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library(irrCAC)

Installation

devtools::install_github(“kgwet/irrCAC”)

Abstract

The irrCAC is an R package that provides several functions for calculating various chance-corrected agreement coefficients. This package closely follows the general framework of inter-rater reliability assessment presented by Gwet (2014). A similar package was developed for STATA users by Klein (2018).

The functions included in this package can handle 3 types of input data: (1) the contingency table, (2) the distribution of raters by subject and by category, (3) the raw data, which is essentially a plain dataset where each row represents a subject and each column, the ratings associated with one rater. The list of all datasets containined in this package can be listed as follows:

  data(package="irrCAC")

Computing Agreement Coefficients

Computing agreement Coefficients from Contingency tables

cont3x3abstractors is one of 2 datasets included in this package and that contain rating data from 2 raters organized in the form of a contingency table. The following r script shows how to compute Cohen’s kappa, Scott’s Pi, Gwet’s AC1, Brennan-Prediger, Krippendorff’s alpha, and the percent agreement coefficients from this dataset.

  cont3x3abstractors
#>         Ectopic AIU NIU
#> Ectopic      13   0   0
#> AIU           0  20   7
#> NIU           0   4  56
  kappa2.table(cont3x3abstractors)
#>      coeff.name coeff.val   coeff.se     coeff.ci coeff.pval
#> 1 Cohen's Kappa 0.7964094 0.05891072 (0.68,0.913)      0e+00
  scott2.table(cont3x3abstractors)
#>   coeff.name coeff.val   coeff.se      coeff.ci coeff.pval
#> 1 Scott's Pi 0.7962397 0.05905473 (0.679,0.913)      0e+00
  gwet.ac1.table(cont3x3abstractors)
#>   coeff.name coeff.val   coeff.se      coeff.ci coeff.pval
#> 1 Gwet's AC1 0.8493305 0.04321747 (0.764,0.935)      0e+00
  bp2.table(cont3x3abstractors)
#>         coeff.name coeff.val   coeff.se      coeff.ci coeff.pval
#> 1 Brennan-Prediger     0.835 0.04693346 (0.742,0.928)      0e+00
  krippen2.table(cont3x3abstractors)
#>             coeff.name coeff.val   coeff.se     coeff.ci coeff.pval
#> 1 Krippendorff's Alpha 0.7972585 0.05905473 (0.68,0.914)      0e+00
  pa2.table(cont3x3abstractors)
#>          coeff.name coeff.val   coeff.se      coeff.ci coeff.pval
#> 1 Percent Agreement      0.89 0.03128898 (0.828,0.952)      0e+00

Suppose that you only want to obtain Gwet’s AC1 coefficient, but don’t care about the associated precision measures such as the standard error, confidence intervals or p-values. You can accomplish this as follows:

  ac1 <- gwet.ac1.table(cont3x3abstractors)$coeff.val

Then use the variable ac1 to obtain AC1 = 0.849.

Another contingency table included in this package is named cont3x3abstractors. You may use it to experiment with the r functions listed above.

Computing agreement coefficients from the distribution of raters by subject & category

Included in this package is a small dataset named distrib.6raters, which contains the distribution of 6 raters by subject and category. Each row represents a subject (i.e. a psychiatric patient) and the number of raters (i.e. psychiatrists) who classified it into each category used in the inter-rater reliability study. Here is the dataset and how it can be used to compute the various agreement coefficients:

distrib.6raters
#>    Depression Personality.Disorder Schizophrenia Neurosis Other
#> 1           0                    0             0        6     0
#> 2           0                    3             0        0     3
#> 3           0                    1             4        0     1
#> 4           0                    0             0        0     6
#> 5           0                    3             0        3     0
#> 6           2                    0             4        0     0
#> 7           0                    0             4        0     2
#> 8           2                    0             3        1     0
#> 9           2                    0             0        4     0
#> 10          0                    0             0        0     6
#> 11          1                    0             0        5     0
#> 12          1                    1             0        4     0
#> 13          0                    3             3        0     0
#> 14          1                    0             0        5     0
#> 15          0                    2             0        3     1
gwet.ac1.dist(distrib.6raters)
#>   coeff.name     coeff     stderr      conf.int      p.value        pa
#> 1 Gwet's AC1 0.4448007 0.08418757 (0.264,0.625) 0.0001155927 0.5511111
#>          pe
#> 1 0.1914815
fleiss.kappa.dist(distrib.6raters)
#>      coeff.name     coeff     stderr     conf.int      p.value        pa
#> 1 Fleiss' Kappa 0.4139265 0.08119291 (0.24,0.588) 0.0001622724 0.5511111
#>          pe
#> 1 0.2340741
krippen.alpha.dist(distrib.6raters)
#>             coeff.name     coeff     stderr      conf.int      p.value
#> 1 Krippendorff's Alpha 0.4204384 0.08243228 (0.244,0.597) 0.0001615721
#>          pa        pe
#> 1 0.5560988 0.2340741
bp.coeff.dist(distrib.6raters)
#>         coeff.name     coeff     stderr      conf.int   p.value        pa
#> 1 Brennan-Prediger 0.4388889 0.08312142 (0.261,0.617) 0.0001163 0.5511111
#>    pe
#> 1 0.2

Once again, you can request a single value from these functions. To get only Krippendorff’s alpha coefficient without it’s precission measures, you may proceed as follows:

  alpha <- krippen.alpha.dist(distrib.6raters)$coeff

The newly-created alpha variable gives the coefficient α = 0.4204384.

