Intraclass Correlation Coefficients (ICC) with the irrICC Package"

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irrICC is an R package that provides several functions for calculating various Intraclass Correlation Coefficients (ICC). This package follows closely the general framework of inter-rater and intra-rater reliability presented by Gwet (2014).

All input datasets to be used with this package must contain a mandatory "Target" column of all subjects that were rated, and 2 or more columns "Rater1", "Rater2", .... showing the ratings assigned to the subjects. The Target variable mus represent the first column of the data frame, and every other column is assumed to contained ratings from a rater. Note that all ratings must be numeric values for the ICC to be calculated. For example, here is a dataset "iccdata1" that is included in this package:


The first column "Taget" (the name Target can be replaced with any other name you like) contains subject identifiers, while J1, J2, J3, J4 are the 4 raters (referred to here as Judges) and the ratings they assigned to the subjects. You will notice that the Target column contains duplicates, indicating that some subjects were rated multiple times. Moreover, none of these judges rated all subjects as seen by the presencce of missing ratings identified with the symbol NA.

Two other datasets, iccdata2, and iccdata3 come with the package for you to experiment with. Even if your data frame contains several variuables, note that only the Target and the Rater columns must be supplied as parameters to the functions. For example the iccdata2 data frame contains a variable named Group, which indicates the specific group each Target is categorized. It must be excluded from the input dataset as follows: iccdata2[,2:6].


Computing various ICC values

To determine what function you need, you must first have a statistical description of experimental data. There are essentially 3 statistical models recommended in the literature for describing quantitative inter-rater reliability data. These are commonly refer to as model 1, model 2 and model 3.

Calculating the ICC under Model 1A is done as follows:


It follows that the inter-rater reliability is given by r round(icc1a.fn(iccdata1)$icc1a,3), the first 2 output statistics being the subject variance component r round(icc1a.fn(iccdata1)$sig2s,3) and error variance component r round(icc1a.fn(iccdata1)$sig2e,3) respectively. You may see a description of the other statistics from the function's documentation.

The ICC under Model 1B is calculated as follows:


It follows that the intra-rater reliability is given by r round(icc1b.fn(iccdata1)$icc1b,3), the first 2 output statistics being the rater variance component r round(icc1b.fn(iccdata1)$sig2r,3) and error variance component r round(icc1b.fn(iccdata1)$sig2e,3) respectively. A description of the other statistics can be found in the function's documentation.

Calculating the ICC from the iccdata1 dataset (included in this package) and under the assumption of Model 2 with interaction is done as follows:


This function produces 2 intraclass correlation coefficients icc2r and icc2a. While iccr represents the inter-rater reliability estimated to be r round(icc2.inter.fn(iccdata1)$icc2r,3) , icc2a represents the intra-rater reliability estimated at r round(icc2.inter.fn(iccdata1)$icc2a,3). The first 3 output statistics are respectively the the subject, rater, and interaction variance components.

The ICC calculation with the iccdata1 dataset and under the assumption of Model 2 without interaction is done as follows:


The 2 intraclass correlation coefficients have now become icc2r=r round(icc2.nointer.fn(iccdata1)$icc2r,3) and icc2a=r round(icc2.nointer.fn(iccdata1)$icc2a,3). That is the estimated inter-rater reliability slightly went up while the intra-rater reliability coefficient slightly went down.


Here, the 2 intraclass correlation coefficients are given by icc2r = r round(icc3.inter.fn(iccdata1)$icc2r,3) and icc2a = r round(icc3.inter.fn(iccdata1)$icc2a,3). The estimated inter-rater reliability went up substantially while the intra-rater reliability coefficient went down substantially compared to Model 2 with interaction.
Assuming Model 3 without interaction, the same coefficients are calculated as follows:


It follows that the 2 ICCs are given by icc2r = r round(icc3.nointer.fn(iccdata1)$icc2r,3) and icc2a = r round(icc3.nointer.fn(iccdata1)$icc2a,3). As usual, the omission of an interaction factor leads to a slight increase in inter-rater reliability and a slight descrease in intra-rater reliability. In this case, both become identical.


  1. Gwet, K.L. (2014, ISBN:978-0970806284). "Handbook of Inter-Rater Reliability," 4th Edition. Advanced Analytics, LLC

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irrICC documentation built on Sept. 23, 2019, 5:05 p.m.