Estimation of the interclass correlation coefficient

Abstract

SUMMARY A noniterative method for estimating the interclass correlation coefficient is derived from the technique of weighted sums of squares. The asymptotic variance of this estimator is derived under the assumption of normality. Through extensive Monte Carlo simulations, the sample variance of this estimator is found not to differ greatly from that of the maximum likelihood estimator. An important problem in genetics is the estimation of the degree of resemblance between a mother and her children as measured by the interclass correlation coefficient. Because parents produce differing numbers of offspring during their reproductive period, the maximum likelihood estimation of the interclass correlation presents computational difficulties requiring an iterative solution. Therefore, a number of noniterative estimators have been proposed in the literature. These estimators will be shown to be associated with special cases of the generalized estimator derived from the weighted sums of squares of measurements on parents and offspring. Because our purpose is to provide a comprehensive approach to the noniterative point and interval estimation problems for the interclass correlation coefficient, the asymptotic variance of the proposed estimator is derived under the assumption of normality. Moreover, the sample variances of two special cases of the proposed estimator are compared to that of the maximum likelihood estimator through Monte Carlo simulations. By a theoretical argument, it is shown that the estimator proposed by Srivastava (1984) has a uniformly smaller asymptotic variance than the ensemble estimator proposed by Rosner, Donner & Hennekens (1977). Smith (1957) used the weighted sums-of-squares approach for the estimation problem concerning the intraclass correlation coefficient which measures the degree to which siblings resemble one another. Our results together with those of Smith (1957) provide a unified approach to estimation problems concerning familial correlations among a parent and offspring.