On the estimation and testing of interclass correlations: the general case of multiple replicates for each variable.

Methods have recently been developed for the estimation and testing of mother-child correlations. In this report, these methods are extended to the general case of assessing interclass correlations where multiple replicates are allowed for each of the two classes of individuals under consideration. An algorithm is presented for obtaining the maximal likelihood estimator and an asymptotic test of significance is provided. In addition, a computationally convenient significance test is derived based on the pairwise estimator whereby one estimates the effective number of degrees of freedom in a family as a function of the number of replicates and the estimated intraclass correlation for each of the two types of individuals and sums up the effective degrees of freedom over all families in the sample. These methods are shown to be applicable to more general situations than the analysis of familial data, including the assessment of correlations between two variables measured at one point in time or the same variable measured at two points in time.