Package 'prnsamplr'

Permanent Random Number Sampling in R

Description

This package provides two functions for drawing stratified PRN-assisted samples: srs and pps. The former – simple random sampling – assumes that each unit $k$ in a given stratum $h$ is equally likely to be sampled, with inclusion probability

$\pi_k = \frac{n_h}{N_h}$

for each stratum $h$. The function then samples the $n_h$ elements with the smallest PRN's, for each stratum $h$.

The latter – Pareto $\pi ps$ sampling – assumes that large units are more likely to be sampled than small units. The function approximates this unknown inclusion probability as

$\lambda_k = n_h \frac{x_k}{\sum_{i=1}^{n_h} x_i},$

where $x_k$ is a size measure, and samples the $n_h$ elements with the smallest values of

$Q_k = \frac{PRN_k(1 - \lambda_k)}{\lambda_k(1 - PRN_k)},$

for each stratum $h$.

These two functions can be run standalone or via the wrapper function samp. Input to the functions is the sampling frame, stratification information and PRN's given as variables on the frame, and in the case for pps also a size measure given as variable on the frame. Output is a copy of the sampling frame containing sampling information, and in the case for pps also containing $\lambda$ and $Q$.

Provided is also a function transformprn via which it is possible to select where to start counting and in which direction when enumerating the PRN's in the sampling routines. This is done by specifying starting point and direction to transformprn and then calling srs or pps on its output.

Finally, an example dataset is provided that can be used to illustrate the functionality of the package.

Author(s)

Maintainer: Kira Coder Gylling [email protected] (ORCID)

References

Lindblom, A. (2014). "On Precision in Estimates of Change over Time where Samples are Positively Coordinated by Permanent Random Numbers." Journal of Official Statistics, vol.30, no.4, 2014, pp.773-785. https://doi.org/10.2478/jos-2014-0047.

See Also

srs, pps, samp, transformprn, ExampleData

Examples

dfSRS <- srs(
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands
)

dfPPS <- pps(
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands,
  size = ~sizeM
)

dfPRN <- transformprn(
  frame = ExampleData,
  prn = ~rands,
  direction = "U",
  start = 0.2
)

---

ExampleData

Description

Artificial dataset to be used with samp and transformprn.

Usage

ExampleData

Format

## 'ExampleData'

A data frame with 40,000 rows and 6 columns:

stratum

a character vector

id

a numeric vector

npopul

a numeric vector

nsample

a numeric vector

rands

a numeric vector

sizeM

a numeric vector

Source

Ad-hoc simulation in base R.

See Also

prnsamplr, samp, srs, pps, transformprn

---

Stratified probability-proportional-to-size sampling

Description

Stratified probability-proportional-to-size (Pareto PiPS) sampling using permanent random numbers. Can also be used for non-stratified Pareto PiPS using a dummy stratum taking the same value for each object.

Usage

pps(frame, stratid, nsamp, prn, size)

Arguments

frame	Data frame (or data.table or tibble) containing the elements to sample from.
stratid	Variable in frame containing the strata.
nsamp	Variable in frame containing the sample sizes.
prn	Variable in frame containing the permanent random numbers.
size	Variable in frame containing the size measure.

Value

A copy of the input sampling frame together with the boolean variable sampled, indicating sample inclusion, as well as a numeric variable lambda containing the estimated first-order inclusion probabilities and the numeric variable

$Q = \frac{prn(1 - lambda)}{lambda(1 - prn)}$

that determines which elements are sampled.

See Also

prnsamplr, samp, srs, transformprn, ExampleData

Examples

dfOut <- pps(
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands,
  size = ~sizeM
)

---

Stratified permanent random number sampling

Description

Wrapper for stratified simple random sampling (SRS) and probability-proportional-to-size (PPS) sampling using permanent random numbers. Can also be used for non-stratified sampling using a dummy stratum taking the same value for each object.

Usage

samp(method, frame, ...)

Arguments

method	pps or srs.
frame	Data frame (or data.table or tibble) containing the elements to sample from.
...	Further method-specific arguments.

Value

A copy of the input data frame together with the boolean variable sampled, as well as the numeric variables lambda and Q when pps is used.

See Also

prnsamplr, srs, pps, transformprn, ExampleData

Examples

dfOut <- samp(
  method = pps,
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands,
  size = ~sizeM
)

dfOut <- samp(
  method = srs,
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands
)

---

Stratified simple random sampling

Description

Stratified simple random sampling (SRS) using permanent random numbers. Can also be used for non-stratified SRS using a dummy stratum taking the same value for each object.

Usage

srs(frame, stratid, nsamp, prn)

Arguments

frame	Data frame (or data.table or tibble) containing the elements to sample from.
stratid	Variable in frame containing the strata.
nsamp	Variable in frame containing the sample sizes.
prn	Variable in frame containing the permanent random numbers.

Value

A copy of the input sampling frame together with the boolean variable sampled, indicating sample inclusion.

See Also

prnsamplr, samp, pps, transformprn, ExampleData

Examples

dfOut <- srs(
  frame = ExampleData,
  nsamp = ~nsample,
  stratid = ~stratum,
  prn = ~rands
)

---

Permanent random number transformation

Description

Transformation of the permanent random numbers used in the sampling procedure, to control the overlap between samples, and thus control the sample coordination. The method used is specified in Lindblom and Teterukovsky (2007).

Usage

transformprn(frame, prn, direction, start)

Arguments

frame	Data frame (or data.table or tibble) containing the elements to sample from.
prn	Variable in frame containing the permanent random numbers.
direction	Direction for the enumeration. "U" or "R" for upwards, or equivalently to the right on the real-number line. "D" or "L" for downwards, or equivalently to the left on the real-number line.
start	Starting point for the transformation. For SRS this corresponds to the point at which one wants to start sampling.

Value

A copy of the input data frame with the permanent random numbers transformed according to specification, along with the numeric variable prn.old containing the non-transformed permanent random numbers.

References

Lindblom, A. and Teterukovsky, A. (2007). "Coordination of Stratified Pareto pps Samples and Stratified Simple Random Samples at Statistics Sweden." In Papers presented at the ICES-III, June 18-21, 2007, Montreal, Quebec, Canada.

See Also

prnsamplr, samp, srs, pps, ExampleData

Examples

dfOut <- transformprn(
  frame = ExampleData,
  prn = ~rands,
  direction = "U",
  start = 0.2
)

---