A generalized non‐iterative approach to the analysis of family data

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Abstract
A unified non-iterative approach to point and interval estimation of interclass and intraclass correlations is presented in the context of family studies where there may be more than one individual in each of two classes. The procedure involves a generalization of the Pearson product-moment correlation coefficient, where one permits different weights for the pairs of scores. Unlike the maximum likelihood approach, these estimators are not derived under the assumption of a particular parametric form nor do they require an iterative solution. The asymptotic distributions of the generalized product-moment estimator and of the maximum likelihood estimator are derived under the assumption of normality. Also, several methods for constructing confidence intervals about the interclass correlation parameter are outlined, and the effectiveness of these methods is evaluated by Monte Carlo simulation. Although the focus of this paper is on the analysis of familial data, the methods discussed are applicable to more general situations, including the assessment of correlations between any two variables where each variable is replicated a different number of times for each sample unit.