How does EI relate to the neighborhood model?

The neighborhood model was designed for the purpose of critiquing the Goodman model, and is not thought of as a plausible method of producing ecological inferences in its own right (see pp. 43-44). The neighborhood model's advantage is that it is in the class of models that are consistent with the method of bounds for each precinct and thus cannot be rejected solely from information in the aggregate data (this class of models is described on p. 191). As such, it can be seen as a special case of EI. Its disadvantage is its assumption that $\beta_i^b=\beta_i^w$ , which is of course appropriate in some cases and far off in others, but whichever it is it assumes the answer to the question being asked. A consequence of the neighborhood model assumption having no error term and supposedly holding exactly is that its standard errors are always zero, which is unreasonable. If, somewhat more reasonably, the neighborhood model assumption is approximately plausible for a particular application, then it is best to run EI with priors suitably adjusted to reflect this information. If priors are strong enough and not substantially contradicted by the likelihood, EI will give similar point estimates to the neighborhood model, but it will give more reasonable (nonzero) standard errors and confidence intervals for the precinct-level quantities.

Gary King 2006-09-13