  We prove a family of factorization formulas for the combinatorial
Donaldson--Thomas invariant for an acyclic quiver. A quantum dilogarithm
identity due to Reineke, later interpreted by Rimanyi by counting codimensions
of quiver loci, gives two extremal cases of our formulation in the Dynkin case.
We establish our interpolating factorizations explicitly with a dimension
counting argument by defining certain stratifications of the space of
representations for the quiver and calculating Betti numbers in the
corresponding equivariant cohomology algebras.
