Discriminant Analysis Decision Plot using ggplot.

Discriminant analysis can be more easily understood from plots of the data variables showing how observations are classified. plot_discrim() uses the ideas behind effect plots (Fox, 1987): Visualize predicted classes of the observations for two focal variables over a grid of their values, with other variables in a model held fixed. This differs from the usual effect plots in that the predicted values to be visualized are discrete categories rather than quantitative.

In the case of discriminant analysis, the predicted values are class membership, so this can be visualized by mapping the categorical predicted class to discrete colors used as the background for the plot, or plotting the contours of predicted class membership as lines (for [MASS::lda()]) or qauadratic curves (for [MASS::qda()]) in the plot. The predicted class of any observation in the space of the variables displayed can also be rendered as colored tiles or points in the background of the plot.

Usage

plot_discrim(
  model,
  vars,
  data = insight::get_data(model),
  resolution = 100,
  point.size = 3,
  showgrid = c("tile", "point", "none"),
  contour = TRUE,
  contour.color = "black",
  tile.alpha = 0.2,
  ellipse = FALSE,
  ellipse.args = list(level = 0.68, linewidth = 1.2),
  labels = FALSE,
  labels.args = list(geom = "text", size = 5),
  rev.axes = c(FALSE, FALSE),
  xlim = NULL,
  ylim = NULL,
  ...,
  other.levels
)

Arguments

model: a discriminant analysis model object from MASS::lda() or MASS::qda()
vars: either a character vector of length 2 of the names of the x and y variables, or a formula of form y ~ x specifying the axes in the plot. Can include discriminant dimensions like LD1, LD2, etc.
data: data to use for visualization. Should contain all the data needed to use the model for prediction. The default is to use the data used to fit the model.
resolution: number of points in x, y variables to use for visualizing the predicted class boundaries and regions.
point.size: size of the plot symbols use to show the data observations
showgrid: a character string; how to display predicted class regions: "tile" for ggplot2::geom_tile(), "point" for ggplot2::geom_point(), or "none" for no grid display.
contour: logical (default: TRUE); should the plot display the boundaries of the classes by contours?
contour.color: color of the lines for the contour boundaries (default: "black")
tile.alpha: transparency value for the background tiles of predicted class.
ellipse: logical; if TRUE, 68 percent data ellipses for the groups are added to the plot.
ellipse.args: a named list of arguments passed to ggplot2::stat_ellipse(). Common arguments include level (confidence level, default: 0.68), linewidth (line thickness, default: 1.2), geom (either "path" for unfilled ellipses or "polygon" for filled ellipses), and alpha (transparency for filled ellipses). Any valid argument to stat_ellipse() can be used.
labels: logical; if TRUE, class labels are added to the plot at the group means (default: FALSE).
labels.args: a named list of arguments passed to ggplot2::geom_text() or ggplot2::geom_label(). Common arguments include geom (either "text" or "label", default: "text"), size (text size, default: 5), fontface (e.g., "bold" or "italic"), nudge_x and nudge_y (position offsets), and alpha (transparency for label backgrounds). Any valid argument to geom_text() or geom_label() can be used.
rev.axes: a logical vector of length 2 controlling axis reversal for discriminant dimensions. rev.axes[1] = TRUE reverses the horizontal (x) axis; rev.axes[2] = TRUE reverses the vertical (y) axis. Only applies when plotting discriminant dimensions (e.g., LD2 ~ LD1). Default: c(FALSE, FALSE).
xlim, ylim: numeric vectors of length 2 giving the axis limits. If NULL (default), uses the range of the variable in the data.
...: further parameters passed to predict()
other.levels: a named list specifying the fixed values to use for variables in the model that are not included in vars (the non-focal variables). These values are held constant across the prediction grid. If not specified, the function uses sensible defaults: means for quantitative variables, and the first level for factors or character variables.

Details

Since plot_discrim() returns a "ggplot" object, you can easily customize colors and shapes by adding scale layers after the function call. You can also add other graphic layers, such as annotations, and control the overall appearance of plots using ggplot2::theme() components.

Customizing colors and shapes

Use scale_color_manual() and scale_fill_manual() to control the colors used when using showgrid = "tile", because that maps both both color and fill to the group variable.
Use scale_shape_manual() to control the symbols used for geom_points()

Customizing ellipses

The ellipse.args parameter provides fine control over the appearance of data ellipses. Common arguments include:

level: the confidence level for the ellipse (default: 0.68)
linewidth: thickness of the ellipse line (default: 1.2)
geom: either "path" for unfilled ellipses (default) or "polygon" for filled ellipses
alpha: transparency when using geom = "polygon"

See ggplot2::stat_ellipse() for additional parameters.

