Hierarchical Data Studio

Rivu Basu Mixed Model Lab

Simulate nested data, inspect pooled versus within-cluster relationships, and visualize shrinkage from a random-intercept model in one polished teaching canvas.

Cluster Setup

New cluster label

Active cluster for point editing

Point Editing

Click inside the plot to add a point to the active cluster. Drag points to reposition them. Double-click a point, or select it and press Delete, to remove it.

Enable data spraying

Ready. Generate a dataset or start placing points manually.

Model View

Show fitted model line(s) Show cluster-specific OLS lines Show pooled regression line Show residuals for active model Show random-intercept shrinkage paths

Generate Data

Clusters: 5

Points per cluster: 16

Overall slope: 0.70

Between-cluster SD: 14

Within-cluster SD: 8

Cluster overlap in x: 18

Scenario Presets

Model Comparison

Interactive Mixed Model Canvas

The chart contrasts pooled, within-cluster, and partially pooled fits while keeping the nested data structure visible.

Active model: Pooled OLS

Selected point: None

ICC: 0.000

Learning Journey

Lesson 1

Foundations

Step 1 of 4

Use the simulator to discover how clustering changes what a single regression line can and cannot explain.

Load the lesson scenario, inspect the chart, and answer the quick check.

Quick Check

Why can pooled OLS miss important structure in clustered data?

Select an answer to get immediate feedback.

Interactive Challenge

Complete the lesson task by creating the requested data pattern and model display.

Your progress will be checked against the live simulation.

Mastery: 0 of 4 lesson checkpoints completed.

Model Diagnostics

Clusters

Observations

Between variance

0.000

Within variance

0.000

ICC

0.000

Interpretation

No clustering

ICC measures the share of total outcome variance attributable to cluster-level differences.

Coefficient Summary

Generate data to compute model summaries.

Cluster Summary

No data yet.

Model Notes

Pooled OLS ignores nesting, fixed effects isolates within-cluster variation, and random effects partially pools cluster intercepts toward the grand mean.

Model: y_ij = beta_0 + beta_1 x_ij + u_j + e_ij ICC = tau^2 / (tau^2 + sigma^2)