PikHol {TeachingSampling}R Documentation

Optimal Inclusion Probabilities Under Multi-purpose Sampling

Description

Computes the population vector of optimal inclusion probabilites under teh Holmbergs's Approach

Usage

PikHol(n,sigma,e)

Arguments

n Vector of optimnal sample sizes for each of the characteristics of interest.
sigma A matrix containing the size measures for each characteristics of interest.
e Maximun allowed error under the ANOREL approach.

Details

Assuming that all o fthe characteristic of interest are equally important, the Holmberg's sampling desing yields the following inclusion probabilities

π_{(opt)k}=frac{n^*sqrt{a_{qk}}}{sum_{kin U}sqrt{a_{qk}}}

where

n^*>=q frac{(sum_{kin U}sqrt{a_{qk}})^2}{(1+c)Q+sum_{kin U}a_{qk}}

and

a_{qk}= sum_{q=1}^Q frac{σ^2_{qk}}{sum_{kin U}( frac{1}{π_{qk}}-1)σ^2_{qk}}

Note that σ^2_{qk} is a size measure associated with the k-th element in the q-th characterístic of interest.

Value

The function returns a vector of inclusion probabilities.

Author(s)

Hugo Andrés Gutiérrez Rojas hugogutierrez@usantotomas.edu.co

References

Holmberg, A. (2002), On the Choice of Sampling Design under GREG Estimation in Multiparameter Surveys. RD Department, Statistics Sweden.
Särndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutiérrez, H. A. (2009), Estrategias de muestreo: Diseño de encuestas y estimación de parámetros. Editorial Universidad Santo Tomás

Examples

# Uses the Marco and Lucy data to draw an otpimal sample
# in a multipurpose survey context
data(Lucy)
attach(Lucy)
# Different sample sizes for two characteristics of interest: Employees and Taxes
N <- dim(Lucy)[1]
n <- c(350,400)
# The size measure is the same for both characteristics of interest,
# but the relationship in between is different
sigy1 <- sqrt(Income^(1))
sigy2 <- sqrt(Income^(2))
# The matrix containign the size measures for each characteristics of interest
sigma<-cbind(sigy1,sigy2)
# The vector of optimal inclusion probabilities under the Holmberg's approach
Piks<-PikHol(n,sigma,0.03)
# The optimal sample size is given by the sum of piks
sum(Piks)
# Performing the S.piPS function in order to select the optimal sample of size n=400
res<-S.piPS(375,Piks)
sam <- res[,1]
# The information about the units in the sample is stored in an object called data
data <- Lucy[sam,]
attach(data)
names(data)
# Pik.s is the vector of inclusion probability of every single unit
# in the selected sample
Pik.s <- res[,2]
# The variables of interest are: Income, Employees and Taxes
# This information is stored in a data frame called estima
estima <- data.frame(Income, Employees, Taxes)
E.piPS(estima,Pik.s)

[Package TeachingSampling version 1.1.9 Index]