss", "rqss:sfn", "rqss:sfnc", "rqss:lasso"	`rqss()`	'quantreg'	"rqss"
"SMA", "MA", "RMA", "OLS"	`lmodel2()`	'lmodel2'	("list")

References

Cardoso, G. C. (2019) Double quantile regression accurately assesses distance to boundary trade-off. Methods in ecology and evolution, 10(8), 1322-1331.

Aesthetics

stat_quant_line() understands the following aesthetics. Required aesthetics are displayed in bold and defaults are displayed for optional aesthetics:

•	`x`
•	`y`
•	`group`	→ `after_stat(group)`
•	`weight`	→ `1`

stat_quant_band() understands the following aesthetics. Required aesthetics are displayed in bold and defaults are displayed for optional aesthetics:

•	`x`
•	`y`
•	`group`	→ inferred

stat_quant_eq() understands the following aesthetics. Required aesthetics are displayed in bold and defaults are displayed for optional aesthetics:

•	`x`
•	`y`
•	`group`	→ inferred
•	`grp.label`
•	`hjust`	→ `"inward"`
•	`label`	→ `after_stat(eq.label)`
•	`npcx`	→ `after_stat(npcx)`
•	`npcy`	→ `after_stat(npcy)`
•	`vjust`	→ `"inward"`

Learn more about setting these aesthetics in vignette("ggplot2-specs").

Examples

# generate artificial data
set.seed(4321)
x <- 1:100
y <- (x + x^2 + x^3) + rnorm(length(x), mean = 0, sd = mean(x^3) / 4)
y <- y / max(y)
my.data <- data.frame(x = x, y = y,
                      group = c("A", "B"),
                      y2 = y * c(1, 2) + max(y) * c(0, 0.1),
                      w = sqrt(x))

# Predictions as lines
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line()


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(quantiles = 0.5, se = TRUE)


# Predictions as band
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_band()


# y as explanatory variable (orientation = y)
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_band(formula = x ~ y)


# Using splines
library(quantreg)
#> Loading required package: SparseM

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(method = "rqss",
                  formula = y ~ qss(x, constraint = "D"),
                  quantiles = 0.5, se = FALSE)


# Adding annotations
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line() +
  stat_quant_eq()
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line() +
  stat_quant_eq(mapping = use_label("eq"))
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line() +
  stat_quant_eq(mapping = use_label("eq"), decreasing = TRUE)
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line() +
  stat_quant_eq(mapping = use_label("eq", "method"))
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# same formula as default
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = y ~ x) +
  stat_quant_eq(formula = y ~ x)
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# explicit formula "x explained by y"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = x ~ y) +
  stat_quant_eq(formula = x ~ y)
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# using color
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(mapping = aes(color = after_stat(quantile.f))) +
  stat_quant_eq(mapping = aes(color = after_stat(quantile.f))) +
  labs(color = "Quantiles")
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# location and colour
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(mapping = aes(color = after_stat(quantile.f))) +
  stat_quant_eq(mapping = aes(color = after_stat(quantile.f)),
                label.y = "bottom", label.x = "right") +
  labs(color = "Quantiles")
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# give a name to a formula
formula <- y ~ poly(x, 3, raw = TRUE)

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula, linewidth = 0.5) +
  stat_quant_eq(formula = formula)


# angle
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula, linewidth = 0.5) +
  stat_quant_eq(formula = formula, angle = 90, hstep = 0.04, vstep = 0,
                label.y = 0.02, hjust = 0, size = 3) +
  expand_limits(x = -15) # make space for equations


# user set quantiles
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula, quantiles = 0.5) +
  stat_quant_eq(formula = formula, quantiles = 0.5)


ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_band(formula = formula,
                  quantiles = c(0.1, 0.5, 0.9)) +
  stat_quant_eq(formula = formula, parse = TRUE,
                quantiles = c(0.1, 0.5, 0.9))


# grouping
ggplot(my.data, aes(x, y2, color = group)) +
  geom_point() +
  stat_quant_line(formula = formula, linewidth = 0.5) +
  stat_quant_eq(formula = formula)


ggplot(my.data, aes(x, y2, color = group)) +
  geom_point() +
  stat_quant_band(formula = formula, linewidth = 0.75) +
  stat_quant_eq(formula = formula) +
  theme_bw()


# labelling equations
ggplot(my.data, aes(x, y2,  shape = group, linetype = group,
       grp.label = group)) +
  geom_point() +
  stat_quant_band(formula = formula, color = "black", linewidth = 0.75) +
  stat_quant_eq(mapping = use_label("grp", "eq", sep = "*\": \"*"),
                formula = formula) +
  expand_limits(y = 3) +
  theme_classic()


# modifying the explanatory variable within the model formula
# modifying the response variable within aes()
formula.trans <- y ~ I(x^2)
ggplot(my.data, aes(x, y + 1)) +
  geom_point() +
  stat_quant_line(formula = formula.trans) +
  stat_quant_eq(mapping = use_label("eq"),
               formula = formula.trans,
               eq.x.rhs = "~x^2",
               eq.with.lhs = "y + 1~~`=`~~")
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


