Multigraph Representations of Hierarchical Loglinear Models
We introduce a notion of generator multigraph as an alternative to interaction graphs for the study of hierarchical loglinear models. Generator multigraphs are defined directly from the generator class of the model and are shown to be natural for recognizing decomposable models, obtaining maximum likelihood estimators, and finding conditional independencies in a model. The graph theory involved focuses on maximum spanning trees and edge cutsets (rather than on chordal graphs and minimal vertex separators as with interaction graphs).
Khamis, H. J.,
& McKee, T. A.
(1996). Multigraph Representations of Hierarchical Loglinear Models. Journal of Statistical Planning and Inference, 53 (1), 63-74.