Selection methods

The sixteen selection methods samplyr ships, what each one requires, and how registered methods extend the set. draw() chooses among them with its method argument.

Details

Sixteen methods are built in, in three families: equal probability, PPS (probability proportional to size, all requiring mos), and balanced.

Method	Replacement	Size	`mos`	Other input	Notes
`srswor`	Without	Fixed	-	-	The default. Standard SRS
`srswr`	With	Fixed	-	-	Allows duplicates
`systematic`	Without	Fixed	-	-	Periodic selection
`bernoulli`	Without	Random	-	`prn`	Independent trial per unit
`pps_systematic`	Without	Fixed	Required	-	Simple, some bias
`pps_brewer`	Without	Fixed	Required	-	Fast, joint prob > 0
`pps_cps`	Without	Fixed	Required	-	Highest entropy, exact joint prob
`pps_sampford`	Without	Fixed	Required	-	Exact Sampford joint probabilities
`pps_poisson`	Without	Random	Required	`prn`	PPS analog of Bernoulli
`pps_sps`	Without	Fixed	Required	`prn`	Sequential Poisson
`pps_pareto`	Without	Fixed	Required	`prn`	Pareto sampling
`pps_multinomial`	With	Fixed	Required	-	Any hit count, Hansen-Hurwitz
`pps_chromy`	Min. repl.	Fixed	Required	-	SAS default PPS_SEQ
`cube`	Without	Fixed	Optional	`aux` optional	Deville & Tillé 2004
`lpm2`	Without	Fixed	Optional	`spread` required	Spatial spread
`scps`	Without	Fixed	Optional	`spread` required	Spatial spread

Every method takes either n or frac, except pps_cps, which requires n. With frac the size follows the round parameter (ceiling by default). The prn column marks the methods that accept permanent random numbers for coordination. It is always optional.

"Min. repl." is probability minimum replacement: pps_chromy draws a unit either \(\lfloor E \rfloor\) or \(\lceil E \rceil\) times, where \(E\) is its expected number of hits, so a unit is never hit more often than its size warrants.

Fixed vs random sample size

Where the table says Fixed, n is the realized sample size. Where it says Random, n is the expected size: it is converted to frac = n / N (with N the stratum or frame size) and the realized count varies around it.

For pps_poisson, the raw inclusion probabilities are computed as \(\pi_i = f \cdot x_i / \bar{x}\) where \(f\) is frac and \(x_i\) is the MOS value. Any \(\pi_i > 1\) is clipped to 1, so the expected sample size \(E[n] = \sum \min(\pi_i, 1)\) can be less than \(f \cdot N\) when large units dominate the MOS distribution. Use certainty_size or certainty_prop to handle these dominant units explicitly.

Declaring certainty units does more than remove them. The remainder is re-resolved over the reduced target and the reduced MOS total, so the surviving chances rise and the expectation returns to the target. That is a different design from the clipped one, not a repair of it.

This is not silent. execute() warns with class samplyr_warning_poisson_shortfall once per stage when a pool's resolved expectation falls more than 5% below what that pool could reach, naming the pools affected and how many chances were clipped. The comparison is against the reachable target rather than the request: a pool asked for more units than it holds has already had its target reduced by the population, which samplyr_warning_nominal_cap reports, and only the further reduction that saturation caused is charged here. A design reduced both ways gets both warnings.

The shortfall is a gap between the nominal and realized design, not a bias. Horvitz-Thompson estimates from a saturated Poisson design remain unbiased, because the weights are the reciprocals of the resolved probabilities.

When an allocation method is set in stratify_by() (equal, proportional, neyman, optimal, power), specify total sample size via n. Combining alloc with frac is not supported.

References

srswor, srswr, systematic, bernoulli, pps_systematic, pps_multinomial: Cochran, W.G. (1977). Sampling Techniques, 3rd ed. Wiley.

pps_brewer: Brewer, K.R.W. (1975). A simple procedure for sampling PPS WOR. Australian Journal of Statistics, 17(3), 166-172.

pps_cps: Hájek, J. (1964). Asymptotic theory of rejective sampling with varying probabilities from a finite population. Annals of Mathematical Statistics, 35(4), 1491-1523.

Chen, X.-H., Dempster, A.P. and Liu, J.S. (1994). Weighted finite population sampling to maximize entropy. Biometrika, 81(3), 457-469.

pps_poisson: Tillé, Y. (2006). Sampling Algorithms. Springer.

pps_sps: Ohlsson, E. (1998). Sequential Poisson sampling. Journal of Official Statistics, 14(2), 149-162.

pps_pareto: Rosén, B. (1997). Asymptotic theory for order sampling. Journal of Statistical Planning and Inference, 62(2), 135-158.

pps_chromy: Chromy, J.R. (1979). Sequential sample selection methods. Proceedings of the Survey Research Methods Section, ASA, 401-406.

balanced: Deville, J.-C. and Tillé, Y. (2004). Efficient balanced sampling: the cube method. Biometrika, 91(4), 893-912.

Chauvet, G. (2009). Stratified balanced sampling. Survey Methodology, 35(1), 115-119.

Details

Fixed vs random sample size

References

See also