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Intraclass correlation coefficients

Highlights

  • Absolute agreement
  • Consistency of agreement
  • One- and two-way random-effects models
  • Two-way mixed-effects models
  • For individual and average measurements

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Stata's icc can measure absolute agreement and consistency of agreement.

Consider a dataset containing 24 ratings of 6 targets by 4 judges. Assume that a different set of four judges is used to rate each target so that we have a one-way random-effects model.

We can estimate the correlation of ratings made on the same targets by typing

. icc rating target

Intraclass correlations
One-way random-effects model
Absolute agreement

Random effects: target           Number of targets =         6
                                 Number of raters  =         4

rating ICC [95% Conf. Interval]
Individual .1657418 -.1329323 .7225601
Average .4427971 -.8844422 .9124154
F test that ICC=0.00: F(5.0, 18.0) = 1.79 Prob > F = 0.165 Note: ICCs estimate correlations between individual measurements and between average measurements made on the same target.

The correlation of measurements made on the same individual is 0.1657.

The correlation among mean ratings for each team of judges is 0.4428. The average ICC can be used when teams of different raters are used to rate a target. Teams of physicians are sometimes evaluated in this manner.

Now let's pretend the same team of judges rated each target. If the judges were drawn randomly from the population, then we would have a two-way random-effects model. We can estimate the correlations by typing

. icc rating target judge

Intraclass correlations
Two-way random-effects model
Absolute agreement

Random effects: target           Number of targets =         6
Random effects: judge            Number of raters  =         4

rating ICC [95% Conf. Interval]
Individual .2897638 .0187865 .7610844
Average .6200505 .0711368 .927232
F test that ICC=0.00: F(5.0, 15.0) = 11.03 Prob > F = 0.000 Note: ICCs estimate correlations between individual measurements and between average measurements made on the same target.

The correlation of measurements made on the same individual is 0.2898.

The correlation among mean team ratings with those that might be produced by another team is 0.6201.

Finally, suppose the four judges are the only judges of interest. Judge is now a fixed effect in the model, and we have a two-way mixed-effects model. We can obtain the correlations by typing

. icc rating target judge, mixed

Intraclass correlations
Two-way mixed-effects model
Consistency of agreement

Random effects: target           Number of targets =         6
 Fixed effects: judge            Number of raters  =         4

rating ICC [95% Conf. Interval]
Individual .7148407 .3424648 .9458583
Average .9093155 .6756747 .9858917
F test that ICC=0.00: F(5.0, 15.0) = 11.03 Prob > F = 0.000 Note: ICCs estimate correlations between individual measurements and between average measurements made on the same target.

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See the manual entry.

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