R/ss2s4m.R

In samplesize4surveys: Sample Size Calculations for Complex Surveys

#' @import TeachingSampling
#' @export
#' 
#' @title
#' Sample Sizes in Two-Stage sampling Designs for Estimating Signle Means
#' @description 
#' This function computes a grid of possible sample sizes for estimating single means under two-stage sampling designs.
#' @return 
#' This function returns a grid of possible sample sizes. 
#' The first column represent the design effect,
#' the second column is the number of clusters to be selected, 
#' the third column is the number of units to be selected inside the clusters, 
#' and finally, the last column indicates the full sample size induced by this particular strategy.
#' @details
#' In two-stage (2S) sampling, the design effect is defined by
#' \deqn{DEFF = 1 + (m-1)\rho} 
#' Where \eqn{\rho} is defined as the intraclass correlation coefficient,  
#' m is the average sample size of units selected inside each cluster. 
#' The relationship of the full sample size of the two stage design (2S) with the 
#' simple random sample (SI) design is given by
#' \deqn{ n_{2S} =  n_{SI}*DEFF} 
#' @author Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
#' @param N The population size.
#' @param mu The value of the estimated mean of a variable of interest.
#' @param sigma The value of the estimated standard deviation of a variable of interest.
#' @param conf The statistical confidence. By default conf = 0.95. By default \code{conf = 0.95}.
#' @param delta The maximun relative margin of error that can be allowed for the estimation.
#' @param M Number of clusters in the population.
#' @param to (integer) maximum number of final units to be selected per cluster. By default \code{to = 20}.
#' @param rho The Intraclass Correlation Coefficient.
#' 
#' @references 
#' Gutierrez, H. A. (2009), \emph{Estrategias de muestreo: Diseno de encuestas y estimacion de parametros}. Editorial Universidad Santo Tomas
#' @seealso \code{\link{ICC}}
#' 
#' @examples
#' 
#' ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, rho=0.01)
#' ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.1)
#' ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.03, M=50, to=40, rho=0.2)
#' ss2s4m(N=100000, mu=10, sigma=2, conf=0.95, delta=0.05, M=50, to=40, rho=0.3)
#' 
#' ##########################################
#' # Almost same mean in each cluster       #
#' #                                        #
#' # - Heterogeneity within clusters        #
#' # - Homogeinity between clusters         #
#' #                                        #
#' #  Decision rule:                        #
#' #    * Select a lot of units per cluster #
#' #    * Select a few of clusters          #
#' ##########################################
#' 
#' # Population size
#' N <- 1000000
#' # Number of clusters in the population
#' M <- 1000
#' # Number of elements per cluster
#' N/M
#' 
#' # The variable of interest
#' y <- c(1:N)
#' # The clustering factor
#' cl <- rep(1:M, length.out=N)
#' 
#' rho = ICC(y,cl)$ICC
#' rho
#' 
#' ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)
#' 
#' 
#' ##########################################
#' # Very different means per cluster       #
#' #                                        #
#' # - Heterogeneity between clusters       #
#' # - Homogeinity within clusters          #
#' #                                        #
#' #  Decision rule:                        #
#' #    * Select a few of units per cluster #
#' #    * Select a lot of clusters          #
#' ##########################################
#' 
#' # Population size
#' N <- 1000000
#' # Number of clusters in the population
#' M <- 1000
#' # Number of elements per cluster
#' N/M
#' 
#' # The variable of interest
#' y <- c(1:N)
#' # The clustering factor
#' cl <- kronecker(c(1:M),rep(1,N/M))
#' 
#' rho = ICC(y,cl)$ICC
#' rho
#' 
#' ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)
#' 
#' ##########################
#' # Example with Lucy data #
#' ##########################
#' 
#' data(BigLucy)
#' attach(BigLucy)
#' N <- nrow(BigLucy)
#' P <- prop.table(table(SPAM))[1]
#' y <- Income
#' cl <- Segments
#' 
#' rho <- ICC(y,cl)$ICC
#' M <- length(levels(Segments))
#' 
#' ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)
#' 
#' ##########################
#' # Example with Lucy data #
#' ##########################
#' 
#' data(BigLucy)
#' attach(BigLucy)
#' N <- nrow(BigLucy)
#' P <- prop.table(table(SPAM))[1]
#' y <- Years
#' cl <- Segments
#' 
#' rho <- ICC(y,cl)$ICC
#' M <- length(levels(Segments))
#' 
#' ss2s4m(N, mu=mean(y), sigma=sd(y), conf=0.95, delta=0.03, M=M, rho=rho)

ss2s4m <- function(N, mu, sigma, conf = 0.95, delta = 0.03, M, to = 20, rho) {
  
  mseq <- seq(from = 1, to = to)
  nIseq <- Deffseq <- n2seq <- rep(NA, times = length(mseq))
  
  for (i in 1:length(mseq)) {
    Deffseq[i] = 1 + (mseq[i] - 1) * rho
    n2seq[i] = ss4m(N, mu = mu, sigma = sigma, DEFF = Deffseq[i], 
      conf = conf, error = "rme", delta = delta)
    nIseq[i] <- ifelse(n2seq[i]/mseq[i] > M,
                       M, ceiling(n2seq[i]/mseq[i])) 
                      
  }
  
  result <- data.frame(Deff = Deffseq, nI = nIseq, m = mseq, 
    n2s = n2seq)
  result.adj <- result[(result$nI <= M), ]
  result.adj
}