sondage: Fast Survey Sampling Algorithms

Fast implementations of survey sampling algorithms for single-stage probability sampling from finite populations. Provides equal probability methods (simple random sampling, systematic, Bernoulli), unequal probability methods (conditional Poisson / maximum entropy, Brewer, systematic PPS, Pareto piPS, sequential Poisson, Poisson, Chromy's minimum replacement, multinomial), and balanced sampling via the cube method. All sampling functions return design objects carrying sample indices, inclusion probabilities, and design metadata. Generics compute joint inclusion probabilities, pairwise expectations, and sampling covariances for variance estimation. Mostly based on algorithms from Tille (2006, doi:10.1007/0-387-34240-0 ).

Unequal Probability Sampling

unequal_prob_wor() - Without replacement: CPS (maximum entropy), Brewer, systematic PPS, Poisson, SPS (sequential Poisson), Pareto
unequal_prob_wr() - With replacement: Chromy (minimum replacement), multinomial PPS

Equal Probability Sampling

equal_prob_wor() - Without replacement: SRS, systematic, Bernoulli (random size)
equal_prob_wr() - With replacement: SRS

Balanced Sampling

balanced_wor() - Cube method (Deville & Tille, 2004) for balanced sampling with unequal probabilities, with optional stratification (Chauvet & Tille, 2006)

Design Queries

All sampling functions return objects of class "sondage_sample". Use these generics to query the design:

inclusion_prob() - First-order inclusion probabilities
expected_hits() - Expected number of selections (WR)
joint_inclusion_prob() - Joint inclusion probabilities (WOR)
joint_expected_hits() - Pairwise expectations (WR)
sampling_cov() - Sampling covariance matrix

For without-replacement designs, the stored pik vector is the design-defining target inclusion probability vector. For methods with exact first-order guarantees, this equals the true first-order inclusion probabilities. For order-sampling methods such as sequential Poisson ("sps") and Pareto ("pareto"), the true finite-population first-order inclusion probabilities are only approximately equal to the stored target vector.

Utilities

inclusion_prob() - Compute inclusion probabilities from size measures
expected_hits() - Compute expected hits from size measures

References

Tille, Y. (2006). Sampling Algorithms. Springer Series in Statistics.

Chromy, J.R. (2009). Some generalizations of the Horvitz-Thompson estimator. Memorial JSM.

Author

Maintainer: Ahmadou Dicko mail@ahmadoudicko.com (ORCID)

Other contributors:

Thomas Lumley t.lumley@auckland.ac.nz [contributor]