Fleiss Kappa Torchmetrics

A torchmetrics (Pytorch) implementation of Fleiss Kappa for interrater agreement.

Fleiss Kappa

While Cohens Kappa can only measure the inter-rater agreement of 2 raters, Fleiss Kappa is a measure of inter-rater agreement for an arbitrary number of raters and classes.

Implementation

This implementation is meant to be used for Pytorch. It follows the torchmetrics guidelines and inherits from torchmetrics.Metric. The metric can be importet from fleiss_kappa.py.

Tests

My torchmetrics implementation is tested against the statsmodels package. Both implementations yield the same results up to a tolerance of 0.0005. The following test protocol was used:

1 A correlation matrix is sampled for the raters. 2 Predictive logits are sampled from a Multivariate normal distribution using this covariance matrix. 3 The torchmetric implementation is computed as implemented from the logits. 4 The logits are transformed into count data (counts of raters per class for each participant). 5 The statsmodels implementation is used on the count data. 6 Both metric outputs are compared.

In 100k runs, with a tolerance of 0.0005, number of raters and classes varying between 2 and 20, rater variances between 0 and 1, and number of subjects varying between 10 and 100, no errors were found.

Tests conducted on

• CPU
• MacOS 11.4
• Python 3.9.2
• Pytorch 1.9.0
• Pytorch Lightning 1.3.8
• Numpy 1.20.2
• torchmetrics 0.4.1
• statsmodels 0.12.2

Contribute

I appreciate contributions.

References

• Wikipedia
• Fleiss, J. L. (1971) "Measuring nominal scale agreement among many raters." Psychological Bulletin, Vol. 76, No. 5 pp. 378–382