Strata.RdStratified sampling with equal/unequal probabilities.
Strata(x, stratanames = NULL, size,
method = c("srswor", "srswr", "poisson", "systematic"),
pik, description = FALSE)a data frame or a matrix; its number of rows is n, the population size.
vector of stratification variables.
vector of stratum sample sizes (in the order in which the strata are given in the input data set).
method to select units; implemented are: a) simple random
sampling without replacement ("srswor"), b) simple random sampling with replacement ("srswr"),
c) Poisson sampling ("poisson"), d) systematic sampling ("systematic") (default is "srswor").
vector of inclusion probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson and systematic). If an auxiliary information is provided, the function uses the inclusionprobabilities function for computing these probabilities. If the method is "srswr" and the sample size is larger than the population size, this vector is normalized to one.
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, the value is FALSE.
The function produces an object, which contains the following information:
the identifier of the selected units.
the unit stratum.
the final unit inclusion probability.
# Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data)
# generates artificial data (a 235X3 matrix with 3 columns: state, region, income).
# the variable "state" has 2 categories ('nc' and 'sc').
# the variable "region" has 3 categories (1, 2 and 3).
# the sampling frame is stratified by region within state.
# the income variable is randomly generated
m <- rbind(matrix(rep("nc",165), 165, 1, byrow=TRUE),
matrix(rep("sc", 70), 70, 1, byrow=TRUE))
m <- cbind.data.frame(m, c(rep(1, 100), rep(2,50), rep(3,15),
rep(1, 30), rep(2, 40)), 1000 * runif(235))
names(m) <- c("state", "region", "income")
# computes the population stratum sizes
table(m$region, m$state)
#>
#> nc sc
#> 1 100 30
#> 2 50 40
#> 3 15 0
# not run
# nc sc
# 1 100 30
# 2 50 40
# 3 15 0
# there are 5 cells with non-zero values
# one draws 5 samples (1 sample in each stratum)
# the sample stratum sizes are 10,5,10,4,6, respectively
# the method is 'srswor' (equal probability, without replacement)
s <- Strata(m, c("region", "state"), size=c(10, 5, 10, 4, 6), method="srswor")
# extracts the observed data
data.frame(income=m[s$id, "income"], s)
#> income state region income.1 stratum size id
#> 1.65 866.10058 nc 1 866.10058 1 10 65
#> 1.93 592.34629 nc 1 592.34629 1 10 93
#> 1.29 286.04175 nc 1 286.04175 1 10 29
#> 1.64 547.19689 nc 1 547.19689 1 10 64
#> 1.34 200.38347 nc 1 200.38347 1 10 34
#> 1.45 482.35179 nc 1 482.35179 1 10 45
#> 1.26 52.49346 nc 1 52.49346 1 10 26
#> 1.8 598.38073 nc 1 598.38073 1 10 8
#> 1.52 329.42273 nc 1 329.42273 1 10 52
#> 1.62 895.92032 nc 1 895.92032 1 10 62
#> 2.120 507.15857 nc 2 507.15857 2 5 120
#> 2.143 232.86548 nc 2 232.86548 2 5 143
#> 2.147 688.35110 nc 2 688.35110 2 5 147
#> 2.109 451.99868 nc 2 451.99868 2 5 109
