PikHol {TeachingSampling} | R Documentation |
Computes the population vector of optimal inclusion probabilites under teh Holmbergs's Approach
PikHol(n,sigma,e)
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. |
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.
The function returns a vector of inclusion probabilities.
Hugo Andrés Gutiérrez Rojas hugogutierrez@usantotomas.edu.co
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
# 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)