1. Bayesian Multilevel Estimation with Poststratification: State-Level Estimates from National Polls
2. See Peress and Spirling (2010) for an alternative utility model that results in the same statistical model.
3. All of the code necessary to reproduce the results in this paper can be downloaded from the Dataverse as Bullock, Imai, and Shapiro (2011). The replication code also can be altered for applications to other studies.
4. Formally, the sign of the first derivative of equation (3) with respect to is the same as the sign of βj.
5. Formally, the randomization implies for all i and j, and hence, we have E(Yij (k) – Yij (0)) = E(Yij = Tij = k) – E(Yij | Tij = 0) for any k.