CPS ASEC sampling variances are not constant over all counties. We avoid giving observations with a great deal of uncertainty (larger variances) the same influence on the regression as observations with less uncertainty (smaller variances) by, in effect, weighting each observation by the inverse of its variance. Representing this uncertainty requires recognizing that it arises from two sources:
To estimate the two components of variance, we model them as having different forms. We model the sampling error variance to depend on the sample size and on the proportion insured. The lack-of-fit component, on the other hand, is modeled as constant across all counties. Then the components can be distinguished using our Bayesian estimation method.