Predicted line from quantile regression fit

Predicted values are computed and, by default, plotted. Depending on the fit method, a confidence band can be computed and plotted. The confidence band can be interpreted similarly as that produced by stat_smooth() and stat_poly_line().

Usage

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,
  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.
se: logical Passed to quantreg::predict.rq().
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.
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.
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().
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.

Value

The value returned by the statistic is a data frame, that will have n rows of predicted values and and their confidence limits for each quantile, with quantiles creating groups, or expanding existing groups. The variables are x and y with y containing predicted values. In addition, quantile and quantile.f indicate the quantile used and and edited group preserves the original grouping adding a new "level" for each quantile. Is se = TRUE, a confidence band is computed and values for it returned in ymax and ymin.

Details

stat_quant_line() behaves similarly to ggplot2::stat_smooth() and stat_poly_line() but supports fitting regressions for multiple quantiles in the same plot layer. This statistic interprets the argument passed to formula accepting y as well as x as explanatory variable, matching stat_quant_eq(). While stat_quant_eq() supports only method "rq", stat_quant_line() and stat_quant_band() support both "rq" and "rqss", In the case of "rqss" the model formula makes normally use of qss() to formulate the spline and its constraints.

geom_smooth, which is used by default, treats each axis differently and thus is dependent on orientation. If no argument is passed to formula, it defaults to y ~ x. Formulas with y as explanatory variable are treated as if x was the explanatory variable and orientation = "y".

Package 'ggpmisc' does not define a new geometry matching this statistic as it is enough for the statistic to return suitable x, y, ymin, ymax and group values.

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 wise.

There are multiple uses for double regression on x and y. 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. 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".

Computed variables

`stat_quant_line()` provides the following variables, some of which depend on the orientation:

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.

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

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`

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

Examples

ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line()


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(quantiles = 0.5)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(se = TRUE)


# If you need the fitting to be done along the y-axis set the orientation
ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(orientation = "y")


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(orientation = "y", se = TRUE)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(formula = y ~ x)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(formula = x ~ y)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(formula = y ~ poly(x, 3))


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(formula = x ~ poly(y, 3))


# Instead of rq() we can use rqss() to fit an additive model:
library(quantreg)
#> Loading required package: SparseM

ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(method = "rqss",
                  formula = y ~ qss(x, constraint = "D"),
                  quantiles = 0.5, se = FALSE)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(method = "rqss",
                  formula = x ~ qss(y, constraint = "D"),
                  quantiles = 0.5)


ggplot(mpg, aes(displ, hwy)) +
  geom_point()+
  stat_quant_line(method="rqss",
                  interval="confidence",
                  se = TRUE,
                  mapping = aes(fill = factor(after_stat(quantile)),
                                color = factor(after_stat(quantile))),
                  quantiles=c(0.05,0.5,0.95))


# Smooths are automatically fit to each group (defined by categorical
# aesthetics or the group aesthetic) and for each facet.

ggplot(mpg, aes(displ, hwy, colour = drv, fill = drv)) +
  geom_point() +
  stat_quant_line(method = "rqss",
                  formula = y ~ qss(x, constraint = "V"),
                   quantiles = 0.5)


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_line(formula = y ~ poly(x, 2)) +
  facet_wrap(~drv)


# Inspecting the returned data using geom_debug_group()
gginnards.installed <- requireNamespace("gginnards", quietly = TRUE)

if (gginnards.installed)
  library(gginnards)

if (gginnards.installed)
  ggplot(mpg, aes(displ, hwy)) +
    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 1.600000 28.42857   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 2 1.668354 28.16817   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 3 1.736709 27.90778   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 4 1.805063 27.64738   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 5 1.873418 27.38698   NA   NA     0.25 -1-0.25       0.25       FALSE     1
#> 6 1.941772 27.12658   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 1.600000 29.85714   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 82 1.668354 29.61302   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 83 1.736709 29.36890   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 84 1.805063 29.12477   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 85 1.873418 28.88065   NA   NA      0.5 -1-0.5       0.50       FALSE     1
#> 86 1.941772 28.63653   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 PANEL
#> 161 1.600000 32.00000   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#> 162 1.668354 31.76659   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#> 163 1.736709 31.53319   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#> 164 1.805063 31.29978   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#> 165 1.873418 31.06638   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#> 166 1.941772 30.83297   NA   NA     0.75 -1-0.75       0.75       FALSE     1
#>     orientation
#> 161           x
#> 162           x
#> 163           x
#> 164           x
#> 165           x
#> 166           x