#> 2.130 571.54761 nc 2 571.54761 2 5 130
#> 3.165 794.92344 nc 3 794.92344 3 10 165
#> 3.151 628.19458 nc 3 628.19458 3 10 151
#> 3.156 755.49937 nc 3 755.49937 3 10 156
#> 3.160 426.00580 nc 3 426.00580 3 10 160
#> 3.157 578.61374 nc 3 578.61374 3 10 157
#> 3.164 616.97988 nc 3 616.97988 3 10 164
#> 3.152 780.21599 nc 3 780.21599 3 10 152
#> 3.162 507.13136 nc 3 507.13136 3 10 162
#> 3.153 178.19258 nc 3 178.19258 3 10 153
#> 3.159 948.04473 nc 3 948.04473 3 10 159
#> 4.167 427.83172 sc 1 427.83172 4 4 167
#> 4.181 381.52305 sc 1 381.52305 4 4 181
#> 4.170 391.48706 sc 1 391.48706 4 4 170
#> 4.169 27.68708 sc 1 27.68708 4 4 169
#> 5.202 773.62990 sc 2 773.62990 5 6 202
#> 5.231 469.94421 sc 2 469.94421 5 6 231
#> 5.233 196.68003 sc 2 196.68003 5 6 233
#> 5.217 822.34924 sc 2 822.34924 5 6 217
#> 5.229 369.66882 sc 2 369.66882 5 6 229
#> 5.208 152.05055 sc 2 152.05055 5 6 208
# see the result using a contigency table
table(s$region, s$state)
#>
#> nc sc
#> 1 10 4
#> 2 5 6
#> 3 10 0
# The same data as in Example 1
# the method is 'systematic' (unequal probability, without replacement)
# the selection probabilities are computed using the variable 'income'
s <- Strata(m,c("region", "state"), size=c(10, 5, 10, 4, 6),
method="systematic", pik=m$income)
# extracts the observed data
data.frame(income=m[s$id, "income"], s)
#> income state region income.1 stratum size id
#> 1.9 322.88584 nc 1 322.88584 1 10 9
#> 1.29 286.04175 nc 1 286.04175 1 10 29
#> 1.86 636.40332 nc 1 636.40332 1 10 86
#> 1.16 104.97314 nc 1 104.97314 1 10 16
#> 1.8 598.38073 nc 1 598.38073 1 10 8
#> 1.36 793.01949 nc 1 793.01949 1 10 36
#> 1.92 448.64375 nc 1 448.64375 1 10 92
#> 1.100 380.39065 nc 1 380.39065 1 10 100
#> 1.66 655.96816 nc 1 655.96816 1 10 66
#> 1.18 408.09932 nc 1 408.09932 1 10 18
#> 2.145 737.76557 nc 2 737.76557 2 5 145
#> 2.135 80.87036 nc 2 80.87036 2 5 135
#> 2.112 919.35027 nc 2 919.35027 2 5 112
#> 2.150 749.40846 nc 2 749.40846 2 5 150
#> 2.103 552.14334 nc 2 552.14334 2 5 103
#> 3.157 578.61374 nc 3 578.61374 3 10 157
#> 3.160 426.00580 nc 3 426.00580 3 10 160
#> 3.152 780.21599 nc 3 780.21599 3 10 152
#> 3.156 755.49937 nc 3 755.49937 3 10 156
#> 3.158 177.50997 nc 3 177.50997 3 10 158
#> 3.164 616.97988 nc 3 616.97988 3 10 164
#> 3.151 628.19458 nc 3 628.19458 3 10 151
#> 3.163 385.42599 nc 3 385.42599 3 10 163
#> 3.153 178.19258 nc 3 178.19258 3 10 153
#> 3.154 712.35448 nc 3 712.35448 3 10 154
#> 4.183 195.25163 sc 1 195.25163 4 4 183
#> 4.170 391.48706 sc 1 391.48706 4 4 170
#> 4.186 131.10277 sc 1 131.10277 4 4 186
#> 4.184 982.18831 sc 1 982.18831 4 4 184
#> 5.200 388.30586 sc 2 388.30586 5 6 200
#> 5.214 677.27586 sc 2 677.27586 5 6 214
#> 5.229 369.66882 sc 2 369.66882 5 6 229
#> 5.198 483.59321 sc 2 483.59321 5 6 198
#> 5.224 771.66254 sc 2 771.66254 5 6 224
#> 5.205 192.33168 sc 2 192.33168 5 6 205
# see the result using a contigency table
table(s$region, s$state)
#>
#> nc sc
#> 1 10 4
#> 2 5 6
#> 3 10 0