Two additional datasets that represent ratings in the form of a distribution of raters by subject and by category, are included in this package. These datasets are cac.dist4cat and cac.dist4cat. Note that these 2 datasets contain more columns than needed to run the 4 functions presented in this section. Therefore, the columns associated with the response categories must be extracted from the original datasets before running the functions. For example, computing Gwet’s AC1 coefficient using the cac.dist4cat dataset should be done as follows:

  ac1 <- gwet.ac1.dist(cac.dist4cat[,2:4])$coeff

Note that the input dataset supplied to the function is cac.dist4cat[,2:4]. That is, only columns 2, 3, and 4 are extracted from the original datset and used as input data. We know from the value of the newly created variable that AC1 = 0.3518903.

Computing agreement coefficients from raw ratings

One example dataset of raw ratings included in this package is cac.raw4raters and looks like this:

  cac.raw4raters
#>    Rater1 Rater2 Rater3 Rater4
#> 1       1      1     NA      1
#> 2       2      2      3      2
#> 3       3      3      3      3
#> 4       3      3      3      3
#> 5       2      2      2      2
#> 6       1      2      3      4
#> 7       4      4      4      4
#> 8       1      1      2      1
#> 9       2      2      2      2
#> 10     NA      5      5      5
#> 11     NA     NA      1      1
#> 12     NA     NA      3     NA

As you can see, a dataset of raw ratings is merely a listing of ratings that the raters assigned to the subjects. Each row is associated with a single subject.Typically, the same subject would be rated by all or some of the raters. The dataset cac.raw4raters contains some missing ratings represented by the symbol NA, suggesting that some raters did not rate all subjects. As a matter of fact, in this particular case, no rater rated all subjects.

Here is you can compute the various agreement coefficients using the raw ratings:

pa.coeff.raw(cac.raw4raters)
#> $est
#>          coeff.name        pa pe coeff.val coeff.se  conf.int      p.value
#> 1 Percent Agreement 0.8181818  0 0.8181818  0.12561 (0.542,1) 4.345373e-05
#>       w.name
#> 1 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5
gwet.ac1.raw(cac.raw4raters)
#> $est
#>   coeff.name        pa        pe coeff.val coeff.se  conf.int     p.value
#> 1        AC1 0.8181818 0.1903212   0.77544  0.14295 (0.461,1) 0.000208721
#>       w.name
#> 1 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5
fleiss.kappa.raw(cac.raw4raters)
#> $est
#>      coeff.name        pa        pe coeff.val coeff.se  conf.int
#> 1 Fleiss' Kappa 0.8181818 0.2387153   0.76117  0.15302 (0.424,1)
#>       p.value     w.name
#> 1 0.000419173 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5
krippen.alpha.raw(cac.raw4raters)
#> $est
#>             coeff.name    pa   pe coeff.val coeff.se  conf.int
#> 1 Krippendorff's Alpha 0.805 0.24   0.74342  0.14557 (0.419,1)
#>        p.value     w.name
#> 1 0.0004594257 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5
conger.kappa.raw(cac.raw4raters)
#> $est
#>       coeff.name        pa        pe coeff.val coeff.se  conf.int
#> 1 Conger's Kappa 0.8181818 0.2334252   0.76282  0.14917 (0.435,1)
#>        p.value     w.name
#> 1 0.0003367066 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5
bp.coeff.raw(cac.raw4raters)
#> $est
#>         coeff.name        pa  pe coeff.val coeff.se  conf.int      p.value
#> 1 Brennan-Prediger 0.8181818 0.2   0.77273  0.14472 (0.454,1) 0.0002375609
#>       w.name
#> 1 unweighted
#> 
#> $weights
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    1    0    0    0    0
#> [2,]    0    1    0    0    0
#> [3,]    0    0    1    0    0
#> [4,]    0    0    0    1    0
#> [5,]    0    0    0    0    1
#> 
#> $categories
#> [1] 1 2 3 4 5

Most users of this package will only be interessted in the agreement coefficients and possibly in the related statistics such as the standard error and p-values. In this case, you should run these functions as follows (AC1 is used here as an example. Feel free to experiment with the other coefficients):

ac1 <- gwet.ac1.raw(cac.raw4raters)$est
ac1
#>   coeff.name        pa        pe coeff.val coeff.se  conf.int     p.value
#> 1        AC1 0.8181818 0.1903212   0.77544  0.14295 (0.461,1) 0.000208721
#>       w.name
#> 1 unweighted

