Clustering measurements of obscured and unobscured quasars show that obscured quasars reside in more massive dark matter halos than their unobscured counterparts. These results are inconsistent with simple unified (torus) scenarios, but might be explained by models in which the distribution of obscuring material depends on Eddington ratio or galaxy stellar mass. We test these possibilities by constructing simple physical models to compare to observed AGN populations. We find that previously observed relationships between obscuration and Eddington ratio or stellar mass are not sufficient reproduce the observed quasar clustering results ($langle log M_{text{halo}}/M_{odot} rangle = 12.94 ^{+ 0.10}_{- 0.11}$ and $langle log M_{text{halo}}/M_{odot} rangle = 12.49 ^{+ 0.08}_{- 0.08}$ for obscured and unobscured populations, respectively) while maintaining the observed fraction of obscured quasars (30-65$%$). This work suggests that evolutionary models, in which obscuration evolves on the typical timescale for black hole growth, are necessary to understand the observed clustering of mid-IR selected quasars.