Properties of alternative estimators of familial correlations under variable sibship size

Selected distributional properties of a variety of estimators of familial correlations (spouse, parent-child, and sibling) were investigated numerically, focusing particularly on sibling correlations under variable sibship size. Maximum likelihood estimators were evaluated for each of the three familial relationships. An additional parent-offspring estimator was studied using a parent-mid offspring estimate pooled over variable sibship size. For sibling intraclass correlations, three estimators based on analysis of variance and three pairwise estimators using different weighting functions for variable sibship sizes were investigated. Correlations were estimated from data simulated under eight sampling conditions (each replicated 1,000 times) using two sets of true parameter values, moderate and large sample sizes, and normal versus highly non-normal sample distributions of data. The estimators are nearly unbiased and efficient, but none of the sibling correlation estimators are normally distributed in small samples. Estimates from highly non-normal data are nearly unbiased but are less efficient than those from normal data.