TeachingSampling (version 4.1.1)

S.piPS: Probability Proportional to Size Sampling Without Replacement

Description

Draws a probability proportional to size sample without replacement of size \(n\) from a population of size \(N\).

Usage

S.piPS(n, x, e)

Arguments

x

Vector of auxiliary information for each unit in the population

n

Sample size

e

By default, a vector of size \(N\) of independent random numbers drawn from the \(Uniform(0,1)\)

Value

The function returns a matrix of \(m\) rows and two columns. Each element of the first column indicates the unit that was selected. Each element of the second column indicates the selection probability of this unit

Details

The selected sample is drawn according to the Sunter method (sequential-list procedure)

References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer. Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.

See Also

E.piPS

Examples

# NOT RUN {
############
## Example 1
############
# Vector U contains the label of a population of size N=5
U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie")
# The auxiliary information
x <- c(52, 60, 75, 100, 50)
# Draws a piPS sample without replacement of size n=3
res <- S.piPS(3,x)
res
sam <- res[,1] 
sam
# The selected sample is
U[sam]

############
## Example 2
############
# Uses the Lucy data to draw a random sample of units accordind to a
# piPS without replacement design

data(Lucy)
attach(Lucy)
# The selection probability of each unit is proportional to the variable Income
res <- S.piPS(400,Income)
# The selected sample
sam <- res[,1]
# The inclusion probabilities of the units in the sample
Pik.s <- res[,2]
# The information about the units in the sample is stored in an object called data
data <- Lucy[sam,]
data
dim(data)
# }