Interpretation of intrinsic and extrinsic structural relations by path analysis: Theory and applications to assortative mating

The theory of path analysis is extended by considering a multivariate system of correlations from a dual perspective. Intrinsic factors exert a unidirectional influence on both the variance and covariance of dependent factors. In contrast, extrinsic factors have a bidirectional influence on the covariance structure of both antecedent and dependent factors and do not influence intrinsic variability. The mathematical model assumes a formally complete linear system of unitary factors. A coefficient is defined to quantify the influence of adventitious associations and is called a copath. Copaths are compared to path coefficients and to correlations due to common antecedents. The chain properties of these coefficients are derived along with a general formula and computational algorithm. The method is illustrated for multifactorial inheritance in extended pedigrees in the presence of different types of assortative mating.