# Calculating ICC 2.1C in R

Intraclass Correlations using Mcgraw and Wong conventions defines 5 ICC´s for single scores. I am interested in calculating both Two-way random, single measures, absolute agreement (Sometimes abbreviated as ICC 2.1A) and Two-way random, single measures, consistency (Sometimes abbreviated as ICC 2.1C).

Link to Wikipedia page with overview.

The first(ICC 2.1A) is easy as several packages (e.g. "irr", "rel", "psysch") support this:

Two-way random, single measures, absolute agreement (ICC 2.1A)

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


But I am unsure about how to calculate the Two-way random, single measures, consistency. I read the package helpfiles as if the packages support Two-way mixed, single measures, consistency (ICC 3.1C), but not 2.1C.

That is, I think the below code gives me ICC 3.1C and not 2.1C

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


Can anyone help me either find a package that calculates Two-way random, single measures, consistency or alternatively guide me on how to calculate it using a mixed model.

• Wiki link is dead. Could you update it? Aug 15 '18 at 7:17
• In irr icc calculates conformance by default. You can change it by using type parameter. Aug 15 '18 at 7:37
• How would your code look if you wanted to calculate ICC2.1, consistency? I think icc(ratings, model = c("twoway"),type = c("consistency"), unit = c("single"), r0 = 0, conf.level = 0.95) will give 3.1, consistency, but maybe I am mistaken. Aug 15 '18 at 7:53
• According to stats.stackexchange.com/questions/258546/… the numerical result of 2,1 and 3,1 is the same. Aug 15 '18 at 8:02
• Yes, I think you are right. quoteing straight from the McGraw and Wong article: "Not only are ICC calculation formulas the same for random and mixed effect models, so too are the confidence intervals and test statistics". It seems weird to me though that the the two different ICC's can be interpreted so differently given that their numerical result will always be the same. Aug 15 '18 at 9:33

## 1 Answer

According to Which inter-rater equation should I use; ICC(2,1) or ICC(3,1)? and, as you pointed out, the McGraw and Wong article the results of ICC(2,1) and ICC(3,1) are the same. So the following code that you mentioned will give you ICC(2,1) and ICC(3,1) consistency:

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