intraclass

intraclass computes interrater-reliability intraclass correlation coefficients (ICCs) within the generalizability-theory framework, using modern variance-component estimation (linear mixed models) rather than the classical ANOVA / mean-squares approach.

It aims to fit variance components with modern engines, and to compute the correct ICC for a stated design with proper boundary-aware Monte-Carlo interval estimation. It also aims to handle imbalanced, incomplete, and multilevel designs, and to help you decide which ICC to choose, and why. The docs and website are a place to learn ICC best practice, not just call functions.

[!NOTE] This package is approaching its first release. The full interrater-reliability ICC family is implemented. That covers two-way designs (absolute agreement vs. consistency, single vs. average, random vs. fixed raters) and one-way designs. It covers imbalanced and incomplete (missing-cell) data. It also covers multilevel designs, at the subject or cluster level, with raters crossed with or nested in clusters or subjects. Everything just listed comes with boundary-aware Monte-Carlo intervals. Fits run on glmmTMB (the default) or lme4. Bayesian fits run on brms, and SEM fits on lavaan. The engines article says which designs each one supports.

You can install the development version from GitHub with:

# install.packages("pak")
pak::pak("jmgirard/intraclass")

intraclass declares cli, generics, glmmTMB, lifecycle, rlang, and tibble as its non-base Imports:. What an installation retrieves is the full dependency closure of those declarations, which is considerably larger. One member of that closure is worth naming: glmmTMB lists lme4 in its own Imports:, so the lme4 package is already on your library path after a plain install, whatever its Suggests: placement here implies. Having the package is not the same as having the engine, though. engine = "lme4" also needs merDeriv, which every lme4 fit checks for on entry whatever interval method you ask for. merDeriv does not arrive. It sits in this package’s Suggests:, and so do brms, the Bayesian engine, and lavaan, the SEM engine. A plain install fetches none of the three. Asking for merDeriv does bring lavaan along, though, because merDeriv names it in its own Depends:. glmmTMB is the only engine a plain install leaves you ready to use.

ratings is the classic Shrout & Fleiss (1979) example, shipped with the package. With the defaults a single two-way random fit reports every defined formulation: absolute agreement and consistency, single-rater and average. They are grouped by error definition, each with a reproducible Monte-Carlo interval:

library(intraclass)

fit <- icc(ratings, score, subject, rater, seed = 2024)
fit
#> ── Intraclass correlation: two-way random, absolute agreement & consistency ────
#> Subjects: 6 | Raters: 4 (random) | Observations: 24 of 24 cells (complete)
#> Engine: glmmTMB (REML) | CI: 95% montecarlo (10000 draws)
#> 
#>   index     estimate   95% CI
#>   Absolute agreement
#>   ICC(A,1)     0.290   [0.053, 0.714]
#>   ICC(A,k)     0.620   [0.183, 0.909]
#>   Consistency
#>   ICC(C,1)     0.715   [0.334, 0.924]
#>   ICC(C,k)     0.909   [0.667, 0.980]
#> 
#> Variance components: subject 2.556, rater 5.244, residual 1.019
#> Shrout & Fleiss equivalent: ICC(A,1) = ICC(2,1), ICC(A,k) = ICC(2,k)

autoplot() draws the same fit as a forest plot (it needs ggplot2):

library(ggplot2)

autoplot(fit)

Which coefficient you want is a real modeling decision: agreement vs. consistency, single vs. average, fixed vs. random raters, complete vs. incomplete. Each of those is an argument to icc(). Not sure which to report? choose_icc() walks the Choosing an ICC decision tree and hands back the coefficient or coefficients, the reasoning, and the exact call to run. No data or fitting is required:

choose_icc(model = "twoway", type = "consistency", unit = "average", raters = "random")
#> ── Recommended ICC ─────────────────────────────────────────────────────────────
#> Design: two-way random, consistency
#> 
#> Recommendation: ICC(C,k)
#> 
#> Why:
#>   - Crossed (two-way): the same raters judge every subject.
#>   - Consistency: only the rank order must match; a constant per-rater offset is forgiven.
#>   - Average: you will act on the mean of your raters.
#>   - Random raters: a sample you generalize beyond, to the rater universe they were drawn from.
#> 
#> Run this on your data:
#>   icc(data, score, subject, rater, type = "consistency", unit = "average")
#> 
#> Notes:
#>   - Complete vs. incomplete is automatic: icc() uses whatever ratings are present and projects ICC(*,k) to the effective number of ratings (k_eff). The design must stay connected, or icc() fails loudly.

For multilevel data, meaning subjects nested in clusters such as pupils in classrooms or patients in clinics, pass a cluster column. Then icc() reports subject-level and cluster-level reliability separately:

set.seed(1)
grid <- expand.grid(pupil = 1:5, classroom = 1:12, rater = 1:4)
grid$score <- with(grid,
  10 + rnorm(12, sd = 1.2)[classroom] +
    rnorm(60, sd = 0.6)[(classroom - 1) * 5 + pupil] +
    rnorm(4, sd = 0.4)[rater] + rnorm(nrow(grid), sd = 0.7))
school <- data.frame(
  pupil = factor(paste(grid$classroom, grid$pupil, sep = "_")),
  classroom = factor(grid$classroom),
  rater = factor(grid$rater),
  score = grid$score)

icc(school, score, subject = pupil, rater = rater, cluster = classroom, seed = 2024)
#> 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"`.
#> ── Intraclass correlation: multilevel two-way random, absolute agreement & consi
#> Subjects: 60 in 12 clusters | Raters: 4 (random) | Observations: 240 (complete)
#> Engine: glmmTMB (REML) | CI: 95% montecarlo (10000 draws)
#> 
#>   level      index     estimate   95% CI
#>   Absolute agreement
#>   subject    ICC(A,1)     0.322   [0.162, 0.484]
#>   subject    ICC(A,k)     0.655   [0.436, 0.790]
#>   cluster    ICC(A,1)     0.870   [0.005, 0.973]
#>   cluster    ICC(A,k)     0.964   [0.018, 0.993]
#>   Consistency
#>   subject    ICC(C,1)     0.383   [0.245, 0.544]
#>   subject    ICC(C,k)     0.713   [0.565, 0.827]
#>   cluster    ICC(C,1)     0.995   [0.005, 1.000]
#>   cluster    ICC(C,k)     0.999   [0.018, 1.000]
#> 
#> Variance components: cluster 1.036, subject 0.305, rater 0.150, cluster:rater 0.005, residual 0.492
#> 
#> This message is displayed once per session.

d_study() projects the variance components of a fit to other rater counts, carrying the interval with them. So you can ask what reliability two raters would buy, or ten, without running the study again:

autoplot(d_study(fit, m = 1:10))

• Getting started: the guided tour.
• Choosing an ICC: the decision guide behind choose_icc().
• Multilevel designs: incomplete and nested multilevel data.
• Estimation engines: what each engine buys you.
• Confidence-interval methods: the ci_method menu.
• D-studies and replicates: projection and within-cell replicates.
• Comparison with other packages: how the numbers line up.
• Glossary: the vocabulary in one place.

intraclass fills that gap, following ten Hove, Jorgensen & van der Ark.