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

#> [1] "PANEL 1; group(s) -1-0.25; 'draw_function()' input 'data' (head):"
#>          x        y ymin ymax quantile   group   n fm.class fm.method
#> 1 1.600000 28.42857   NA   NA     0.25 -1-0.25 234       rq        rq
#> 2 1.668354 28.16817   NA   NA     0.25 -1-0.25 234       rq        rq
#> 3 1.736709 27.90778   NA   NA     0.25 -1-0.25 234       rq        rq
#> 4 1.805063 27.64738   NA   NA     0.25 -1-0.25 234       rq        rq
#> 5 1.873418 27.38698   NA   NA     0.25 -1-0.25 234       rq        rq
#> 6 1.941772 27.12658   NA   NA     0.25 -1-0.25 234       rq        rq
#>   fm.formula.chr quantile.f flipped_aes PANEL orientation
#> 1          y ~ x       0.25       FALSE     1           x
#> 2          y ~ x       0.25       FALSE     1           x
#> 3          y ~ x       0.25       FALSE     1           x
#> 4          y ~ x       0.25       FALSE     1           x
#> 5          y ~ x       0.25       FALSE     1           x
#> 6          y ~ x       0.25       FALSE     1           x
#> [1] "PANEL 1; group(s) -1-0.5; 'draw_function()' input 'data' (head):"
#>           x        y ymin ymax quantile  group   n fm.class fm.method
#> 81 1.600000 29.85714   NA   NA      0.5 -1-0.5 234       rq        rq
#> 82 1.668354 29.61302   NA   NA      0.5 -1-0.5 234       rq        rq
#> 83 1.736709 29.36890   NA   NA      0.5 -1-0.5 234       rq        rq
#> 84 1.805063 29.12477   NA   NA      0.5 -1-0.5 234       rq        rq
#> 85 1.873418 28.88065   NA   NA      0.5 -1-0.5 234       rq        rq
#> 86 1.941772 28.63653   NA   NA      0.5 -1-0.5 234       rq        rq
#>    fm.formula.chr quantile.f flipped_aes PANEL orientation
#> 81          y ~ x       0.50       FALSE     1           x
#> 82          y ~ x       0.50       FALSE     1           x
#> 83          y ~ x       0.50       FALSE     1           x
#> 84          y ~ x       0.50       FALSE     1           x
#> 85          y ~ x       0.50       FALSE     1           x
#> 86          y ~ x       0.50       FALSE     1           x
#> [1] "PANEL 1; group(s) -1-0.75; 'draw_function()' input 'data' (head):"
#>            x        y ymin ymax quantile   group   n fm.class fm.method
#> 161 1.600000 32.00000   NA   NA     0.75 -1-0.75 234       rq        rq
#> 162 1.668354 31.76659   NA   NA     0.75 -1-0.75 234       rq        rq
#> 163 1.736709 31.53319   NA   NA     0.75 -1-0.75 234       rq        rq
#> 164 1.805063 31.29978   NA   NA     0.75 -1-0.75 234       rq        rq
#> 165 1.873418 31.06638   NA   NA     0.75 -1-0.75 234       rq        rq
#> 166 1.941772 30.83297   NA   NA     0.75 -1-0.75 234       rq        rq
#>     fm.formula.chr quantile.f flipped_aes PANEL orientation
#> 161          y ~ x       0.75       FALSE     1           x
#> 162          y ~ x       0.75       FALSE     1           x
#> 163          y ~ x       0.75       FALSE     1           x
#> 164          y ~ x       0.75       FALSE     1           x
#> 165          y ~ x       0.75       FALSE     1           x
#> 166          y ~ x       0.75       FALSE     1           x