SUMMARY: Widely used probability-proportional-to-size (PPS) selection methods are not well adapted to circumstances requiring sample augmentation. Limitations include: (1) an inability to augment selections while maintaining PPS properties, (2) a failure to recognize changes in census stratum membership which result from sample augmentation, and (3) imprecise control over line item sample size. This paper presents a new method of PPS selection, a modified version of sieve sampling which overcomes these limitations. Simulations indicate the new method effectively maintains sampling stratum PPS properties in single- and multi-stage samples, appropriately recognizes changes in census stratum membership which result from sample augmentation, and provides precise control over line item sample sizes. In single-stage applications the method provides reliable control of sampling risk over varied tainting levels and error bunching patterns. Tightness and efficiency measures are comparable to randomized systematic sampling and superior to sieve sampling.
