Package {SampleSelectR}

SampleSelectR: Randomly Select Samples for Various Probability-Based Methods

Description

Randomly select samples using simple random sampling (SRS), systematic sampling, and various probability proportional to size (PPS) methods, including systematic PPS and sequential PPS (i.e., Chromy's method). Also includes functionality to allocate sample sizes across strata using proportional, power, Neyman, and optimal allocation methods, and to select samples within strata. Designed to make survey sample design and selection reproducible, efficient, and transparent for survey statisticians and researchers. Sampling methods follow Kalton (1983) doi:10.4135/9781412984683 and Chromy (1979) http://www.asasrms.org/Proceedings/papers/1979_081.pdf.

Author(s)

Maintainer: Stephanie Zimmer sazimmer@rti.org

Authors:

• Stephanie Zimmer sazimmer@rti.org

• John David Bunker, Jr.

• Thomas Burkett

• Philip Lee

• Haby Sow

Other contributors:

• RTI International [copyright holder, funder]

See Also

Useful links:

• https://github.com/RTIInternational/SampleSelectR

• https://rtiinternational.github.io/SampleSelectR/

• Report bugs at https://github.com/RTIInternational/SampleSelectR/issues

Sample allocation

Description

Compute the proportional, power, Neyman, and optimal sample allocations.

Usage

allocate(
  allocation,
  N.h,
  n.samp = NULL,
  S.h = NULL,
  c.h = NULL,
  cost = NULL,
  variance = NULL,
  power = NULL,
  lbound = 2,
  outputs = "rounded"
)

Arguments

Value

If one output type is requested, a numeric vector of allocations. If multiple output types are requested, a named list containing the requested allocation vectors.

Method

The allocate function allocates a sample size n on H strata using one of the following allocation methods:

1. Proportional allocation [n.samp, N.h, allocation = "proportional"]

   n_h = n \times \frac{N_h}{\sum\limits_{h=1}^H N_h}

   where
   n: total sample size to be allocated (function input is n.samp), and
   N_h: population size of stratum h (function input is N.h).

2. Power allocation [n.samp, N.h, power, allocation = "power"]

   n_h = n \times \frac{N_h^\alpha}{\sum\limits_{h=1}^H N_h^\alpha}

   where
   \alpha: a power value to control over-under-sampling with 0 \le \alpha \le 1 (function input is power).

3. Neyman allocation [n.samp, N.h, S.h, allocation = "neyman"]

   n_h = n \times \frac{N_h S_h}{\sum\limits_{h=1}^H N_h S_h}

   where
   S_h: standard deviation of stratum h (function input is S.h).

4. Optimal allocation

   • cost-constrained [N.h, S.h, c.h, cost, allocation = "optimal"]

     n_h = (C - c_0) \times \frac{N_h S_h / \sqrt{c_h}}{\sum\limits_{h=1}^H N_h S_h \sqrt{c_h}}

     where
     c_h: cost per unit in stratum h (function input is c.h), and
     (C - c_0): total variable cost (function input is cost)

   • precision-constrained [N.h, S.h, c.h, variance, allocation = "optimal"]

     n_h = N_h S_h / \sqrt{c_h} \times \frac{\sum\limits_{h=1}^H N_h S_h \sqrt{c_h}}{V_0 \left(\sum\limits_{h=1}^H N_h \right)^2 + \sum\limits_{h=1}^H N_h S_h^2}

     where
     V_0: fixed variance target for estimated mean (function input is variance)

The table below presents the relevant inputs for each type; when irrelevant inputs are entered, an error message will be displayed.

Examples

# The first step is getting a frame summary
#  Summarize the IPEDS dataset by OBEREG
# - N: number of universities per region
# - SD_ENRTOT: standard deviation of total enrollment per region
# - Filter out rows with missing ENRTOT to ensure accurate variance estimates

ipeds_summary <- ipeds |>
  tidytable::filter(!is.na(ENRTOT)) |>
  tidytable::group_by(OBEREG) |>
  tidytable::summarize(
    N = tidytable::n(),
    SD_ENRTOT = stats::sd(ENRTOT)
  ) |>
  tidytable::ungroup()

# Example of proportional allocation
ipeds_summary |>
  tidytable::mutate(
    n = allocate("proportional", N.h = N, n.samp = 500)
  )

# Example of power allocation
ipeds_summary |>
  tidytable::mutate(
    n = allocate("power", N.h = N, power = 0.5, n.samp = 500)
  )

# Example of Neyman allocation
ipeds_summary |>
  tidytable::mutate(
    n = allocate("neyman", N.h = N, n.samp = 500, S.h = SD_ENRTOT)
  )

# Example of Neyman allocation with a lower bound of 5
ipeds_summary |>
  tidytable::mutate(
    n = allocate("neyman", N.h = N, n.samp = 500, S.h = SD_ENRTOT, lbound = 5)
  )

Select a sequential PPS sample

Description

Draws a sequential sample of size n. Each unit's probability of selection is proportional to its size measure. This is a minimum replacement method as discussed in Chromy (1979).

