JSM 2005 - Toronto

Abstract #303908

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Activity Number: 321
Type: Contributed
Date/Time: Tuesday, August 9, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Survey Research Methods
Abstract - #303908
Title: An Empirical Comparison of Efficiency between Optimization and Nonoptimization Probability Sampling of Two Units from a Stratum
Author(s): Sun-Woong Kim*+ and Steven G. Heeringa and Peter S. Solenberger
Companies: Dongguk University and University of Michigan and University of Michigan
Address: Jung Gu Pil Dong 3 Ga 26, Seoul, 100-715, South Korea
Keywords: Nonlinear Programming ; Linear Constraints ; Inclusion Probabilities ; IPPS Sampling
Abstract:

Survey samplers seek sampling designs providing the smaller variance and the more stable variance estimator for certain estimators of the population total. To achieve sample selections with these desirable properties, Kim, Heeringa, and Solenberger (2003, 2004) suggested several inclusion probability proportional to size sampling schemes. These optimization approaches use nonlinear programming (NLP) and are useful to select two units per stratum, as is done commonly in the primary stage of a multistage design. Their NLP approaches highly depend on linear constraints based on the inclusion probabilities. In this paper, we first introduce the relationships between the linear constraints and the variances or variance estimators for existing sampling strategies, such as probability proportional to size sampling with replacement and the methods of Brewer, Murthy, and Hanurav. Second, we examine the feasibility of NLP approaches related to those strategies for a set of natural populations. Finally, we compare the efficiency of the various estimators and variance estimators for those populations. We conclude that NLP approaches work well in comparison to the alternatives.

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