Intraclass Correlation Coefficient (ICC)

Computes the ICC using ANOVA-based methods following Shrout & Fleiss (1979). Supports one-way and two-way random/mixed models, agreement and consistency types, and single or average unit measures.

Usage

icc(
  ratings,
  model = c("twoway", "oneway"),
  type = c("agreement", "consistency"),
  unit = c("single", "average")
)

Arguments

ratings

Numeric matrix with subjects as rows and raters/sessions as columns.

model

Character; ICC model type:

"oneway": One-way random effects (ICC(1,1) or ICC(1,k))
"twoway": Two-way random/mixed effects (default)

type

Character; agreement type:

"agreement": Absolute agreement (ICC(2,1) for twoway)
"consistency": Consistency/relative agreement (ICC(3,1) for twoway)

unit

Character; unit of measurement:

"single": Reliability for a single rater/measurement
"average": Reliability for the mean of k raters/measurements

Value

A list with components:

icc: ICC value
ci_lower: Lower bound of 95 percent confidence interval
ci_upper: Upper bound of 95 percent confidence interval
f_value: F statistic from ANOVA
p_value: p-value for testing ICC = 0
model: Model used
type: Agreement type used

Details

The function implements the six ICC forms from Shrout & Fleiss (1979):

ICC(1,1): One-way random, single measures
ICC(1,k): One-way random, average measures
ICC(2,1): Two-way random, absolute agreement, single measures
ICC(2,k): Two-way random, absolute agreement, average measures
ICC(3,1): Two-way mixed, consistency, single measures
ICC(3,k): Two-way mixed, consistency, average measures

References

Shrout PE, Fleiss JL (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420-428.

Examples

# Test-retest reliability
ratings <- 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, ncol = 4, byrow = TRUE)

result <- icc(ratings, model = "twoway", type = "agreement")
result$icc
#> [1] 0.2897638