Usage

chromy_pps(frame, n, mos, outall = FALSE, curstrat = NULL)

Arguments

Value

Returns an object of type tidytable that contains the weight, expected hits (selection probability for nonreplacement designs), and number of hits plus all original variables. Include a SelectionIndicator variable if outall=TRUE

References

Chromy, J. R. (1979). “Sequential Sample Selection Methods.” In Proceedings of the Survey Research Methods Section, 401–406. Washington, DC: American Statistical Association. http://www.asasrms.org/Proceedings/papers/1979_081.pdf

Examples

# PPS sample of counties using population size as MOS
# LA county will be selected two or three times based on expected hits
# Cook, Harris, and Maricopa will be selected one or two times based on expected hits

county_2023 |>
  tidytable::select(GEOID, Name, Pop_Tot) |>
  chromy_pps(n = 75, mos = "Pop_Tot") |>
  tidytable::arrange(desc(ExpectedHits))

county_2023 |>
  tidytable::select(GEOID, Name, Pop_Tot) |>
  chromy_pps(n = 75, mos = "Pop_Tot", outall = TRUE) |>
  tidytable::arrange(desc(ExpectedHits))

American Community Survey (ACS) 5-Year Estimates, 2023 for counties

Description

A select set of estimates from the ACS for all counties in the 50 states and District of Columbia.

Usage

county_2023

Format

A tibble/data.frame with 3,144 rows and 25 columns:

GEOID

Geographic Identifier (GEOID) of county (character)

Name

Name of county (character)

State

State (Abbreviation) (character)

Region

Census Region (factor)

Divison

Census Division (factor)

Pop_Tot

Total population (B03002) (numeric)

Pop_Pct_White_NH

Percent of population who is White alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Black_NH

Percent of population who is Black or African American alone, non-Hispanic (B03002) (numeric)

Pop_Pct_AIAN_NH

Percent of population who is American Indian and Alaska Native alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Asian_NH

Percent of population who is Asian alone, non-Hispanic (B03002) (numeric)

Pop_Pct_NHPI_NH

Percent of population who is Native Hawaiian and Other Pacific Islander alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Other_NH

Percent of population who is another race (including 2 or more races), non-Hispanic (B03002) (numeric)

Pop_Pct_Hispanic

Percent of population who is Hispanic (B03002) (numeric)

HU_Tot

Total number of housing units (B25002) (numeric)

HU_Pct_Occupied

Percent of housing units that are occupied (B25002) (numeric)

HU_Pct_Vacant

Percent of housing units that are vacant (B25002) (numeric)

Pop_Pct_0004

Percent of population that are 0-4 years of age (S0101) (numeric)

Pop_Pct_0509

Percent of population that are 5-9 years of age (S0101) (numeric)

Pop_Pct_1014

Percent of population that are 10-14 years of age (S0101) (numeric)

Pop_Pct_2544

Percent of population that are 15-17 years of age (S0101) (numeric)

Pop_Pct_4564

Percent of population that are 18-24 years of age (S0101) (numeric)

Pop_Pct_6574

Percent of population that are 25-44 years of age (S0101) (numeric)

Pop_Pct_75plus

Percent of population that are 45-64 years of age (S0101) (numeric)

Pop_Pct_1517

Percent of population that are 65-74 years of age (S0101) (numeric)

Pop_Pct_1824

Percent of population that are 75 years of age or older (S0101) (numeric)

Source

U.S. Census Bureau, "American Community Survey 5-Year Estimates" 2023, https://api.census.gov/data/2023/acs/acs5, accessed on May 30, 2025. Tables B03002, B25002, and S0101. Note - the tidycensus package was used to download the data from the Census API. Region and division are coded based on https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us_regdiv.pdf

IPEDS - Post secondary education institutions, Fall 2023

Description

A select set of characteristics for postsecondary educational institutions from the Integrated Postsecondary Education Data System (IPEDS) for operational institutions reporting fall enrollment data for 2023.

