Equation, rho, AIC and BIC from quantile regression

stat_quant_eq fits a polynomial model by quantile regression and generates several labels including the equation, rho, 'AIC' and 'BIC'.

Usage

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 = 3L,
  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
)

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.
formula: a formula object. Using aesthetic names x and y instead of original variable names.
quantiles: numeric vector Values in 0..1 indicating the quantiles.
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.
fit.seed: RNG seed argument passed to set.seed(). Defaults to NA, indicating that set.seed() should not be called.
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", "LaTeX", "text", "markdown" or "numeric". In most cases, instead of using this statistics to obtain numeric values, it is better to use stat_fit_tidy().
na.rm: a logical indicating whether NA values should be stripped before the computation proceeds.
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.
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.

Value

A data frame, with one row per quantile and columns as described under Computed variables. In cases when the number of observations is less than n.min a data frame with no rows or columns is returned rendered as an empty/invisible plot layer.

Details

This statistic interprets the argument passed to formula differently than stat_quantile accepting y as well as x as explanatory variable, matching stat_quant_line().

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. So, from version 0.4.1 'ggpmisc' makes it possible to easily implement the approach described by Cardoso (2019) under the name of "Double quantile regression".

This stat can be used to automatically annotate a plot with rho or the fitted model equation. The model fitting is done using package 'quantreg', please, consult its documentation for the details. It supports only linear models fitted with function rq(), passing method = "br" to it, should work well with up to several thousand observations. The rho, AIC, BIC and n annotations can be used with any linear model formula. The fitted equation label is correctly generated for polynomials or quasi-polynomials through the origin. Model formulas can use poly() or be defined algebraically with terms of powers of increasing magnitude with no missing intermediate terms, except possibly for the intercept indicated by "- 1" or "-1" or "+ 0" in the formula. The validity of the formula is not checked in the current implementation. The default aesthetics sets rho as label for the annotation. This stat generates labels as R expressions by default but LaTeX (use TikZ device), markdown (use package 'ggtext') and plain text are also supported, as well as numeric values for user-generated text labels. The value of parse is set automatically based on output-type, but if you assemble labels that need parsing from numeric output, the default needs to be overridden. This stat only generates annotation labels, the predicted values/line need to be added to the plot as a separate layer using stat_quant_line, stat_quant_band or stat_quantile, so to make sure that the same model formula is used in all steps it is best to save the formula as an object and supply this object as argument to the different statistics.

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. stat_quant_eq() mimics how stat_smooth() works, except that only polynomials can be fitted. In other words, it respects the grammar of graphics. This helps ensure that the model is fitted to the same data as plotted in other layers.

Function rq does not support singular fits, in contrast to lm.

The minimum number of observations with distinct values in the explanatory variable can be set through parameter n.min. The default n.min = 3L is the smallest usable value. However, model fits with very few observations are of little interest and using larger values of n.min than the default is usually wise.

Note

For backward compatibility a logical is accepted as argument for eq.with.lhs. If TRUE, the default is used, either "x" or "y", depending on the argument passed to formula. However, "x" or "y" can be substituted by providing a suitable replacement character string through eq.x.rhs. Parameter orientation is redundant as it only affects the default for formula but is included for consistency with ggplot2::stat_smooth().

R option OutDec is obeyed based on its value at the time the plot is rendered, i.e., displayed or printed. Set options(OutDec = ",") for languages like Spanish or French.

Support for the angle aesthetic is not automatic and requires that the user passes as argument suitable numeric values to override the defaults for label positions.

User-defined methods

User-defined functions can be passed as argument to method. The requirements are 1) that the signature is similar to that of functions from package 'quantreg' and 2) that the value returned by the function is an object belonging to class "rq", class "rqs", or an atomic NA value.

The formula and tau used to build the equation and quantile labels aer extracted from the returned "rq" or "rqs" object and can safely differ from the argument passed to parameter formula in the call to stat_poly_eq(). Thus, user-defined methods can implement both model selection or conditional skipping of labelling.

Warning!

For the formatted equations to be valid, the fitted model must be a polynomial, with or without intercept. If defined using poly() the argument raw = TRUE must be passed. If defined manually as powers of x, the terms must be in order of increasing powers, with no missing intermediate power term. Please, see examples below. A check on the model is used to validate that it is a polynomial, in most cases a warning is issued. Failing to comply with this requirement results in the return of NA as the formatted equation.

Computed variables

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

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

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

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, expression, latex.eqn or markup 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" unless the user passes an argument. Invalid values as argument trigger an Error.

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 no layer is added to the plot 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 valisdity of the values extracted.

The argument to parameter method can be either the name of a function object, possibly using double colon notation, or a character string matching the function name. 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 as an argument to 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!).

The table below 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.

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 table below lists the names for fit methods coded in the statistics as given in the table above. The single colon notation is based on parsing the name and is available whenever 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. In some cases the default formula = y ~ x needs to be overridden with an explicit argument.

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'

References

Written as an answer to question 65695409 by Mark Neal at Stackoverflow.

Aesthetics

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))

# using defaults
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)) +
    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(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()`