Predicted band from quantile regression fits

Predicted values are computed and plotted as a band plus an optional line within. Using the default quantiles, the band plotted is similar to a boxplot in its interpretation.

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,
  method = "rq",
  method.args = list(),
  n.min = 3L,
  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: A numeric vector of length 3, with unique values in \(0\ldots 1\). The three quantile regressions are mapped to y, ymax and ymin aesthetics, and by default plotted as a line and band.
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.
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.

Value

The value returned by the statistic is a data frame, that will have n rows of predicted values for three quantiles as y, ymin and ymax, plus x.

Details

stat_quant_band() fits quantile regression and obtains predictions identically to stat_quant_line(). stat_quant_band() fits 2 or 3 quantiles in the same plot layer always display the area between the predicted regression lines for the extreme quantiles as a band. In contrast stat_quant_line() fits one or more regressions, adding a line for each. stat_quant_line() displays confidence bands for the regression lines when se = TRUE.

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.

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. 'ggpmisc' (>= 0.4.1) supports orientation making it easy implement the approach described by Cardoso (2019) under the name of "Double quantile regression".

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.

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 validity of the values extracted.

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 as 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!).

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.

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 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. 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 with an explicit argument.

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

•	`x`
•	`y`
•	`group`	→ inferred

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

Examples

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


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


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


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


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


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


# Instead of rq() we can use rqss() to fit an additive model:
ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_band(method = "rqss",
                  formula = y ~ qss(x))
#> Warning: Computation failed in `stat_quant_band()`.
#> Caused by error in `qss()`:
#> ! could not find function "qss"


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_band(method = "rqss",
                  formula = x ~ qss(y, constraint = "D"))
#> Warning: Computation failed in `stat_quant_band()`.
#> Caused by error in `qss()`:
#> ! could not find function "qss"


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

ggplot(mpg, aes(displ, hwy, colour = class)) +
  geom_point() +
  stat_quant_band(formula = y ~ x)
#> Warning: Solution may be nonunique
#> Warning: Solution may be nonunique


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


ggplot(mpg, aes(displ, hwy)) +
  geom_point() +
  stat_quant_band(linetype = "dashed", color = "darkred", fill = "red")


ggplot(mpg, aes(displ, hwy)) +
  stat_quant_band(color = NA, alpha = 1) +
  geom_point()


ggplot(mpg, aes(displ, hwy)) +
  stat_quant_band(quantiles = c(0, 0.1, 0.2)) +
  geom_point()


# 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_band(geom = "debug_group")
#> Warning: Ignoring unknown parameters: `se`

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>          x     ymin        y     ymax flipped_aes PANEL group orientation
#> 1 1.600000 28.42857 29.85714 32.00000       FALSE     1    -1           x
#> 2 1.668354 28.16817 29.61302 31.76659       FALSE     1    -1           x
#> 3 1.736709 27.90778 29.36890 31.53319       FALSE     1    -1           x
#> 4 1.805063 27.64738 29.12477 31.29978       FALSE     1    -1           x
#> 5 1.873418 27.38698 28.88065 31.06638       FALSE     1    -1           x
#> 6 1.941772 27.12658 28.63653 30.83297       FALSE     1    -1           x

if (gginnards.installed)
  ggplot(mpg, aes(displ, hwy)) +
    stat_quant_band(geom = "debug_group", fm.values = TRUE)
#> Warning: Ignoring unknown parameters: `se`

#> [1] "PANEL 1; group(s) -1; 'draw_function()' input 'data' (head):"
#>          x     ymin fm1.class fm1.formula.chr        y fm2.class
#> 1 1.600000 28.42857        rq           y ~ x 29.85714        rq
#> 2 1.668354 28.16817        rq           y ~ x 29.61302        rq
#> 3 1.736709 27.90778        rq           y ~ x 29.36890        rq
#> 4 1.805063 27.64738        rq           y ~ x 29.12477        rq
#> 5 1.873418 27.38698        rq           y ~ x 28.88065        rq
#> 6 1.941772 27.12658        rq           y ~ x 28.63653        rq
#>   fm2.formula.chr     ymax fm3.class fm3.formula.chr   n fm.method flipped_aes
#> 1           y ~ x 32.00000        rq           y ~ x 234        rq       FALSE
#> 2           y ~ x 31.76659        rq           y ~ x 234        rq       FALSE
#> 3           y ~ x 31.53319        rq           y ~ x 234        rq       FALSE
#> 4           y ~ x 31.29978        rq           y ~ x 234        rq       FALSE
#> 5           y ~ x 31.06638        rq           y ~ x 234        rq       FALSE
#> 6           y ~ x 30.83297        rq           y ~ x 234        rq       FALSE
#>   PANEL group orientation
#> 1     1    -1           x
#> 2     1    -1           x
#> 3     1    -1           x
#> 4     1    -1           x
#> 5     1    -1           x
#> 6     1    -1           x