The intraclass correlation coefficient: distribution-free definition and test

A definition of the intraclass correlation coefficient is given on the basis of a general class of random effect model. The conventional intraclass correlation coefficient and the intracluster correlation coefficient for binary data are both particular cases of the generalized coefficient. We derive the score test for the hypothesis of null intraclass correlation in the exponential family. The statistic does not depend on the particular distribution in this family and is related to the pairwise correlation coefficient. The test can be adjusted for explanatory variables.