compute_facet_icc: Compute intra-class correlations for each facet

In mfrmr: Estimation and Diagnostics for Many-Facet Measurement Models

Compute intra-class correlations for each facet

Description

Fits a random-effects variance-components model Score ~ 1 + (1 | Person) + (1 | Facet1) + (1 | Facet2) + ... using lme4::lmer (in Suggests) and returns the proportion of observed score variance attributable to each facet. This is a descriptive summary complementary to the Rasch-metric rater separation/reliability reported elsewhere.

Usage

compute_facet_icc(
  data,
  facets,
  score,
  person = NULL,
  reml = TRUE,
  ci_method = c("none", "profile", "boot"),
  ci_level = 0.95,
  ci_boot_reps = 1000L,
  ci_boot_seed = NULL,
  ci_boot_parallel = c("no", "multicore", "snow"),
  ci_boot_ncpus = 1L
)

Arguments

data	Data frame in long format.
facets	Character vector of facet column names.
score	Name of the score column.
person	Optional person column. If supplied it is added as a separate random intercept so Person-level variance is partitioned out.
reml	Logical; whether to fit with REML. Default TRUE.
ci_method	Confidence-interval method for the ICC column. One of "none" (default, point estimate only), "profile" (a first-order approximation: marginal likelihood-profile bounds for each variance-component SD via lme4::confint.merMod() with method = "profile", squared to variances, then plugged into the ICC ratio while holding the other components at their point estimate; fast and deterministic, the default recommendation for reporting), or "boot" (parametric bootstrap via lme4::bootMer(); slower but robust to non-normal ICC sampling distributions because each bootstrap replicate resamples the full variance decomposition jointly).
ci_level	Confidence level when ci_method != "none"; default 0.95. Koo & Li (2016) recommend banding the CI rather than the point estimate when classifying reliability as Poor / Moderate / Good / Excellent.
ci_boot_reps	Number of bootstrap replicates used when ci_method = "boot". Default 1000.
ci_boot_seed	Optional integer seed for the bootstrap path (NULL leaves the RNG state untouched).
ci_boot_parallel	Parallelisation strategy for the parametric-bootstrap CI path, passed through to lme4::bootMer(): "no" (default), "multicore" (POSIX mclapply), or "snow" (PSOCK cluster). "multicore" does nothing on Windows and falls back to serial; in that case use "snow" with parallel::makeCluster() in scope.
ci_boot_ncpus	Number of CPUs to use for the parallel bootstrap path (ignored when ci_boot_parallel = "no"). The per-replicate progress bar is suppressed under parallel execution because worker processes cannot push updates to the parent's cli console.

Value

A data.frame of class mfrm_facet_icc with one row per variance component (including a "Residual" row) and columns:

• Facet: the grouping factor name (or "Residual").

• Variance: REML variance estimate.

• ICC: variance share (Variance / sum(Variance)), in ⁠[0, 1]⁠.

• Interpretation: band label according to the facet's scale.

• InterpretationScale: "Koo-Li reliability" for the person facet, "Variance share" for others.

• ICC_CI_Lower / ICC_CI_Upper / ICC_CI_Level / ICC_CI_Method: CI bounds, level, and method (populated when ci_method != "none"; NA_real_ otherwise).

• ICC_CI_NReps: bootstrap replicate count when ci_method = "boot" (absent otherwise).

Interpreting output

The Interpretation column uses two scales so the same numeric ICC reads correctly for each facet role:

• For the person facet, higher ICC = better. Koo & Li (2016, p. 161) bands are applied: ⁠< 0.5⁠ Poor, ⁠[0.5, 0.75]⁠ Moderate, ⁠(0.75, 0.9]⁠ Good, ⁠> 0.9⁠ Excellent. The strict > boundary at 0.9 follows Koo & Li's wording "values greater than 0.90 indicate excellent reliability" (so an ICC of exactly 0.9 reads as Good).

• For non-person facets (Rater, Criterion, Task, Region, ...) the same numeric value is a variance share: how much of the total observed score variance sits at that facet. The bands used here are different (⁠Trivial share⁠ < 0.05, ⁠Small share⁠ < 0.15, ⁠Moderate share⁠ < 0.30, ⁠Large share⁠ >= 0.30), and a large rater share is generally bad news (raters disagree about averages), not good news.

The InterpretationScale column explicitly records which scale applies to each row, so downstream reporting does not confuse the two. FACETS (Linacre, 2026) reports rater separation/reliability on the Rasch metric instead of an ICC; mfrmr surfaces both, with the Rasch-metric version in diagnostics$reliability and this variance-share view here.

Note: Koo & Li (2016) recommend applying the reliability bands to the 95% confidence interval of the ICC rather than to the point estimate alone. Set ci_method = "profile" (default "none") to obtain likelihood-profile CI bounds alongside the point estimate, or ci_method = "boot" for a parametric bootstrap with ci_boot_reps replicates. The returned data frame gains ICC_CI_Lower / ICC_CI_Upper columns so downstream reporting can apply the band to the CI rather than the point estimate. The Interpretation column still uses the point estimate so callers who want CI-aware banding can implement it externally from the supplied bounds.

Typical workflow

1. Fit the MFRM model with fit_mfrm() for the Rasch-metric separation/reliability.

2. Call compute_facet_icc(data, facets, score, person) to get the complementary variance-share summary.

3. Feed into compute_facet_design_effect() to convert ICCs and average cluster sizes into Kish (1965) design effects.

References

Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155-163.

Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1-48.

See Also

compute_facet_design_effect(), analyze_hierarchical_structure(), detect_facet_nesting(), facet_small_sample_review().

Examples

toy <- load_mfrmr_data("example_core")
if (requireNamespace("lme4", quietly = TRUE)) {
  icc <- compute_facet_icc(toy, facets = c("Rater", "Criterion"),
                           score = "Score", person = "Person")
  print(icc)
  # Look for:
  # - Person ICC reads as Koo & Li (2016) reliability: < 0.5 poor,
  #   0.5-0.75 moderate, 0.75-0.9 good, > 0.9 excellent.
  # - Rater / Criterion ICC reads as variance share, NOT reliability;
  #   here SMALL values are desirable (raters / items agree), and
  #   shares > 0.10 hint at meaningful systematic facet differences.
  # - `Interpretation` summarises the variance-share band the helper
  #   has assigned to each row.
}

mfrmr documentation built on June 13, 2026, 1:07 a.m.