Compound regressive models for family data

The regressive models for the analysis of family data are extended to include cases in which the within-sibship covariation may exceed that implied by the class A regressive model, but for which birth order is not required. In addition to specified major genes, if any, and common parental phenotypes, the excess within-sibship covariation may come from a common cumulative risk from unspecified factors such as a shared environment, and other genes. The within-sibship cumulative risk has a probability distribution in the population. The sib-sib correlation (more generally within-sibship statistical dependence) is equal for all pairs within a given sibship. The compound regressive model is thus a version of the class D regressive model with the property of within-sibship interchangeability. The work is motivated here by comparing and contrasting the Elston-Stewart algorithm and the Morton-MacLean algorithm for the mixed model of inheritance. This points the way to derive practical algorithms for the compound regressive models proposed, with easy extensions to pedigrees of arbitrary structure, and to multilocus problems.