VANISHING TETRAD DIFFERENCES AND MODEL STRUCTURE

The tetrad representation theorem, due to Spirtes, Glymour, and Scheines (1993), gives a graphical condition necessary and sufficient for the vanishing of an individual tetrad difference in a recursive path model with uncorrelated errors. In this paper, we generalize their result from individual tetrad differences to sets of tetrad differences of a certain form, and we simplify their proof. The generalization allows tighter constraints to be placed on the set of models compatible with given data and thereby facilitates the search for parsimonious models for large data sets.