inclusion_prob: Calculate inclusion probabilities

In sps: Sequential Poisson Sampling

Calculate inclusion probabilities

Description

Calculate stratified (first-order) inclusion probabilities.

Usage

inclusion_prob(x, n, strata = gl(1, length(x)), alpha = 0.001, cutoff = Inf)

Arguments

x	A positive and finite numeric vector of sizes for units in the population (e.g., revenue for drawing a sample of businesses).
n	A positive integer vector giving the sample size for each stratum, ordered according to the levels of strata. A single value is recycled for all strata. Non-integers are truncated towards 0.
strata	A factor, or something that can be coerced into one, giving the strata associated with units in the population. The default is to place all units into a single stratum.
alpha	A numeric vector with values between 0 and 1 for each stratum, ordered according to the levels of strata. Units with inclusion probabilities greater than or equal to 1 - alpha are set to 1 for each stratum. A single value is recycled for all strata. The default is slightly larger than 0.
cutoff	A positive numeric vector of cutoffs for each stratum, ordered according to the levels of strata. Units with x >= cutoff get an inclusion probability of 1 for each stratum. A single value is recycled for all strata. The default does not apply a cutoff.

Details

Within a stratum, the inclusion probability for a unit is given by \pi = nx / \sum x. These values can be greater than 1 in practice, and so they are constructed iteratively by taking units with \pi \geq 1 - \alpha (from largest to smallest) and assigning these units an inclusion probability of 1, with the remaining inclusion probabilities recalculated at each step. If \alpha > 0, then any ties among units with the same size are broken by their position.

Value

A numeric vector of inclusion probabilities for each unit in the population.

See Also

sps() for drawing a sequential Poisson sample.

Examples

# Make a population with units of different size
x <- c(1:10, 100)

# Use the inclusion probabilities to calculate the variance of the
# sample size for Poisson sampling
pi <- inclusion_prob(x, 5)
sum(pi * (1 - pi))

sps documentation built on Oct. 16, 2023, 9:07 a.m.