  We express the maximum likelihood (ML) degrees of a family toric varieties in
terms of Mobius invariants of matroids. The family of interest are those
parametrized by monomial maps given by Lawrence lifts of totally unimodular
matrices with even circuits. Specifying these matrices to be vertex-edge
incidence matrices of bipartite graphs gives the ML degrees of some
hierarchical models and three dimensional quasi-independence models. Included
in this list are the no-three-way interaction models with one binary random
variable, for which, we give closed formulae.
