Multivariate path analysis of familial resemblance

A method is presented for applying path analysis to general multivariate models of familial resemblance. In path models formulated using this approach, variables are defined as column vectors, path coefficients are defined as matrices of path coefficients, and correlations are defined as matrices of correlations. By applying a few simple rules for multivariate path analysis, general multivariate expected correlations can be derived from a path diagram which is essentially as simple as a univariate diagram and which can be used to analyze any number of variables. Multivariate expected correlations for three models of familial resemblance are derived, with particular attention given to the modeling of assortative mating: nuclear families with a phenotypic homogamy model of assortative mating, nuclear families with a social homogamy model of assortative mating, and twins and their parents with phenotypic homogamy. These models are applicable to many of the types of studies commonly undertaken in genetic epidemiology. The simplicity of the technique facilitates analyses of the etiology of variation and covariation among variables measured in such studies.