ggpmisc (version 0.4.3)

stat_quant_eq: Equation, p-value, R^2, AIC or BIC from quantile regression

Description

stat_quant_eq fits a polynomial model by quantile regression and generates several labels including the equation, p-value, coefficient of determination (R^2), 'AIC' and 'BIC'.

Usage

stat_quant_eq(
  mapping = NULL,
  data = NULL,
  geom = "text_npc",
  position = "identity",
  ...,
  formula = NULL,
  quantiles = c(0.25, 0.5, 0.75),
  eq.with.lhs = TRUE,
  eq.x.rhs = NULL,
  coef.digits = 3,
  coef.keep.zeros = TRUE,
  rho.digits = 2,
  label.x = "left",
  label.y = "top",
  label.x.npc = NULL,
  label.y.npc = NULL,
  hstep = 0,
  vstep = NULL,
  output.type = "expression",
  na.rm = FALSE,
  orientation = NA,
  parse = NULL,
  show.legend = FALSE,
  inherit.aes = TRUE
)

Arguments

mapping

The aesthetic mapping, usually constructed with aes or 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.

formula

a formula object. Using aesthetic names instead of original variable names.

quantiles

numeric vector Values in 0..1 indicating the quantiles.

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.

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.

label.x.npc, label.y.npc

numeric with range 0..1 (npc units) DEPRECATED, use label.x and label.y instead; together with a geom using npcx and npcy aesthetics.

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.

orientation

character Either "x" or "y" controlling the default for formula.

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.

Aesthetics

stat_quant_eq understands x and y, to be referenced in the formula and weight passed as argument to parameter weights of lm(). All three must be mapped to numeric variables. In addition, the aesthetics undertood by the geom used ("text" by default) are understood and grouping respected.

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

coef.ls, r.squared, adj.r.squared, AIC, BIC

as numric values extracted from fit object

eq.label

equation for the fitted polynomial as a character string to be parsed

rho.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.

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.

Details

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

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 R^2, adjusted R^2 or the fitted model equation. It supports only linear models fitted with function lm(). The R^2 and adjusted R^2 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, and for this reason the default aesthetics sets R^2 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 overriden. 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 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.

References

Written as an answer to a question by Mark Neal at Stackoverflow. https://stackoverflow.com/questions/65695409/is-there-a-neat-approach-to-label-a-ggplot-plot-with-the-equation-and-other-stat

See Also

This stat_quant_eq statistic can return ready formatted labels depending on the argument passed to output.type. This is possible because only polynomial models are supported. For other types of models, statistics stat_fit_glance, stat_fit_tidy and stat_fit_glance should be used instead and the code for construction of character strings from numeric values and their mapping to aesthetic label needs to be explicitly supplied in the call.

Other ggplot statistics for quantile regression: stat_quant_band(), stat_quant_line()

Examples

# NOT RUN {
# 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)
my.data <- data.frame(x = x, y = y,
                      group = c("A", "B"),
                      y2 = y * c(0.5,2),
                      w = sqrt(x))

# using defaults
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line() +
  stat_quant_eq()

# same formula as default
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = y ~ x) +
  stat_quant_eq(formula = y ~ x)

# 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)

# using color
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(aes(color = after_stat(quantile.f))) +
  stat_quant_eq(aes(color = after_stat(quantile.f))) +
  labs(color = "Quantiles")

# location and colour
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(aes(color = after_stat(quantile.f))) +
  stat_quant_eq(aes(color = after_stat(quantile.f)),
                label.y = "bottom", label.x = "right") +
  labs(color = "Quantiles")

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

# no weights
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula)

# angle
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula, angle = 90, hstep = 0.05, vstep = 0,
                label.y = 0.98, hjust = 1)

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula, angle = 90,
                hstep = 0.05, vstep = 0, hjust = 0,
                label.y = 0.25)

# 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)

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

ggplot(my.data, aes(x, y, color = group)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula, angle = 90,
                hstep = 0.05, vstep = 0, hjust = 0,
                size = 3, label.y = 0.3)

# labelling equations
ggplot(my.data, aes(x, y,  shape = group, linetype = group,
       grp.label = group)) +
  geom_point() +
  stat_quant_line(formula = formula, color = "black") +
  stat_quant_eq(aes(label = paste(after_stat(grp.label), after_stat(eq.label), sep = "*\": \"*")),
                formula = formula) +
  theme_classic()

# setting non-default quantiles
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(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))

# Location of equations
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula, label.y = "bottom", label.x = "right")

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_quant_line(formula = formula) +
  stat_quant_eq(formula = formula, label.y = 0.03, label.x = 0.95, vstep = 0.04)

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

# user specified label
ggplot(my.data, aes(x, y, color = group, grp.label = group)) +
  geom_point() +
  stat_quant_line(method = "rq", formula = formula,
                quantiles = c(0.05, 0.5, 0.95)) +
  stat_quant_eq(aes(label = paste(after_stat(grp.label), "*\": \"*",
                                   after_stat(eq.label), sep = "")),
                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(method = "rq", formula = formula, quantiles = 0.5) +
  stat_quant_eq(label.x = "left", label.y = "top",
                formula = formula)

# Inspecting the returned data using geom_debug()
if (requireNamespace("gginnards", quietly = TRUE)) {
  library(gginnards)

# This provides a quick way of finding out the names of the variables that
# are available for mapping to aesthetics.

  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(formula = formula, geom = "debug")

  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_quant_eq(aes(label = after_stat(eq.label)),
                  formula = formula, geom = "debug",
                  output.type = "markdown")

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

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

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

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

# }