  This paper initiates a study of Hodge integrals on moduli spaces of
pseudostable curves. We prove an explicit comparison formula that allows one to
effectively compute any pseudostable Hodge integral in terms of intersection
numbers on moduli spaces of stable curves, and we use this comparison to prove
that pseudostable Hodge integrals are equal to their stable counterparts when
they are linear in lambda classes, but not when they are nonlinear. This
suggests that pseudostable Gromov-Witten invariants are equal to usual
Gromov-Witten invariants for target curves, but not for higher-dimensional
target varieties.
