icc: Intraclass correlation coefficient (ICC) for oneway and twoway models

Description

Computes single score or average score ICCs as an index of interrater reliability of quantitative data. Additionally, F-test and confidence interval are computed.

Usage

icc(ratings, model = c("oneway", "twoway"), 
    type = c("consistency", "agreement"), 
    unit = c("single", "average"), r0 = 0, conf.level = 0.95)

Value

A list with class icclist containing the following components:

subjects: the number of subjects examined.
raters: the number of raters.
model: a character string describing the selected model for the analysis.
type: a character string describing the selected type of interrater reliability.
unit: a character string describing the unit of analysis.
icc.name: a character string specifying the name of ICC according to McGraw & Wong (1996).
value: the intraclass correlation coefficient.
r0: the specified null hypothesis.
Fvalue: the value of the F-statistic.
df1: the numerator degrees of freedom.
df2: the denominator degrees of freedom.
p.value: the p-value for a two-sided test.
conf.level: the confidence level for the interval.
lbound: the lower bound of the confidence interval.
ubound: the upper bound of the confidence interval.

Arguments

ratings: n*m matrix or dataframe, n subjects m raters.
model: a character string specifying if a oneway model (default) with row effects random, or a twoway model with column and row effects random should be applied. You can specify just the initial letter.
type: a character string specifying if '"consistency"' (default) or '"agreement"' between raters should be estimated. If a '"oneway"' model is used, only '"consistency"' could be computed. You can specify just the initial letter.
unit: a character string specifying the unit of analysis: Must be one of single (default) or average. You can specify just the initial letter.
r0: specification of the null hypothesis r = r0. Note that a one sided test (H1: r > r0) is performed.
conf.level: confidence level of the interval.

Author

Matthias Gamer

Details

This function was created by Matthias Gamer for the irr package. For more details, see:

http://rss.acs.unt.edu/Rdoc/library/irr/html/icc.html

Details for the function:

Missing data are omitted in a listwise way. When considering which form of ICC is appropriate for an actual set of data, one has take several decisions (Shrout & Fleiss, 1979):

1. Should only the subjects be considered as random effects (oneway model) or are subjects and raters randomly chosen from a bigger pool of persons (twoway model).

2. If differences in judges' mean ratings are of interest, interrater agreement instead of consistency should be computed.

3. If the unit of analysis is a mean of several ratings, unit should be changed to average. In most cases, however, single values (unit = single) are regarded.

References

Bartko, J.J. (1966). The intraclass correlation coefficient as a measure of reliability. Psychological Reports, 19, 3-11.

McGraw, K.O., & Wong, S.P. (1996), Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1, 30-46.

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

Examples

Run this code

# sample data

study <- c(1,1,2,2,3,3)
rater <- c(rep(1:2,3))
mod1 <- round(rnorm(6, 10, 1))
mod2 <- c(5,5, 9, 9, 8, 8)
mod3 <- c(10,10, 9, 9, 8, 8)
w <-data.frame(study, rater, mod1, mod2, mod3)
w


# if data is in this format:

# study rater mod1 mod2 mod3
#     1     1    9    9   10
#     1     2   11    8   10
#     2     1    9   10   11
#     2     2    9   10   11
#     3     1    9    9    8
#     3     2   12    9    8
#
# the data will need to be reshaped to be processed by the 
# icc function:

long <- reshape(w, varying=colnames(w)[3:5], v.names="Code", 
            idvar=c('study', 'rater'), timevar="mods", direction='long')
wide <- reshape(long, idvar=c('mods', 'study'), timevar='rater')

# icc function (created by Matthias Gamer for the 'irr' package)

icc(cbind(wide$Code.1, wide$Code.2), type= "consistency")

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