Date of Award
Doctor of Philosophy
A unified noniterative 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. Subsequently, a Monte Carlo study is carried out to examine the asymptotic and small sample properties of these estimators under different weighting schemes. Also, several methods for constructing confidence intervals about the interclass correlation parameter are discussed, and the effectiveness of these methods is evaluated by Monte Carlo simulation.;It is recommended that for family studies, the individual-weighted estimator be used as a point estimator of interclass correlations and the method based upon a modification of Fisher's Z-transformation be used for interval estimation. In addition, it is recommended that the weighted pairwise estimator using the proposed weighting scheme replace the analysis of variance estimator in the estimation of intraclass correlations.;Although the focus of this dissertation 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.
Eliasziw, Michael, "Contributions To The Analysis Of Familial Data" (1989). Digitized Theses. 1831.