Interval estimation for the intraclass correlation in Dirichlet-multinomial data

When the underlying distribution is discrete with a limited number of categ ories, methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use. On the basis of larg e sample theory, this paper develops an asymptotic closed-form interval est imate of the intraclass correlation for the case where there is a natural s core associated with each category. This paper employs Monte Carlo simulati on to demonstrate that when the underlying intraclass correlation is large, the traditional interval estimator which assumes normality can be misleadi ng. 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 int erval estimator is invariant with respect to a linear transformation. When the data are on a nominal scale, an extension of the proposed method to acc ount 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 li mitation of the corresponding kappa-type estimator are given.