Maximum likelihood degree of three-way independence models

In algebraic statistics, three-way independence models arise from scaled toric varieties whose lattice polytope is the product of three simplices.

Their ML degree coincides with the signed Euler characteristic of a hypersurface in the torus. It deviates from its generic value if and only if the given scaling vector lies in the vanishing locus of the principal A-determinant. The question arises: how does the intersection of components of this locus influence the Euler characteristic and ML degree? For comparison, for two-way independence models, the combination of vanishing factors completely determines the ML degree. Based on the paper "The Euler Stratification for P1xP1xPn".