ggpmisc (version 0.4.3)

stat_poly_eq: Equation, p-value, R^2, AIC or BIC of fitted polynomial

Description

stat_poly_eq fits a polynomial by default with stats::lm() but alternatively using robust regression. From the fitted model it generates several labels including the equation, p-value, F-value, coefficient of determination (R^2), 'AIC', 'BIC', and number of observations.

Usage

stat_poly_eq(
  mapping = NULL,
  data = NULL,
  geom = "text_npc",
  position = "identity",
  ...,
  method = "lm",
  method.args = list(),
  formula = NULL,
  eq.with.lhs = TRUE,
  eq.x.rhs = NULL,
  small.r = FALSE,
  small.p = FALSE,
  coef.digits = 3,
  coef.keep.zeros = TRUE,
  rr.digits = 2,
  f.digits = 3,
  p.digits = 3,
  label.x = "left",
  label.y = "top",
  label.x.npc = NULL,
  label.y.npc = NULL,
  hstep = 0,
  vstep = NULL,
  output.type = NULL,
  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.

method

function or character If character, "lm" and "rlm" are accepted. If a function, it must have formal parameters formula and data and return a model fit object for which summary() and coefficients() are consistent with those for lm fits.

method.args

named list with additional arguments.

formula

a formula object. Using aesthetic names x and y instead of original variable names.

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.

small.r, small.p

logical Flags to switch use of lower case r and p for coefficient of determination and p-value.

coef.digits, f.digits

integer Number of significant digits to use for the fitted coefficients and F-value.

coef.keep.zeros

logical Keep or drop trailing zeros when formatting the fitted coefficients and F-value.

rr.digits, p.digits

integer Number of digits after the decimal point to use for R^2 and P-value in labels.

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".

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

Computed variables

If output.type different from "numeric" the returned tibble contains columns listed below. If the model fit function used does not return a value, the label is set to character(0L).

x,npcx

x position

y,npcy

y position

eq.label

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

rr.label

\(R^2\) of the fitted model as a character string to be parsed

adj.rr.label

Adjusted \(R^2\) of the fitted model as a character string to be parsed

f.value.label

F value and degrees of freedom for the fitted model as a whole.

p.value.label

P-value for the F-value above.

AIC.label

AIC for the fitted model.

BIC.label

BIC for the fitted model.

n.label

Number of observations used in the fit.

grp.label

Set according to mapping in aes.

r.squared, adj.r.squared, p.value, n

numeric values, from the model fit object

If output.type is "numeric" the returned tibble contains columns listed below. If the model fit function used does not return a value, the variable is set to NA_real_.

x,npcx

x position

y,npcy

y position

coef.ls

list containing the "coefficients" matrix from the summary of the fit object

r.squared, adj.r.squared, f.value, f.df1, f.df2, p.value, AIC, BIC, n

numeric values, from the model fit object

grp.label

Set according to mapping in aes.

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 last examples below.

Details

This stat can be used to automatically annotate a plot with R^2, adjusted R^2 or the fitted model equation. It supports linear regression, robust linear regression and median regression fitted with functions lm(), MASS::rlm() or quanreg::rq(). 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_poly_line or stat_smooth, 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_poly_eq() mimics how stat_smooth() works, except that only polynomials can be fitted. Similarly to these statistics the model fits respect grouping, so the scales used for x and y should both be continuous scales rather than discrete.

References

Written as an answer to a question at Stackoverflow. https://stackoverflow.com/questions/7549694/adding-regression-line-equation-and-r2-on-graph

See Also

This stat_poly_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 quantile regression stat_quant_eq should be used instead of stat_poly_eq while for model II or major axis regression stat_ma_eq should be used. For other types of models such as non-linear models, statistics stat_fit_glance and stat_fit_tidy should be used and the code for construction of character strings from numeric values and their mapping to aesthetic label needs to be explicitly supplied by the user.

Other ggplot statistics for linear and polynomial regression: stat_poly_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))

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

# no weights
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula)

# grouping
ggplot(my.data, aes(x, y, color = group)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula)

# rotation
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula, angle = 90, hjust = 1)

# label location
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula, label.y = "bottom", label.x = "right")

ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula, label.y = 0.1, label.x = 0.9)

# using weights
ggplot(my.data, aes(x, y, weight = w)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula)

# no weights, digits for R square
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula, rr.digits = 4)

# user specified label
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(aes(label =  paste(after_stat(rr.label),
                                  after_stat(n.label), sep = "*\", \"*")),
               formula = formula)

ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(aes(label =  paste(after_stat(eq.label),
                                  after_stat(adj.rr.label), sep = "*\", \"*")),
               formula = formula)

ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(aes(label =  paste(after_stat(f.value.label),
                                  after_stat(p.value.label),
                                  sep = "*\", \"*")),
               formula = formula)

# x on y regression
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula, orientation = "y") +
  stat_poly_eq(aes(label =  paste(after_stat(eq.label),
                                  after_stat(adj.rr.label),
                                  sep = "*\", \"*")),
               formula = x ~ poly(y, 3, raw = TRUE))

# conditional user specified label
ggplot(my.data, aes(x, y, color = group)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(aes(label =  ifelse(after_stat(adj.r.squared) > 0.96,
                                   paste(after_stat(adj.rr.label),
                                         after_stat(eq.label),
                                         sep = "*\", \"*"),
                                   after_stat(adj.rr.label))),
               rr.digits = 3,
               formula = formula)

# geom = "text"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(geom = "text", label.x = 100, label.y = 0, hjust = 1,
               formula = formula)

# using numeric values
# Here we use columns b_0 ... b_3 for the coefficient estimates
my.format <-
  "b[0]~`=`~%.3g*\", \"*b[1]~`=`~%.3g*\", \"*b[2]~`=`~%.3g*\", \"*b[3]~`=`~%.3g"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  geom_smooth(method = "lm", formula = formula) +
  stat_poly_eq(formula = formula,
               output.type = "numeric",
               parse = TRUE,
               mapping =
                aes(label = sprintf(my.format,
                                    after_stat(b_0), after_stat(b_1),
                                    after_stat(b_2), after_stat(b_3))))

# 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.

# the whole of data
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug")

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

# names of the variables
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug",
                 summary.fun = colnames)

# only data$eq.label
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug",
                 output.type = "expression",
                 summary.fun = function(x) {x[["eq.label"]]})

# only data$eq.label
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(aes(label = after_stat(eq.label)),
                 formula = formula, geom = "debug",
                 output.type = "markdown",
                 summary.fun = function(x) {x[["eq.label"]]})

# only data$eq.label
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug",
                 output.type = "latex",
                 summary.fun = function(x) {x[["eq.label"]]})

# only data$eq.label
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug",
                 output.type = "text",
                 summary.fun = function(x) {x[["eq.label"]]})

# show the content of a list column
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    geom_smooth(method = "lm", formula = formula) +
    stat_poly_eq(formula = formula, geom = "debug", output.type = "numeric",
                 summary.fun = function(x) {x[["coef.ls"]][[1]]})
}

# }