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DMAR (version 1.0.0)

icc: Intraclass Correlation Coefficients With Confidence Intervals

Description

Computes one or more of the six standard intraclass correlation coefficients (ICC) of Shrout and Fleiss (1979) for an \(n \times k\) matrix of ratings (rows = subjects, columns = raters/measurements), along with the F-distribution-based confidence interval for each.

Usage

icc(x, type = "ICC(2,1)", conf_level = 0.95)

Value

A data.frame (class dmar_tbl) with one row per requested ICC type and columns type, value (point estimate), lower_limit,

upper_limit, F_value, df_1, df_2, and

p_value (for the implicit null \(H_0\!: \mathrm{ICC} = 0\)).

Arguments

x

An \(n \times k\) numeric matrix or data.frame: each row is a subject (target) and each column is a rater (or repeated measurement). Missing values are not supported; remove or impute first.

type

Which ICC variant(s) to return. Aliases include "1", "2", "3" (single rater versions of types 1, 2, 3) and "1k", "2k", "3k" (average-of-\(k\)-raters versions). The full names "ICC(1,1)", "ICC(2,1)", "ICC(3,1)", "ICC(1,k)", "ICC(2,k)", "ICC(3,k)" are also accepted, as is "all". Vectors are accepted; a row is returned for each type.

conf_level

Confidence level for the interval (default 0.95).

Author

Ken Kelley [email protected]

Details

The six variants follow Shrout and Fleiss's (1979) classification:

  • ICC(1,1): one-way random model, single rater. Each subject is rated by a different (random) rater; appropriate when raters are not crossed with subjects.

  • ICC(1,k): one-way random model, average of \(k\) raters.

  • ICC(2,1): two-way random model, single rater, absolute agreement. Subjects \(\times\) raters fully crossed; both effects random.

  • ICC(2,k): two-way random model, average of \(k\) raters, absolute agreement.

  • ICC(3,1): two-way mixed model, single rater, consistency. Raters are fixed (the only ones of interest); rates differences in mean across raters are not penalized.

  • ICC(3,k): two-way mixed model, average of \(k\) raters, consistency.

Confidence intervals follow the F-distribution-based formulas of Shrout and Fleiss (1979, pp.\ 425--426); the ICC(2,1) interval uses their asymmetric approximate-df formulation.

References

Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420--428.

McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1(1), 30--46. tools:::Rd_expr_doi("10.1037/1082-989X.1.1.30")

See Also

ci_r, descriptives

Other reliability: cohen_kappa(), diagnosis_agreement, fleiss_kappa(), reliability(), reliability_H(), reliability_alpha(), reliability_kr20(), reliability_omega(), reliability_omega_categorical()

Examples

Run this code
# Shrout & Fleiss (1979), Table 1: 4 raters, 6 targets.
shrout_fleiss <- matrix(
  c(9, 2, 5, 8,
    6, 1, 3, 2,
    8, 4, 6, 8,
    7, 1, 2, 6,
    10, 5, 6, 9,
    6, 2, 4, 7),
  nrow = 6, byrow = TRUE,
  dimnames = list(paste0("Target_", 1:6),
                  paste0("Judge_",  1:4))
)

icc(shrout_fleiss, type = "all")

# Just the two-way mixed-model single-rater consistency ICC:
icc(shrout_fleiss, type = "ICC(3,1)")

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