# using weights
ggplot(my.data, aes(x, y, weight = w)) +
  geom_point() +
  stat_quant_line(formula = formula, linewidth = 0.5) +
  stat_quant_eq(formula = formula)


# no weights, quantile set to upper boundary
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula, quantiles = 0.95) +
  stat_quant_eq(formula = formula, quantiles = 0.95)
#> Warning: 2 non-positive fis


# manually assemble and map a specific label using paste() and aes()
ggplot(my.data, aes(x, y2, color = group, grp.label = group)) +
  geom_point() +
  stat_quant_line(method = "rq", formula = formula,
                  quantiles = c(0.05, 0.5, 0.95),
                  linewidth = 0.5) +
  stat_quant_eq(mapping = aes(label = paste(after_stat(grp.label), "*\": \"*",
                                            after_stat(eq.label), sep = "")),
                quantiles = c(0.05, 0.5, 0.95),
                formula = formula, size = 3)


# manually assemble and map a specific label using sprintf() and aes()
ggplot(my.data, aes(x, y2, color = group, grp.label = group)) +
  geom_point() +
  stat_quant_band(method = "rq", formula = formula,
                  quantiles = c(0.05, 0.5, 0.95)) +
  stat_quant_eq(mapping = aes(label = sprintf("%s*\": \"*%s",
                                              after_stat(grp.label),
                                              after_stat(eq.label))),
                quantiles = c(0.05, 0.5, 0.95),
                formula = formula, size = 3)


# geom = "text"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula, quantiles = 0.5) +
  stat_quant_eq(label.x = "left", label.y = "top",
                formula = formula,
                quantiles = 0.5)


# Inspecting the returned data using geom_debug_group()
# This provides a quick way of finding out the names of the variables that
# are available for mapping to aesthetics using after_stat().

gginnards.installed <- requireNamespace("gginnards", quietly = TRUE)

if (gginnards.installed)
  library(gginnards)

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    stat_quant_line(geom = "debug_group")

#> [1] "PANEL 1; group(s) -1-0.25; 'draw_function()' input 'data' (head):"
#>          x          y ymin ymax quantile   group quantile.f flipped_aes PANEL
#> 1 1.000000 -0.1915446   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 2 2.253165 -0.1828353   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 3 3.506329 -0.1741260   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 4 4.759494 -0.1654167   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 5 6.012658 -0.1567074   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 6 7.265823 -0.1479981   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#>   orientation
#> 1           x
#> 2           x
#> 3           x
#> 4           x
#> 5           x
#> 6           x
#> [1] "PANEL 1; group(s) -1-0.5; 'draw_function()' input 'data' (head):"
#>           x          y ymin ymax quantile  group quantile.f flipped_aes PANEL
#> 81 1.000000 -0.1811913   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 82 2.253165 -0.1711435   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 83 3.506329 -0.1610958   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 84 4.759494 -0.1510480   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 85 6.012658 -0.1410002   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 86 7.265823 -0.1309525   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#>    orientation
#> 81           x
#> 82           x
#> 83           x
#> 84           x
#> 85           x
#> 86           x
#> [1] "PANEL 1; group(s) -1-0.75; 'draw_function()' input 'data' (head):"
#>            x           y ymin ymax quantile   group quantile.f flipped_aes
#> 161 1.000000 -0.08699579   NA   NA     0.75 -1-0.75       0.75       FALSE
#> 162 2.253165 -0.07642220   NA   NA     0.75 -1-0.75       0.75       FALSE
#> 163 3.506329 -0.06584862   NA   NA     0.75 -1-0.75       0.75       FALSE
#> 164 4.759494 -0.05527503   NA   NA     0.75 -1-0.75       0.75       FALSE
#> 165 6.012658 -0.04470145   NA   NA     0.75 -1-0.75       0.75       FALSE
#> 166 7.265823 -0.03412786   NA   NA     0.75 -1-0.75       0.75       FALSE
#>     PANEL orientation
#> 161     1           x
#> 162     1           x
#> 163     1           x
#> 164     1           x
#> 165     1           x
#> 166     1           x

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    stat_quant_band(geom = "debug_group")

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>          x       ymin          y        ymax flipped_aes PANEL group
#> 1 1.000000 -0.1915446 -0.1811913 -0.08699579       FALSE     1    -1
#> 2 2.253165 -0.1828353 -0.1711435 -0.07642220       FALSE     1    -1
#> 3 3.506329 -0.1741260 -0.1610958 -0.06584862       FALSE     1    -1
#> 4 4.759494 -0.1654167 -0.1510480 -0.05527503       FALSE     1    -1
#> 5 6.012658 -0.1567074 -0.1410002 -0.04470145       FALSE     1    -1
#> 6 7.265823 -0.1479981 -0.1309525 -0.03412786       FALSE     1    -1
#>   orientation
#> 1           x
#> 2           x
#> 3           x
#> 4           x
#> 5           x
#> 6           x

