Interval estimation for the intraclass correlation in Dirichlet-multinomial data

When the underlying distribution is discrete with a limited number of categories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of large sample theory, this paper develops an asymptotic closed-form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category. This paper employs Monte Carlo simulation to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleading. We find that when the number of classes is greater than or equal to 20, the interval estimator proposed here can generally perform reasonably well in a variety of situations. This paper further notes that the proposed interval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to account for this case, as well as a discussion on the relationship between the intraclass correlation and a kappa-type measure defined here and on the limitation of the corresponding kappa-type estimator are given.