Delta path methods for modeling the effects of multiple selective associations in adoption designs

In analyses of family data, multiple direct association processes can be modeled by the use of delta path methods derived by Van Eerdewegh (1982), especially the transitivity principle. The method is described for the case of an adoption study involving potential selective matching of adopting parents to two sets of biological parents of adopted offspring in the presence of assortative mating for both wed and unwed couples. Second- and third-order delta paths may be derived by application of the transitivity principle, and these higher-order paths are very convenient in formulating expectations that are due to direct and indirect association processes. Expectations are derived for resemblance among all adults in this three-couple adoption system; examples are given also for deriving parent-offspring expectations to illustrate the general use of higher-order delta paths in structural models of familial resemblance. Matrix notation is employed in order to facilitate the application of the methods in developmental and/or multivariate models.