Small area random effects models for capture/recapture methods with applications to estimating coverage error in the...

The synthetic estimation approach currently in use for estimating net coverage error in the U.S. Census is evaluated using random effects models. The synthetic estimates from the 2000 Accuracy and Coverage Evaluation (ACE) Revision II are evaluated in two parts. First, a model is used, which produces the synthetic estimate components and, second, the model is enlarged to include random effects at the small area level. Retaining all the fixed effects that characterize the synthetic model produces an extremely large, saturated random effects model. Hence, we selectively reduce the random effects model with an aim towards keeping all fixed effects in order to fairly evaluate the synthetic model. A super-population model is used for the bivariate outcome of erroneous enumeration rate and census omission rate. Both these outcomes were previously estimated using the current synthetic estimation approach. A major hurdle in this project was the development of defensible input data for the small areas due to the large number of effects in the synthetic model, which render simple design-based estimates for small areas crossed with post-strata, mostly, unusable. For this initial approach, the small areas were the 540 local census offices. Bayesian methods are employed to evaluate these models. The advantage of this model is that it can evaluate a key assumption about the homogeneity of rates within a post-stratum and if the assumption holds, then this model reduces to the current synthetic model.