Usage

ipeds

Format

A tibble with 5914 rows and 16 columns:

UNITID

Unique identification number of the institution (numeric)

INSTNM

Institution (entity) name (character)

STABBR

State abbreviation (character)

FIPS

FIPS state code (numeric)

OBEREG

Bureau of Economic Analysis (BEA) regions (factor)

ICLEVEL

Level of institution (factor)

SECTOR

Sector of institution (factor)

LOCALE

Degree of urbanization (Urban-centric locale) (factor)

DEGGRANT

Degree-granting status (factor)

HLOFFER

Highest level of offering (factor)

ENRTOT

Total enrollment (numeric)

EFUG

Undergraduate enrollment (numeric)

EFUG1ST

First-time degree/certificate-seeking undergraduate enrollment (numeric)

EFUGFT

Full-time undergraduate enrollment (numeric)

EFGRAD

Graduate enrollment (numeric)

EFGRADFT

Full-time graduate enrollment (numeric)

Source

National Center for Education Statistics, "Integrated Postsecondary Education Data System " 2023, https://nces.ed.gov/ipeds/datacenter/DataFiles.aspx?year=2023&surveyNumber=-1&sid=4737d338-5121-4355-bb91-01ffa92243ef&rtid=7, downloaded on May 2, 2025.

American Community Survey (ACS) 5-Year Estimates, 2023 for Public Use Microdata Areas (PUMAs)

Description

A select set of estimates from the ACS for all PUMAs in the 50 states and District of Columbia.

Usage

puma_2023

Format

A tibble/data.frame with 2,462 rows and 25 columns:

GEOID

Geographic Identifier (GEOID) of PUMA (character)

Name

Name of PUMA (character)

State

State (Abbreviation) (character)

Region

Census Region (factor)

Division

Census Division (factor)

Pop_Tot

Total population (B03002) (numeric)

Pop_Pct_White_NH

Percent of population who is White alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Black_NH

Percent of population who is Black or African American alone, non-Hispanic (B03002) (numeric)

Pop_Pct_AIAN_NH

Percent of population who is American Indian and Alaska Native alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Asian_NH

Percent of population who is Asian alone, non-Hispanic (B03002) (numeric)

Pop_Pct_NHPI_NH

Percent of population who is Native Hawaiian and Other Pacific Islander alone, non-Hispanic (B03002) (numeric)

Pop_Pct_Other_NH

Percent of population who is another race (including 2 or more races), non-Hispanic (B03002) (numeric)

Pop_Pct_Hispanic

Percent of population who is Hispanic (B03002) (numeric)

HU_Tot

Total number of housing units (B25002) (numeric)

HU_Pct_Occupied

Percent of housing units that are occupied (B25002) (numeric)

HU_Pct_Vacant

Percent of housing units that are vacant (B25002) (numeric)

Pop_Pct_0004

Percent of population that are 0-4 years of age (S0101) (numeric)

Pop_Pct_0509

Percent of population that are 5-9 years of age (S0101) (numeric)

Pop_Pct_1014

Percent of population that are 10-14 years of age (S0101) (numeric)

Pop_Pct_2544

Percent of population that are 15-17 years of age (S0101) (numeric)

Pop_Pct_4564

Percent of population that are 18-24 years of age (S0101) (numeric)

Pop_Pct_6574

Percent of population that are 25-44 years of age (S0101) (numeric)

Pop_Pct_75plus

Percent of population that are 45-64 years of age (S0101) (numeric)

Pop_Pct_1517

Percent of population that are 65-74 years of age (S0101) (numeric)

Pop_Pct_1824

Percent of population that are 75 years of age or older (S0101) (numeric)

Source

U.S. Census Bureau, "American Community Survey 5-Year Estimates" 2023, https://api.census.gov/data/2023/acs/acs5, accessed on May 30, 2025. Tables B03002, B25002, and S0101. Note - the tidycensus package was used to download the data from the Census API. Region and division are coded based on https://www2.census.gov/geo/pdfs/maps-data/maps/reference/us_regdiv.pdf

Sample selection function

Description

Selects a random sample using a specified method and sample size. Selection can also optionally be stratified and/or include a measure of size (mos) if a PPS method is used.

Usage

select_sample(
  frame,
  method,
  n,
  outall = FALSE,
  strata = NULL,
  mos = NULL,
  sort_vars = NULL,
  sort_method = NULL
)

Arguments

Value

A tidytable object containing the entire frame with a selection indicator or just the sample, dependent on the value of outall. Selection probability and sampling weight are also included. May include various summary messages to the console when applicable for certain sampling methods.

Examples

# SRS of 100 US counties, using geographic region as strata
# n is a data frame containing the strata values and corresponding desired sample size
# Sample size column must be titled 'sample_size'

n_df_srs <- data.frame(
  Region = as.factor(c("Northeast", "Midwest", "South", "West")),
  sample_size = c(25, 25, 25, 25)
)

county_2023 |>
  select_sample(method = "srs", n = n_df_srs, strata = "Region")


# Systematic sample of 250 US universities. Each unit has an equal probability of being selected
# Includes a nested sort of enrollment total within sector
# Returns all obs from original data frame with a selection indicator column

sample_sys_eq <- ipeds |>
  select_sample(
    method = "sys_eq", n = 250, outall = TRUE,
    sort_vars = c("SECTOR", "ENRTOT"), sort_method = "nest"
  )