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, geom = "debug_group")

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>                                                                                                      eq.label
#> 1 italic(y)~`=`~-0.0257 + 0.000496*~italic(x) + 2.22%*% 10^{-06}*~italic(x)^2 + 8.10%*% 10^{-07}*~italic(x)^3
#> 2 italic(y)~`=`~-0.0122 + 0.000971*~italic(x) - 9.60%*% 10^{-06}*~italic(x)^2 + 9.45%*% 10^{-07}*~italic(x)^3
#> 3  italic(y)~`=`~0.0413 + 0.000437*~italic(x) - 1.26%*% 10^{-05}*~italic(x)^2 + 1.04%*% 10^{-06}*~italic(x)^3
#>                 AIC.label               rho.label           n.label grp.label
#> 1 plain(AIC)~`=`~"-269.2" italic(rho)~`=`~"1.725" italic(n)~`=`~100          
#> 2  plain(AIC)~`=`~"-293." italic(rho)~`=`~"2.042" italic(n)~`=`~100          
#> 3 plain(AIC)~`=`~"-275.9" italic(rho)~`=`~"1.668" italic(n)~`=`~100          
#>              qtl.label    method.label      rho rq.method quantile quantile.f
#> 1 italic(q)~`=`~"0.25" "method: rq:br" 1.724867        br     0.25       0.25
#> 2 italic(q)~`=`~"0.50" "method: rq:br" 2.042215        br     0.50       0.50
#> 3 italic(q)~`=`~"0.75" "method: rq:br" 1.667752        br     0.75       0.75
#>     n fm.method fm.class                 fm.formula             fm.formula.chr
#> 1 100     rq:br      rqs y ~ poly(x, 3, raw = TRUE) y ~ poly(x, 3, raw = TRUE)
#> 2 100     rq:br      rqs y ~ poly(x, 3, raw = TRUE) y ~ poly(x, 3, raw = TRUE)
#> 3 100     rq:br      rqs y ~ poly(x, 3, raw = TRUE) y ~ poly(x, 3, raw = TRUE)
#>   x npcx         y npcy PANEL group
#> 1 1   NA 0.8912737   NA     1    -1
#> 2 1   NA 0.9456369   NA     1    -1
#> 3 1   NA 1.0000000   NA     1    -1
#>                                                                                                         label
#> 1 italic(y)~`=`~-0.0257 + 0.000496*~italic(x) + 2.22%*% 10^{-06}*~italic(x)^2 + 8.10%*% 10^{-07}*~italic(x)^3
#> 2 italic(y)~`=`~-0.0122 + 0.000971*~italic(x) - 9.60%*% 10^{-06}*~italic(x)^2 + 9.45%*% 10^{-07}*~italic(x)^3
#> 3  italic(y)~`=`~0.0413 + 0.000437*~italic(x) - 1.26%*% 10^{-05}*~italic(x)^2 + 1.04%*% 10^{-06}*~italic(x)^3
#>   orientation
#> 1           x
#> 2           x
#> 3           x

if (FALSE) { # \dontrun{
if (gginnards.installed)
  ggplot(mpg, aes(displ, hwy)) +
    stat_quant_line(geom = "debug_group", fm.values = TRUE)

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    stat_quant_band(geom = "debug_group", fm.values = TRUE)

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(mapping = aes(label = after_stat(eq.label)),
                  formula = formula, geom = "debug_group",
                  output.type = "markdown")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, geom = "debug_group", output.type = "text")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, geom = "debug_group", output.type = "numeric")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, quantiles = c(0.25, 0.5, 0.75),
                  geom = "debug_group", output.type = "text")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, quantiles = c(0.25, 0.5, 0.75),
                  geom = "debug_group", output.type = "numeric")
} # }

Statistic	\(f\)	Supported model fit methods
`stat_poly_line()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with methods `predict()` or `fitted()`
`stat_poly_eq()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", others with needed accesors
`stat_quant_line()`	G	"rq", "rqss"
`stat_quant_band()`	G	"rq", "rqss"
`stat_quant_eq()`	G	"rq", "rqss"
`stat_ma_line()`	G	"SMA", "MA", "RMA", "OLS"
`stat_ma_eq()`	G	"SMA", "MA", "RMA", "OLS"
`stat_fit_residuals()`	G	"lm", "rlm", "lts", "sma", "ma", "gls", "rq", "rqss" others with method `residuals()`
`stat_fit_fitted()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with method `fitted()`
`stat_fit_deviations()`	G	"lm", "rlm", "lts", "gls", "rq", "rqss" others with methods `fitted()` and `weights()`
`stat_fit_augment()`	G	any with 'broom' method `augment()`
`stat_fit_glance()`	G	any with 'broom' method `glance()`
`stat_fit_tidy()`	G	any with 'broom' method `tidy()`
`stat_fit_tb()`	P	any with 'broom' method `tidy()`