The Census Bureau has implemented a new imputation program to enhance ACS estimates of the group quarters (GQ) population for small areas. The GQ imputation presents novel challenges for variance estimation, both because it is a mass imputation with roughly as much imputed data as sampled data, and because the GQ facilities being imputed to are not missing, but rather, not-in-sample.

In previous years, the ACS has implemented successive differences replication (SDR) to estimate variances (Fay and Train, 1995). We understood that naively applying SDR to data augmented by imputation, i.e., treating the imputed records as sample, would lead to a serious underestimation of variances. Hence, starting with the 2011 1-year, 2009-2011 3-year, and 2007-2011 5-year ACS estimates, the ACS program has implemented a method that applies inflation factors to the replicates weights of GQ persons (Asiala and Castro, 2012). While this method is better than the naive variance estimator, it is crude, with the same inflation factor used for all characteristics and for the entire state. A better method would reflect the variances by characteristic and for substate geographies. It was the search for such improvements which was the impetus for exploring reimputation methods.

In this study we assessed the feasibility and soundness of using random groups with reimputation to estimate variances for the 2013 data-year products. We note that ACS GQ data lends itself to the formation of random groups, and thus to reimputation with random groups. We also evaluated the previously used SDR methodology, and the current methodology for estimating variances of the GQ population, SDR with inflation factors. We compared the variances for SDR with inflation factors and random groups with reimputation methods for the 2012 1-year ACS estimates for states and for larger counties. We used standard errors obtained through simulations of the ACS GQ population sampling as a benchmark to compare the alternative methods.