Simulated data, not a real study. Sixteen classrooms hold five pupils each, and the same four raters score every pupil. The classroom standard deviation (1.3) is larger than the pupil one within a classroom (0.6), so the cluster-level ICC comes out above the subject-level ICC. The "Multilevel designs" article and the README use it.
Format
A data frame with 320 rows and 4 columns:
- classroom
Factor with 16 levels: the cluster.
- pupil
Factor with 80 levels: the subject, labeled
classroom_pupil.- rater
Factor with 4 levels: the rater.
- score
Numeric rating.
Source
Simulated by data-raw/make-vignette-data.R with set.seed(2025).
The score is 10 plus a classroom effect, a pupil effect, a rater effect,
and noise (standard deviation 0.7), all normal draws.
See also
school_incomplete for the same design with a fifth of the ratings removed.
Examples
str(school)
#> 'data.frame': 320 obs. of 4 variables:
#> $ classroom: Factor w/ 16 levels "1","2","3","4",..: 1 1 1 1 1 2 2 2 2 2 ...
#> $ pupil : Factor w/ 80 levels "1_1","1_2","1_3",..: 1 2 3 4 5 6 7 8 9 10 ...
#> $ rater : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
#> $ score : num 10.5 10.1 10 11.7 9 ...
icc(school, score, subject = pupil, rater = rater, cluster = classroom,
type = "agreement", seed = 1)
#> ℹ Treating raters with the same label in different clusters as the same raters
#> (crossed with clusters, Design 1).
#> ℹ If each cluster has its own raters, give them cluster-unique labels or pass
#> `design = "nested_in_clusters"`.
#> This message is displayed once per session.
#> ── Intraclass correlation: multilevel two-way random, absolute agreement ───────
#> Subjects: 80 in 16 clusters | Raters: 4 (random) | Observations: 320 (complete)
#> Engine: glmmTMB (REML) | CI: 95% montecarlo (10000 draws)
#>
#> level index estimate 95% CI
#> subject ICC(A,1) 0.431 [0.254, 0.561]
#> subject ICC(A,k) 0.751 [0.576, 0.836]
#> cluster ICC(A,1) 0.880 [0.000, 0.972]
#> cluster ICC(A,k) 0.967 [0.000, 0.993]
#>
#> Variance components: cluster 0.998, subject 0.461, rater 0.136, cluster:rater 0.000, residual 0.473