stat_ma_eq: Equation, p-value, R^2 of major axis regression

Description

stat_ma_eq fits model II regressions. From the fitted model it generates several labels including the equation, p-value, coefficient of determination (R^2), and number of observations.

Usage

stat_ma_eq(
  mapping = NULL,
  data = NULL,
  geom = "text_npc",
  position = "identity",
  ...,
  orientation = NA,
  formula = NULL,
  method = "lmodel2:MA",
  method.args = list(),
  n.min = 2L,
  range.y = NULL,
  range.x = NULL,
  nperm = 99,
  fit.seed = NA,
  eq.with.lhs = TRUE,
  eq.x.rhs = NULL,
  small.r = getOption("ggpmisc.small.r", default = FALSE),
  small.p = getOption("ggpmisc.small.p", default = FALSE),
  coef.digits = 3,
  coef.keep.zeros = TRUE,
  decreasing = getOption("ggpmisc.decreasing.poly.eq", FALSE),
  rr.digits = 2,
  theta.digits = 2,
  p.digits = max(1, ceiling(log10(nperm))),
  label.x = "left",
  label.y = "top",
  hstep = 0,
  vstep = NULL,
  output.type = NULL,
  na.rm = FALSE,
  parse = NULL,
  show.legend = FALSE,
  inherit.aes = TRUE
)

Value

A data frame, with a single row 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.

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.
method: function or character If character, "MA", "SMA" , "RMA" or "OLS", alternatively "lmodel2" 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. "lmodel2:MA"). If a function different to lmodel2(), it must accept arguments named formula, data, range.y, range.x and nperm and return a model fit object of class lmodel2.
method.args: named list with additional arguments. Not data or weights which are always passed through aesthetic mappings.
n.min: integer Minimum number of distinct values in the explanatory variable (on the rhs of formula) for fitting to the attempted.
range.y, range.x: character Pass "relative" or "interval" if method "RMA" is to be computed.
nperm: integer Number of permutation used to estimate significance.
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.
small.r, small.p: logical Flags to switch use of lower case r and p for coefficient of determination and p-value.
coef.digits: integer Number of significant digits to use for the fitted coefficients.
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.
rr.digits, theta.digits, p.digits: integer Number of digits after the decimal point to use for R^2, theta and P-value in labels. If Inf, use exponential notation with three decimal places.
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".
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.

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 function lmodel2() and 2) that the value returned by the function is an object as returned by lmodel2() or an atomic NA value. Thus, user-defined methods can implement conditional skipping of labelling.

Computed variables

If output.type is different from "numeric" the returned tibble contains columns listed below. If the fitted model does not contain a given 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
p.value.label: P-value if available, depends on method.
theta.label: Angle in degrees between the two OLS lines for lines estimated from y ~ x and x ~ y linear model (lm) fits.
n.label: Number of observations used in the fit.
grp.label: Set according to mapping in aes.
method.label: Set according method used.
r.squared, theta, 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, theta, p.value, 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 two 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.

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'

Aesthetics

stat_ma_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(rr.label)`
•	`npcx`	→ `after_stat(npcx)`
•	`npcy`	→ `after_stat(npcy)`
•	`vjust`	→ `"inward"`

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

Details

This stat can be used to automatically annotate a plot with $R^2$, $P$-value, $n$ and/or the fitted model equation. It supports linear major axis (MA), standard major axis (SMA) and ranged major axis (RMA) regression by means of function lmodel2. Formulas describing a straight line and including an intercept are the only ones currently supported. Please see the documentation, including the vignette of package 'lmodel2' for details. The parameters in stat_ma_eq() follow the same naming as in function lmodel2().

It is important to keep in mind that although the fitted line does not depend on whether the $x$ or $y$ appears on the rhs of the model formula, the numeric estimates for the parameters do depend on this.

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_ma_eq() mimics how stat_smooth() works, except that Model II regressions can be fitted. Similarly to stat_smooth() the model is fitted separately to data from each group, so the variables mapped to x and y should both be continuous rather than discrete as well as the corresponding scales.

The minimum number of observations with distinct values can be set through parameter n.min. The default n.min = 2L is the smallest possible value. However, model fits with very few observations are of little interest and using a larger number for n.min than the default is usually wise. As model fitting functions can depend on the RNG, fit.seed if different to NA is used as argument in a call to set.seed() immediately ahead of model fitting.

Examples

Run this code

# generate artificial data
set.seed(98723)
my.data <- data.frame(x = rnorm(100) + (0:99) / 10 - 5,
                      y = rnorm(100) + (0:99) / 10 - 5,
                      group = c("A", "B"))

# using defaults (major axis regression)
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line() +
  stat_ma_eq()

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line() +
  stat_ma_eq(mapping = use_label("eq"))

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line() +
  stat_ma_eq(mapping = use_label("eq"), decreasing = TRUE)

# use_label() can assemble and map a combined label
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line(method = "MA") +
  stat_ma_eq(mapping = use_label("eq", "R2", "P"))

ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line(method = "MA") +
  stat_ma_eq(mapping = use_label("R2", "P", "theta", "method"))

# using ranged major axis regression
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line(method = "RMA",
               range.y = "interval",
               range.x = "interval") +
  stat_ma_eq(mapping = use_label("eq", "R2", "P"),
             method = "RMA",
             range.y = "interval",
             range.x = "interval")

# No permutation-based test
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line(method = "MA") +
  stat_ma_eq(mapping = use_label("eq", "R2"),
             method = "MA",
             nperm = 0)

# explicit formula "x explained by y"
ggplot(my.data, aes(x, y)) +
  geom_point() +
  stat_ma_line(formula = x ~ y) +
  stat_ma_eq(formula = x ~ y,
             mapping = use_label("eq", "R2", "P"))

# modifying both variables within aes()
ggplot(my.data, aes(log(x + 10), log(y + 10))) +
  geom_point() +
  stat_poly_line() +
  stat_poly_eq(mapping = use_label("eq"),
               eq.x.rhs = "~~log(x+10)",
               eq.with.lhs = "log(y+10)~~`=`~~")

# grouping
ggplot(my.data, aes(x, y, color = group)) +
  geom_point() +
  stat_ma_line() +
  stat_ma_eq()

# labelling equations
ggplot(my.data,
       aes(x, y,  shape = group, linetype = group, grp.label = group)) +
  geom_point() +
  stat_ma_line(color = "black") +
  stat_ma_eq(mapping = use_label("grp", "eq", "R2")) +
  theme_classic()

# 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 with after_stat().

gginnards.installed <- requireNamespace("gginnards", quietly = TRUE)

if (gginnards.installed)
  library(gginnards)

# default is output.type = "expression"
if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_ma_eq(geom = "debug_group")

if (FALSE) {
if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_ma_eq(mapping = aes(label = after_stat(eq.label)),
               geom = "debug_group",
               output.type = "markdown")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_ma_eq(geom = "debug_group", output.type = "text")

if (gginnards.installed)
  ggplot(my.data, aes(x, y)) +
    geom_point() +
    stat_ma_eq(geom = "debug_group", output.type = "numeric")
}

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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()`