A shiny app for clusters that are not there

clusters
shiny
An app for inferential risks and power in cluster analysis
Published

September 23, 2024

Overview

Clusters That Are Not There is a Shiny application designed to help researchers quantify inferential risks when applying clustering methods such as Gaussian Mixture Models (GMM) or k-means. Inspired by the article Clusters That Are Not There (Toffalini et al., 2024), the app provides an accessible interface to run Monte Carlo simulations that evaluate Type I error, power, and classification accuracy under conditions commonly found in psychological research.

The core message of the paper is simple but crucial:

Clustering methods can easily “detect” clusters even when none exist — especially when assumptions such as normality or local independence are violated.
This app offers an intuitive way to test these risks before running cluster analyses on real data.

➡️ Explore the app: https://psicostat.shinyapps.io/clustersimulation-demo/
➡️ Manuscript: Toffalini et al., https://doi.org/10.1002/ijop.13246 (Open Access)

What the App Does

The app implements the simulation logic described in the manuscript, allowing users to:

  • Simulate datasets with custom characteristics:
    • sample size
    • number of indicators
    • correlations
    • skewness and kurtosis
    • effect size (d) between true clusters
  • Estimate Type I error
    How often does a method detect multiple clusters when the data truly come from one population? (e.g., GMM may show inflated Type I error under modest skewness)
  • Estimate Power
    How often does the method correctly detect two clusters when they truly exist? (e.g., with d = .50 and N = 700, power is extremely low for both GMM and k-means)
  • Assess classification accuracy
    Using the Adjusted Rand Index, the app reveals how often detected clusters actually match the true underlying structure (k-means may detect “two clusters” with 100% power but classify individuals no better than chance (Adjusted Rand Index ≈ .06)).

Why This Matters

Clustering is popular in psychology, but the assumptions behind common methods are often unmet. The manuscript shows several scenarios where:

  • Moderate skewness (skew = .50) yields 48% false positives for GMM in our simulation (p.7)
  • Modest correlations (r = .35) produce 100% false positives for k-means (p.8–9)
  • Large sample sizes exacerbate the problem for GMM (p.12)
  • GMM may “create” clusters to compensate for skewed distributions (Figure 6, p.13)

These are exactly the pitfalls the app helps users explore and understand.

Features at a Glance

  • 🧮 Monte Carlo simulation interface
  • 🔢 Data Specification mode (define your own distributions)
  • 📂 Data Upload mode (upload your dataset and test risks)
  • 📊 GMM and k-means implementations following the paper
  • 🔍 Visual summaries of detected cluster counts
  • ⏱️ Time-limited simulation mode for web performance
  • 📥 Downloadable simulation settings