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Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative.
Francesco Innocenti1, Math Jjm Candel1, Frans Es Tan1
1Department of Methodology and Statistics, Care and Public Health Research Institute (CAPHRI), Maastricht University, Maastricht, the Netherlands.
For hierarchical populations, probability proportional to size cluster sampling is the most efficient two-stage sampling method. This approach optimizes sample sizes under budget constraints for accurate mean estimation.
Area of Science:
- Statistics
- Survey Methodology
Background:
- Estimating population means often involves hierarchical data structures.
- Two-stage sampling, selecting clusters then individuals, is logistically practical.
- Informative cluster sizes, related to outcome means, complicate sampling design.
Purpose of the Study:
- To compare the efficiency of different two-stage sampling designs.
- To determine optimal sample sizes for these designs under a budget.
- To recommend the most efficient sampling strategy for hierarchical populations.
Main Methods:
- Considered three two-stage sampling designs: probability proportional to size (PPS) cluster sampling, equal probability (EP) cluster sampling with fixed percentage, and EP cluster sampling with fixed number of individuals.
- Derived optimal sample sizes for each design under a budget constraint.
- Compared designs' efficiency against each other and simple random sampling.
Main Results:
- Probability proportional to size cluster sampling demonstrated superior efficiency.
- Optimal sample sizes were derived, balancing cost and precision.
- Maximin designs were developed to mitigate reliance on unknown parameters.
Conclusions:
- Probability proportional to size cluster sampling is recommended for hierarchical populations with informative cluster sizes.
- The derived methods provide a framework for efficient survey planning.
- Illustrative example applied to adolescent alcohol consumption survey planning.
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