StratifiedSampling (version 0.4.2)

stratifiedcube: Stratified Sampling

Description

This function implements a method for selecting a stratified sample. It really improves the performance of the function fbs and balstrat.

Usage

stratifiedcube(
  X,
  strata,
  pik,
  EPS = 1e-07,
  rand = TRUE,
  landing = TRUE,
  lp = TRUE
)

Value

A vector with elements equal to 0 or 1. The value 1 indicates that the unit is selected while the value 0 is for rejected units.

Arguments

X

A matrix of size (\(N\) x \(p\)) of auxiliary variables on which the sample must be balanced.

strata

A vector of integers that specifies the stratification..

pik

A vector of inclusion probabilities.

EPS

epsilon value

rand

if TRUE, the data are randomly arranged. Default TRUE

landing

if FALSE, no landing phase is done.

lp

if TRUE, landing by linear programming otherwise supression of variables. Default TRUE

Details

The function is selecting a balanced sample very quickly even if the sum of inclusion probabilities within strata are non-integer. The function should be used in preference. Firstly, a flight phase is performed on each strata. Secondly, the function findB is used to find a particular matrix to apply a flight phase by using the cube method proposed by Chauvet, G. and Tillé, Y. (2006). Finally, a landing phase is applied by suppression of variables.

References

Chauvet, G. and Tillé, Y. (2006). A fast algorithm of balanced sampling. Computational Statistics, 21/1:53-62

See Also

fbs, balstrat, landingRM, ffphase

Examples

# EXAMPLE WITH EQUAL INCLUSION PROBABILITES AND SUM IN EACH STRATA INTEGER
N <- 100
n <- 10
p <- 4
X <- matrix(rgamma(N*p,4,25),ncol = p)
strata <- rep(1:n,each = N/n)
pik <- rep(n/N,N)

s <- stratifiedcube(X,strata,pik)

t(X/pik)%*%s
t(X/pik)%*%pik

Xcat <- disj(strata)

t(Xcat)%*%s
t(Xcat)%*%pik


# EXAMPLE WITH UNEQUAL INCLUSION PROBABILITES AND SUM IN EACH STRATA INTEGER
N <- 100
n <- 10
X <- cbind(rgamma(N,4,25),rbinom(N,20,0.1),rlnorm(N,9,0.1),runif(N))
colSums(X)
strata <- rbinom(N,10,0.7)
strata <- sampling::cleanstrata(strata)
pik <- as.vector(sampling::inclusionprobastrata(strata,ceiling(table(strata)*0.10)))
EPS = 1e-7

s <- stratifiedcube(X,strata,pik)
test <- stratifiedcube(X,strata,pik,landing = FALSE)

t(X/pik)%*%s
t(X/pik)%*%test
t(X/pik)%*%pik

Xcat <- disj(strata)

t(Xcat)%*%s
t(Xcat)%*%test
t(Xcat)%*%pik


# EXAMPLE WITH UNEQUAL INCLUSION PROBABILITES AND SUM IN EACH STRATA NOT INTEGER
set.seed(3)
N <- 100
n <- 10
X <- cbind(rgamma(N,4,25),rbinom(N,20,0.1),rlnorm(N,9,0.1),runif(N))
strata <- rbinom(N,10,0.7)
strata <- sampling::cleanstrata(strata)
pik <- runif(N)
EPS = 1e-7
tapply(pik,strata,sum)
table(strata)


s <- stratifiedcube(X,strata,pik,landing = TRUE)
test <- stratifiedcube(X,strata,pik,landing = FALSE)


t(X/pik)%*%s
t(X/pik)%*%test
t(X/pik)%*%pik

Xcat <- disj(strata)

t(Xcat)%*%s
t(Xcat)%*%pik
t(Xcat)%*%test