Department of Statistics Unitmark
Dietrich College of Humanities and Social Sciences

Polyhedral Conditions for the Nonexistence of the MLE for Hierarchical Log-linear Models

Publication Date

May, 2006

Publication Type

Tech Report


Nick Eriksson, Stephen E. Fienberg, Alessandro Rinaldo and Seth Sullivant


We provide a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model. The MLE exists if and only if the observed margins lie in the relative interior of the marginal cone. Using this description, we give an algorithm for determining if the MLE exists. If the tree width is bounded, the algorithm runs in polynomial time. We also perform a computational study of the case of three random variables under the no three-factor effect model.