Adding class labels

The labels and labels.args parameters allow you to add text labels for each class, positioned at the group means. Common arguments for labels.args include:

geom: either "text" (default) for simple text or "label" for text with a background box
size: text size (default: 5)
fontface: font style such as "bold" or "italic"
nudge_x, nudge_y: offsets for label positioning
alpha: transparency for label backgrounds when using geom = "label"

See ggplot2::geom_text() and ggplot2::geom_label() for additional parameters.

Plotting in discriminant space

When vars specifies discriminant dimensions (e.g., LD2 ~ LD1), the function automatically:

Calculates discriminant scores using predict_discrim()
Creates a new LDA model in the discriminant space
Plots the observations and decision boundaries in this transformed space

This is particularly useful for visualizing how well the discriminant dimensions separate the groups, since by construction the groups are maximally separated in discriminant space.

Reversing discriminant axes

The orientation of discriminant axes (LD1, LD2, etc.) is arbitrary in the sense that multiplying any discriminant dimension by -1 does not change the discriminant solution or model fit. The rev.axes parameter allows you to reverse the direction of one or both axes when plotting in discriminant space. This can be useful for:

Aligning the discriminant plot with conventional interpretations (e.g., having "positive" on the right)
Making the orientation consistent across different analyses or visualizations
Improving the interpretability of the axes in relation to the original variables

The rev.axes parameter only affects plots of discriminant dimensions (e.g., LD2 ~ LD1) and has no effect when plotting original observed variables. To reverse the horizontal axis (x-axis), set rev.axes[1] = TRUE; to reverse the vertical axis (y-axis), set rev.axes[2] = TRUE. Both axes can be reversed simultaneously with rev.axes = c(TRUE, TRUE).

References

Fox, J. (1987). Effect Displays for Generalized Linear Models. In C. C. Clogg (Ed.), Sociological Methodology, 1987 (pp. 347–361). Jossey-Bass

Author

Original code by Oliver on SO https://stackoverflow.com/questions/63782598/quadratic-discriminant-analysis-qda-plot-in-r.

Generalized by Michael Friendly

Examples

library(MASS)
library(ggplot2)
library(dplyr)

iris.lda <- lda(Species ~ ., iris)
# formula call: y ~ x
plot_discrim(iris.lda, Petal.Length ~ Petal.Width)


# add data ellipses
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             ellipse = TRUE) 


# add filled ellipses with transparency
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             ellipse = TRUE,
             ellipse.args = list(geom = "polygon", alpha = 0.2)) 


# customize ellipse level and line thickness
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             ellipse = TRUE,
             ellipse.args = list(level = 0.95, linewidth = 2)) 


# without contours
# data ellipses
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             contour = FALSE) 


# specifying `vars` as character names for x, y
plot_discrim(iris.lda, c("Petal.Width", "Petal.Length"))


# Define custom colors and shapes, modify theme() and legend.position
iris.colors <- c("red", "darkgreen", "blue")
iris.pch <- 15:17
plot_discrim(iris.lda, Petal.Length ~ Petal.Width) +
  scale_color_manual(values = iris.colors) +
  scale_fill_manual(values = iris.colors) +
  scale_shape_manual(values = iris.pch) +
  theme_bw(base_size = 14) +
  theme(legend.position = "inside",
        legend.position.inside = c(.8, .25))


# Quadratic discriminant analysis gives quite a different result
iris.qda <- qda(Species ~ ., iris)
plot_discrim(iris.qda, Petal.Length ~ Petal.Width)


# Add class labels, with custom styling
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             labels = TRUE,
             labels.args = list(geom = "label", size = 6, fontface = "bold"))


# Add labels with position adjustments
plot_discrim(iris.lda, Petal.Length ~ Petal.Width, 
             labels = TRUE,
             labels.args = list(nudge_y = 0.1, size = 5))


# Plot in discriminant space
plot_discrim(iris.lda, LD2 ~ LD1)


# Reverse the horizontal axis in discriminant space
plot_discrim(iris.lda, LD2 ~ LD1, rev.axes = c(TRUE, FALSE))


# Control axis limits
plot_discrim(iris.lda, LD2 ~ LD1,
             xlim = c(-10, 10), ylim = c(-8, 8))