# For samples taken with outall = TRUE, the sample size can be verified by summing
# the SelectionIndicator column.

sample_sys_eq
sum(sample_sys_eq$SelectionIndicator)


# Systematic PPS sample of 250 US universities. Each unit's probability of selection
# is proportional to its size measure.
# Using enrollment total as MOS
# Includes a nested sort of enrollment total within sector

sample_sys_pps <- ipeds |>
  select_sample(
    method = "sys_pps", n = 250, mos = "ENRTOT",
    sort_vars = c("SECTOR", "ENRTOT"), sort_method = "nest"
  )

# For pps samples, it is possible for a single sampling unit to be selected multiple times
# due to a large mos value. This is especially true as desired sample size increases. The
# result is the final sample may not meet the desired sample size. To verify the pps sample,
# the NumberHits column can be summed and should total to the desired sample size.

sample_sys_pps
sum(sample_sys_pps$NumberHits)


# Sequential aka Chromy's method PPS sample of 500 PUMAs, using geographic region as strata
# Includes a serpentine sort of geographic division then state
# Using population total as MOS, each unit's probability of selection is proportional to its
# size measure.
# Note that there may be a discrepancy between the desired and final sample sizes. The final
# sample size can be verified by totaling NumberHits.

n_df_chr <- data.frame(
  Region = as.factor(c("Northeast", "Midwest", "South", "West")),
  sample_size = c(125, 125, 125, 125)
)

puma_2023 |>
  select_sample(
    method = "chromy_pps", n = n_df_chr, strata = "Region", mos = "Pop_Tot",
    sort_vars = c("Division", "State"), sort_method = "serpentine"
  )

Serpentine sort function

Description

Sorts the rows in a given data frame in a hierarchical fashion given a list of variables (...)

Usage

serp_sort(.data, ..., naorder = TRUE, sortID = FALSE)

Arguments

Value

A copy of .data that is hierarchically sorted and, if specified, includes the sort group variables created for sorting

Examples

# Sort counties by Region, then Division, in a serpentine pattern
county_2023 |>
  serp_sort("Region", "Division")

# Keep the intermediate sort-group columns (sortSerp1, sortSerp2)
county_2023 |>
  serp_sort("Region", "Division", sortID = TRUE)

Simple random sampling function

Description

Draws a simple random sample of size n.

Usage

srs(frame, n, outall = FALSE, curstrat = NULL)

Arguments

Value

A tidytable object containing the entire frame with a selection indicator or just the sample, dependent on the value of outall. Selection probability and sampling weight are also included. The sample size, n, and the population size, N, are printed to the console.

Examples

# Random sample of 200 universities, only sampled rows returned
ipeds |>
  tidytable::filter(!is.na(ENRTOT)) |>
  srs(n = 200, outall = FALSE)

# Return full dataset with selection indicators
ipeds |>
  tidytable::filter(!is.na(ENRTOT)) |>
  srs(n = 200, outall = TRUE)

Systematic Sampling Without Replacement

Description

Draws a systematic sample of size n from a data frame. Each unit has an equal probability of being selected.

Usage

sys(frame, n, curstrat = NULL, outall = FALSE)

Arguments

Value

a data.table with the original columns plus:

SelectionProbability

Equal to n / N for all units.

SamplingWeight

Equal to N / n for all units.

SelectionIndicator

TRUE if selected, FALSE otherwise.-only included if outall=TRUE

NumberHits

1 if selected, 0 otherwise.

ExpectedHits

Equal to SelectionProbability.

References

Kalton, G. (1983). Introduction to Survey Sampling. SAGE Publications. https://doi.org/10.4135/9781412984683

Examples

# Sort by REGION, DIVISION, and Pop_Tot, then take a sample
puma_2023 |>
  tidytable::arrange(Region, Division, Pop_Tot) |>
  sys(n = 50, outall = FALSE)

# Return full dataset with selection indicators
puma_2023 |>
  tidytable::arrange(Region, Division, Pop_Tot) |>
  sys(n = 50, outall = TRUE)

Select a systematic PPS sample

Description

Draws a systematic sample of size n. Each unit's probability of selection is proportional to its size measure.

Usage

sys_pps(frame, n, mos, outall = FALSE, curstrat = NULL)

Arguments

Value

Returns an object of type tidytable that contains the weight, selection probability, number of hits, etc plus all original variables.

Examples

# PPS sample of 75 counties using Pop_Tot as the measure of size
# Return only the sampled counties
sys_pps(county_2023, mos = "Pop_Tot", n = 75, outall = FALSE)

# Return the full dataset with selection indicators
sys_pps(county_2023, mos = "Pop_Tot", n = 75, outall = TRUE)