Purpose

Public preview: This page shows the analysis output, figures, diagnostics, and reporting guidance without exposing the R code. The paid version includes the complete editable R Markdown source, reusable functions, all analysis code, synthetic data, documentation, and exported results.

Educational observations are rarely independent. Students share classrooms, classrooms share schools, and repeated assessments share students. Multilevel models represent those dependencies directly while separating within-cluster and between-cluster relationships.

This workflow audits the hierarchy before modeling, estimates variance at each level, separates student and school context, fits random-intercept and random-slope models, probes a cross-level interaction, checks model stability, and extends the framework to a binary outcome.

The included dataset is entirely synthetic. It contains students nested in classrooms nested in schools, unequal cluster sizes, student and contextual predictors, a random prior-achievement slope, and a cross-level socioeconomic-context interaction. No real student or school records are included.

Learning outcomes and prerequisites

After completing the example, the user should be able to:

  • identify levels, nesting, repeated measures, and possible cross-classification;
  • audit cluster identifiers, sizes, variation, and missingness;
  • fit unconditional, random-intercept, and random-slope models;
  • calculate and interpret variance partition coefficients;
  • separate within-school and between-school relationships;
  • explain grand-mean, group-mean, and within-between centering choices;
  • probe and plot a cross-level interaction;
  • diagnose singularity, convergence, residual patterns, and influential clusters;
  • extend the model to a binary educational outcome; and
  • report estimates without turning clustered associations into causal claims.

The workflow assumes familiarity with ordinary regression. Cross-classified models, multiple membership, complex survey weights, plausible values, spatial dependence, and causal multilevel mediation require additional methods.

User settings

Simulate and import the example

First eight synthetic student records
student_id classroom_id school_id locale achievement on_track prior_z ses_z implementation_z resources_z
SCH01-C01-S001 SCH01-C01 SCH01 Suburban 81.83 0 0.71 1.43 0.66 -1.78
SCH01-C01-S002 SCH01-C01 SCH01 Suburban 57.53 1 -1.18 -0.65 0.66 -1.78
SCH01-C01-S003 SCH01-C01 SCH01 Suburban 76.35 1 1.04 0.74 0.66 -1.78
SCH01-C01-S004 SCH01-C01 SCH01 Suburban 91.99 1 1.39 -0.19 0.66 -1.78
SCH01-C01-S005 SCH01-C01 SCH01 Suburban 73.82 0 -0.43 0.58 0.66 -1.78
SCH01-C01-S006 SCH01-C01 SCH01 Suburban 73.73 0 -0.83 1.00 0.66 -1.78
SCH01-C01-S007 SCH01-C01 SCH01 Suburban 57.74 1 -2.62 0.09 0.66 -1.78
SCH01-C01-S008 SCH01-C01 SCH01 Suburban 82.96 1 0.80 -1.28 0.66 -1.78

Hierarchy and data audit

Cluster integrity

quantity result
Students 3301
Schools 36
Classrooms 153
Median students per school 88.5
School-size range 50b