Inclusion Probabilities in Stratified Proportional to Size Sampling Designs
For a given sample size, in each stratum, this function returns a vector of first order inclusion probabilities for an stratified sampling design proportional to an auxiliary variable.
PikSTPPS(S, x, nh)
S |
Vector identifying the membership to the strata of each unit in the population. |
x |
Vector of auxiliary information for each unit in the population. |
nh |
The vector defningn the sample size in each stratum. |
is not always less than unity. A sequential algorithm must be used in order to ensure that for every unit in the population the inclusion probability gives a proper value; i.e. less or equal to unity.
A vector of inclusion probablilities in a stratified finite population.
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas Sarndal, C-E. and Swensson, B. and Wretman, J. (2003), Model Assisted Survey Sampling. Springer.
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## Example 1
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# 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)
# Vector Strata contains an indicator variable of stratum membership
Strata <- c("A", "A", "A", "B", "B")
# The sample size in each stratum
nh <- c(2,2)
# The vector of inclusion probablities for a stratified piPS sample
# without replacement of size two within each stratum
Pik <- PikSTPPS(Strata, x, nh)
Pik
# Some checks
sum(Pik)
sum(nh)
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## Example 2
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# Uses the Lucy data to compute the vector of inclusion probablities
# for a stratified random sample according to a piPS design in each stratum
data(Lucy)
attach(Lucy)
# Level is the stratifying variable
summary(Level)
# Defines the size of each stratum
N1<-summary(Level)[[1]]
N2<-summary(Level)[[2]]
N3<-summary(Level)[[3]]
N1;N2;N3
# Defines the sample size at each stratum
n1<-70
n2<-100
n3<-200
nh<-c(n1,n2,n3)
nh
# Computes the inclusion probabilities for the stratified population
S <- Level
x <- Employees
Pik <- PikSTPPS(S, x, nh)
# Some checks
sum(Pik)
sum(nh)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.