Comparison of Two Weighting Schemes for Sampling with Minimal Replacement

• Activity Number: 104
• Type: Contributed
• Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Pedro J. Saavedra*+
• Companies: ORC Macro International, Inc.
• Keywords: two-stage sample ; estimator ; simulations ; sequential sampling

Abstract

In his 1979 paper on PPS sampling with minimal replacement (SMR) for multistage samples, Chromy developed an estimator based on the inverse of the expected number of times a PSU would be selected. This yields an unbiased Horvitz-Thompson estimator, which takes into account the sampling process at every stage. An alternative estimator also is used with SMR based on Stage 1 weights computed as the inverse of the PSU probabilities of selection. With this approach, the allocations at the second stage are taken as a given and not as the result of a probabilistic process at Stage 1. This is exactly the estimator most commonly used for sampling without replacement, and thus many statisticians may be more familiar with it than with the Chromy estimator. It is not clear whether the difference in terms of design effect is major. This study compares the design effect for the two estimators using real sampling frames with varying numbers of selected PSUs with and without perfect correspondence of the number of units per PSU and the size measure. Results indicate that which estimator performs better depends on the frame, the variables, and the measure of size.