Interactive 2D and 3D Visualization of Data and Statistical Concepts

Interactive gadgets and plotting functions for visualizing data sets and statistical concepts in two and three dimensions. Explore a data frame as a 3D point cloud you can rotate, fit a moderated (interaction) regression and view its surface as a 3D wireframe, or plot principal components and regression fits in two dimensions. Each interactive gadget returns the call that reproduces its final view, including the viewing angle, so an exploratory session can be pasted into a script or report. Also provides simulation-based demonstrations of sampling distributions, confidence intervals, t-tests, and matrix inversion for teaching and self-study.

compstatslib

compstatslib is a collection of interactive gadgets and plotting functions for visualizing data sets and statistical concepts in two and three dimensions.

Some of it works on your own data: explore any data frame as a rotatable 3D point cloud, or fit a moderated (interaction) regression and rotate its fitted surface to see how the interaction twists it away from a plane. The rest simulates a concept rather than plotting your data — sampling distributions, confidence intervals, t-statistics, matrix inversion — and is built for in-class demonstration, homework, and self-study.

Every interactive gadget prints the plot_*() call that reproduces its final view, viewing angle included. Exploration in the viewer pane becomes one line you can paste into a script, an Rmd, or a figure-generating file.

The 3D visualizations are the part of the package meant to grow beyond the classroom, toward figures good enough for textbooks and manuscripts. They are not there yet — see docs/future-work.md for the specific gaps.

How the functions are organized

Three kinds of function are provided:

• Interactive functions let you use your mouse and/or keyboard to interact with a visualization of a technique (e.g., regression, PCA)
• Plot functions functions produce plots of data, distributions, or particular statistical concepts (often a non-interactive counterpart to an interactive function)
• Code functions are provided as examples of code that one might want to see (they are executable, but the major value is in seeing their code)

They are grouped below by what they are for, since that varies more than the interaction style does.

Visualizing Data Sets in 3D

These accept arbitrary data frames and model formulas, with control over axes, color mapping, aspect ratio, and viewing angle.

3D Scatterplots

• interactive_scatter3d() Interactive Shiny gadget for exploring three numeric columns of a data frame as a rotatable 3D point cloud. Column pickers swap x / y / z (and an optional color mapping) at runtime; aspect, opacity, and marker-size sliders tune the view. Rotation and zoom persist across slider/picker changes within the gadget. On Done, prints a reproducible plot_scatter3d(...) call to the console — including the captured camera position — so the exact rotation and zoom can be pasted into an Rmd or script.
• plot_scatter3d() Non-interactive counterpart that returns a plotly htmlwidget for a 3D scatterplot of three numeric columns. Supports optional color mapping (numeric → continuous scale; factor / character → discrete palette), aspect-ratio control, marker opacity / size, custom axis titles, and an explicit camera argument for reproducing a specific view captured from the gadget.

Moderation (Interaction Effects)

• interactive_moderation_3d() Interactive Shiny gadget that fits a moderated regression and renders the fitted surface as a rotatable 3D wireframe. Two sliders control the viewing angle, so you can see how an interaction term twists the surface relative to an additive (planar) model.
• plot_moderation_3d() Non-interactive counterpart that returns a lattice::wireframe trellis object for the moderation surface. Accepts any model formula (y ~ x * z, y ~ x + z, or larger models with extra controls — pass iv and mod to choose which two predictors are plotted; the rest are held at typical values).
• moderation_data Bundled synthetic dataset used as the default example for the two functions above; calibrated to make the interaction effect visually obvious. Includes an unrelated noise variable w for demonstrating multi-predictor formulas.

Fitting and Visualizing 2D Relationships

These plot a dataframe of x / y points that you supply, together with a fitted model. They are sized for small data — points you click in by hand or a modest dataframe — rather than for arbitrary data: plot_regression() draws in a fixed −5 to 50 window, and plot_pca() expects exactly two columns named x and y.

Linear Regression

• interactive_regression() Interactive visualization function that lets you point-and-click to add data points, while it automatically plots and updates a regression line and associated statistics.
• plot_regression() Plotting function that takes a dataframe of points (x, y) and plots them with a regression line and associated statistics.

Logistic Regression

• interactive_logit() Interactive visualization function that lets you point-and-click to add data points, while it automatically plots and updates a logistic regression line and associated statistics.
• plot_logit() Plotting function that takes a dataframe of points (x, y) and plots them with a logistic regression curve and associated statistics. The x-axis range adapts to the data you pass.

Principal Components Analysis

• interactive_pca() Interactive visualization function that lets you point-and-click to add data points, while it automatically plots and updates principal component vectors.
• plot_pca() Plotting function that takes a dataframe of points (x, y) and plots them with their principal component vectors. Supports optional mean-centering.

Simulations and Concept Demonstrations

These do not plot your data. They simulate a process, or draw a geometric object, so that a concept can be watched rather than described.

Statistical Tests

• interactive_t_test() Interactive visualization function that will show you a simulation of null and alternative distributions of the t-statistic. You will be able to play with the different parameters that affect hypothesis tests in order to see how their variation influences the null t and alternative t distributions, as well as statistical power.
• plot_t_test() Non-interactive visualization that plots null and alternative t distributions of a t-test. Shows the rejection zone and statistical power as shaded areas under the curves. Accepts parameters for the test difference, standard deviation, sample size, significance level, and an optional type I/II error matrix overlay.

Statistical Sampling

• interactive_sampling() Interactive sampling simulation that will sample given population data to show how a sampling statistic is distributed across repetitions of sampling exercise.
• plot_sampling() Plotting function that shows the distribution of a population alongside samples drawn from it and the distribution of a given sampling statistic (e.g., mean or median).
• plot_sample_ci() Simulated visualization of samples drawn from a given population function, with each sample’s confidence intervals displayed.

Linear Algebra

• interactive_matrix_inverse() Interactive function that allows one to manipulate a matrix inversion.
• plot_matrix_inverse() Plotting function that visualizes a matrix and its inverse as vector pairs, showing their geometric relationship.

Precision

• machine_precision() Code function that shows how to find the smallest number your computer can effectively represent

Reproducing an Interactive Session

Every interactive_*() gadget hands its final state back when you click Done, and prints the plot_*() call that reproduces what was on screen. Assign the result and you can either paste that call into a script or feed the object straight back:

result <- interactive_moderation_3d()
#> plot_moderation_3d(formula = y ~ x * z, data = moderation_data, z_rot = 125)

do.call(plot_moderation_3d, result)   # same surface, same viewing angle

Gadgets whose state is a set of points return a dataframe you can use as one (nrow(), [, passing it to the plot function). Gadgets whose state is a set of settings return a plain named list suitable for do.call(). Derived results a user would not retype — the prcomp() fit from interactive_pca(), the accumulated draws from interactive_sampling() — ride along as attributes.

Installation

You can install the current development version from GitHub using the devtools package:

# install.packages("devtools")
devtools::install_github("compstatslib/compstatslib")

Feel free to send open issues or send pull requests. Happy hacking!

Contributors

compstatslib is maintained by Soumya Ray.

Daniele Melotti is a co-author of the package. Several of the plotting and interactive functions grew out of work he did as a student under Soumya Ray’s supervision, and were then folded back into the package.