You can even request only the AC1 coefficient estimate 0.77544. You will then proceed as follows:

ac1 <- gwet.ac1.raw(cac.raw4raters)$est
ac1$coeff.val
#> [1] 0.77544

References:

  1. Gwet, K.L. (2014, ISBN:978-0970806284). “Handbook of Inter-Rater Reliability,” 4th Edition. Advanced Analytics, LLC
  2. Klein, D. (2018) doi:https://doi.org/10.1177/1536867X1801800408. “Implementing a general framework for assessing interrater agreement in Stata,” The Stata Journal Volume 18, Number 4, pp. 871-901.

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Version

Install

install.packages('irrCAC')

Monthly Downloads

713

Version

1.0

License

GPL (>= 2)

Maintainer

Kilem Gwet

Last Published

September 23rd, 2019

Functions in irrCAC (1.0)

fleiss

Dataset describing Fleiss' Benchmarking Scale
distrib.6raters

Distribution of 6 psychiatrists by Subject/patient and diagnosis Category.
gwet.ac1.raw

Gwet's AC1/AC2 agreement coefficient among multiple raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
gwet.ac1.dist

Gwet's AC1/AC2 agreement coefficient among multiple raters (2, 3, +) when the input dataset is the distribution of raters by subject and category.
cont4x4diagnosis

Distribution of 223 Psychiatric Patients by Type of of Psychiatric Disorder and Diagnosis Method.
landis.koch

Dataset describing the Landis & Koch Benchmarking Scale
landis.koch.bf

Computing Landis-Koch Benchmark Scale Membership Probabilities
fleiss.bf

Computing Fleiss Benchmark Scale Membership Probabilities
krippen.alpha.dist

Krippendorff's agreement coefficient among multiple raters (2, 3, +) when the input dataset is the distribution of raters by subject and category.
kappa2.table

Kappa coefficient for 2 raters
altman.bf

Computing Altman's Benchmark Scale Membership Probabilities
gwet.ac1.table

Gwet's AC1/AC2 coefficient for 2 raters
cont3x3abstractors

Distribution of 100 pregnant women by pregnancy type and by abstractor.
identity.weights

Function for computing the Identity Weights
conger.kappa.raw

Conger's generalized kappa coefficient for an arbitrary number of raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
radical.weights

Function for computing the Radical Weights
krippen.alpha.raw

Krippendorff's alpha coefficient for an arbitrary number of raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
circular.weights

Function for computing the Circular Weights
krippen2.table

Krippendorff's Alpha coefficient for 2 raters
cac.raw5obser

Scores assigned by 5 observers to 20 experimental units.
cac.raw.gender

Rating Data from 4 Raters and 15 human Subjects, 9 of whom are female and 6 males.
cac.raw4raters

Rating Data from 4 Raters and 12 Subjects.
quadratic.weights

Function for computing the Quadratic Weights
pa2.table

Percent Agreement coefficient for 2 raters
ordinal.weights

Function for computing the Ordinal Weights
linear.weights

Function for computing the Linear Weights
trim

An r function for trimming leading and trealing blanks
ratio.weights

Function for computing the Ratio Weights
scott2.table

Scott's coefficient for 2 raters
fleiss.kappa.raw

Fleiss' generalized kappa among multiple raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
pa.coeff.dist

Percent agreement coefficient among multiple raters (2, 3, +) when the input dataset is the distribution of raters by subject and category.
fleiss.kappa.dist

Fleiss' agreement coefficient among multiple raters (2, 3, +) when the input dataset is the distribution of raters by subject and category.
pa.coeff.raw

Percent agreement among multiple raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
bp2.table

Brenann-Prediger coefficient for 2 raters
cac.raw.g1g2

Dataset of raw ratings from 4 Raters on 14 Subjects that belong to 2 groups named "G1" and "G2"
bp.coeff.raw

Brennan \& Prediger's (BP) agreement coefficient for an arbitrary number of raters (2, 3, +) when the input data represent the raw ratings reported for each subject and each rater.
cac.dist4cat

Distribution of 4 raters by Category and Subject - Subjects allocated in 2 groups A and B.
altman

Dataset describing the Altman's Benchmarking Scale
bipolar.weights

Function for computing the Bipolar Weights
bp.coeff.dist

Brennan-Prediger's agreement coefficient among multiple raters (2, 3, +) when the input dataset is the distribution of raters by subject and category.
cac.ben.gerry

Ratings of 12 units from 2 raters named Ben and Gerry
cac.dist.g1g2

Distribution of 4 raters by subject and by category, for 14 Subjects that belong to 2 groups "G1" and "G2"