Successive Difference Replication Variance Estimation in Two-Phase Sampling

Abstract

Successive difference replication (SDR) is a method of variance estimation under systematic sampling. The method has been used at the U.S. Census Bureau for important studies, including the Current Population Survey and the American Community Survey. The statistical properties of SDR are evaluated in the context of other variance estimators applicable to single-phase systematic sampling. A simulation study is conducted to compare the behavior of SDR and balanced repeated replication (BRR) under various choices of their respective tuning constants. Further, SDR has been used to estimate variances in a two-phase setting, such as the National Survey of College Graduates (NSCG), a subsample of the American Community Survey (ACS). We study properties of a two-phase SDR variance estimator using a phase-one sample of ACS data and repeated phase-two samples from the ACS following the NSCG design. The estimator accounts for systematic sampling in phase one and stratified sampling in phase two. The estimator is conservative for some NSCG variables because the NSCG uses not only explicit stratification on some ACS variables but also systematic sampling within strata after sorting on additional ACS variables. The simulation results suggest that the two-phase SDR variance estimator, with an appropriate adjustment to account for the systematic sampling in phase two, performs well in this context of subsampling the NSCG from the ACS sample.