mstage: Multistage sampling

Description

Implements multistage sampling with equal/unequal probabilities.

Usage

mstage(data, stage=c("stratified","cluster",""), varnames, size, 
method=c("srswor","srswr","poisson","systematic"), pik, description=FALSE)

Value

The function returns a list, which contains the stages (if m is this list, the stage i is m$'i' etc) and the following information:

ID_unit: the identifier of selected units at each stage.
Prob_ number _stage: the inclusion probability at stage 'number'.
Prob: the final unit inclusion probability given in the last stage; it is the product of unit inclusion probabilities at each stage.

Arguments

data: data frame or data matrix; its number of rows is N, the population size.
stage: list of sampling types at each stage; the possible values are: "stratified", "cluster" and "" (without stratification or clustering). For multistage element sampling, this argument is not necessary.
varnames: list of stratification or clustering variables.
size: list of sample sizes (in the order in which the samples appear in the multistage sampling).
method: list of methods to select units at each stage; the following methods are implemented: simple random sampling without replacement (srswor), simple random sampling with replacement (srswr), Poisson sampling (poisson), systematic sampling (systematic); if the method is not specified, by default the method is "srswor". The method can be different at each stage.
pik: list of selection probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson, systematic). If an auxiliary information is provided, the function uses the inclusionprobabilities function for computing these probabilities.
description: a message is printed if its value is TRUE; the message gives the number of selected units and the number of the units in the population. By default, its value is FALSE.

Details

The data should be sorted in ascending order by the columns given in the varnames argument before applying the function. Use, for example, data[order(data$state,data$region),].

Examples

Run this code

############
## Example 1
############
# Two-stage cluster sampling
# Uses the 'swissmunicipalities' data 
data(swissmunicipalities)
b=swissmunicipalities
b=b[order(b$REG,b$CT),]
attach(b)
# the variable 'REG' (region) has 7 categories;
# it is used as clustering variable in the first-stage sample
# the variable 'CT' (canton) has 26 categories; 
# it is used as clustering variable in the second-stage sample
# 4 clusters (regions) are selected in the first-stage 
# 1 canton is selected in the second-stage from each sampled region 
# the method is simple random sampling without replacement in each stage
# (equal probability, without replacement)
m=mstage(b,stage=list("cluster","cluster"), varnames=list("REG","CT"),
size=list(4,c(1,1,1,1)), method=list("srswor","srswor"))
# the first stage is m[[1]], the second stage is m[[2]]
#the selected regions
unique(m[[1]]$REG)
#the selected cantons
unique(m[[2]]$CT)
# extracts the observed data
x=getdata(b,m)[[2]]
# check the output
table(x$REG,x$CT)
############
## Example 2
############
# Two-stage element sampling
# Generates artificial data (a 235X3 matrix with 3 columns: state, region, income).
# The variable "state" has 2 categories ('n','s'). 
# The variable "region" has 5 categories ('A', 'B', 'C', 'D', 'E').
# The variable "income" is generated using the U(0,1) distribution. 
data=rbind(matrix(rep('n',165),165,1,byrow=TRUE),matrix(rep('s',70),70,1,byrow=TRUE))
data=cbind.data.frame(data,c(rep('A',115),rep('D',10),rep('E',40),rep('B',30),rep('C',40)),
100*runif(235))
names(data)=c("state","region","income")
data=data[order(data$state,data$region),]
table(data$state,data$region)
# the method is simple random sampling without replacement
# 25 units are drawn in the first-stage
# in the second-stage, 10 units are drawn from the already 25 selected units
m=mstage(data,size=list(25,10),method=list("srswor","srswor")) 
# the first stage is m[[1]], the second stage is m[[2]]
# extracts the observed data
xx=getdata(data,m)[[2]]
# check the result 
table(xx$state,xx$region)
############
## Example 3
############
# Stratified one-stage cluster sampling
# The same data as in Example 2
# the variable 'state' is used as stratification variable 
# 165 units are in the first stratum and 70 in the second one
# the variable 'region' is used as clustering variable
# 1 cluster (region) is drawn in each state using "srswor" 
m=mstage(data, stage=list("stratified","cluster"), varnames=list("state","region"), 
size=list(c(165,70),c(1,1)),method=list("","srswor")) 
# check the first stage
table(m[[1]]$state)
# check the second stage
table(m[[2]]$region)
# extracts the observed data
xx=getdata(data,m)[[2]]
# check the result
table(xx$state,xx$region)
############
## Example 4
############
# Two-stage cluster sampling
# The same data as in Example 1
# in the first-stage, the clustering variable is 'REG' (region) with 7 categories
# 4 clusters (regions) are drawn in the first-stage 
# each region is selected with the probability 4/7
# in the second-stage, the clustering variable is 'CT'(canton) with 26 categories
# 1 cluster (canton) is drawn in the second-stage from each selected region 
# in region 1, there are 3 cantons; one canton is selected with prob. 0.2, 0.4, 0.4, resp. 
# in region 2, there are 5 cantons; each canton is selected with the prob. 1/5
# in region 3, there are 3 cantons; each canton is selected with the prob. 1/3
# in region 4, there is 1 canton, which it is selected with the prob. 1
# in region 5, there are 7 cantons; each canton is selected with the prob. 1/7
# in region 6, there are 6 cantons; each canton is selected with the prob. 1/6
# in region 7, there is 1 canton, which it is selected with the prob. 1
# it is necessary to use a list of selection probabilities at each stage
# prob is the list of the selection probabilities
# the method is systematic sampling (unequal probabilities, without replacement)
# ls is the list of sizes
ls=list(4,c(1,1,1,1))
prob=list(rep(4/7,7),list(c(0.2,0.4,0.4),rep(1/5,5),rep(1/3,3),rep(1,1),rep(1/7,7),
rep(1/6,6),rep(1,1)))
m=mstage(b,stage=list("cluster","cluster"),varnames=list("REG","CT"),
size=ls, method=c("systematic","systematic"),pik=prob)
#the selected regions
unique(m[[1]]$REG)
#the selected cantons
unique(m[[2]]$CT)
# extracts the observed data
xx=getdata(b,m)[[2]]
# check the result
table(xx$REG,xx$CT)
############
## Example 5
############
# Stratified two-stage cluster sampling
# The same data as in Example 1
# the variable 'REG' is used as stratification variable
# there are 7 strata  
# the variable 'CT' is used as first clustering variable
# first stage, clusters (cantons) are drawn from each region using "srswor" 
# 3 clusters are drawn from the regions 1,2,3,5, and 6, respectively
# 1 cluster is drawn from the regions 4 and 7, respectively
# the variable 'COM' is used as second clustering variable
# second stage, 2 clusters (municipalities) are drawn from each selected canton using "srswor" 
m=mstage(b,stage=list("stratified","cluster","cluster"), varnames=list("REG","CT","COM"),
size=list(size1=table(b$REG),size2=c(rep(3,3),1,3,3,1), size3=rep(2,17)), 
method=list("","srswor","srswor"))
# extracts the observed data
getdata(b,m)[[3]]