20 Sampling
20.1 Simple Sampling
Simple (random) Sampling
library(dplyr)
iris_df <- iris
set.seed(1)
sample_n(iris_df, 10)
#> Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> 1 5.8 2.7 4.1 1.0 versicolor
#> 2 6.4 2.8 5.6 2.1 virginica
#> 3 4.4 3.2 1.3 0.2 setosa
#> 4 4.3 3.0 1.1 0.1 setosa
#> 5 7.0 3.2 4.7 1.4 versicolor
#> 6 5.4 3.0 4.5 1.5 versicolor
#> 7 5.4 3.4 1.7 0.2 setosa
#> 8 7.6 3.0 6.6 2.1 virginica
#> 9 6.1 2.8 4.7 1.2 versicolor
#> 10 4.6 3.4 1.4 0.3 setosa
library(sampling)
# set unique id number for each row
iris_df$id = 1:nrow(iris_df)
# Simple random sampling with replacement
srswor(10, length(iris_df$id))
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1
#> [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
#> [75] 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0
#> [112] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [149] 0 0
# Simple random sampling without replacement (sequential method)
srswor1(10, length(iris_df$id))
#> [1] 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [75] 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [112] 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
#> [149] 0 0
# Simple random sampling with replacement
srswr(10, length(iris_df$id))
#> [1] 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 0
#> [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#> [75] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
#> [112] 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
#> [149] 0 0
library(survey)
data("api")
srs_design <- svydesign(data = apistrat,
weights = ~pw,
fpc = ~fpc,
id = ~1)Identify missing points between sample and collected data
20.2 Stratified Sampling
A stratum is a subset of the population that has at least one common characteristic.
Steps:
- Identify relevant stratums and their representation in the population.
- Randomly sample to select a sufficient number of subjects from each stratum.
Stratified sampling reduces sampling error.
library(dplyr)
# by number of rows
sample_iris <- iris %>%
group_by(Species) %>%
sample_n(5)
sample_iris
#> # A tibble: 15 × 5
#> # Groups: Species [3]
#> Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> <dbl> <dbl> <dbl> <dbl> <fct>
#> 1 4.4 3 1.3 0.2 setosa
#> 2 5.2 3.5 1.5 0.2 setosa
#> 3 5.1 3.8 1.5 0.3 setosa
#> 4 5.2 3.4 1.4 0.2 setosa
#> 5 4.5 2.3 1.3 0.3 setosa
#> 6 5.5 2.5 4 1.3 versicolor
#> 7 7 3.2 4.7 1.4 versicolor
#> 8 6.7 3 5 1.7 versicolor
#> 9 6.1 2.9 4.7 1.4 versicolor
#> 10 5.5 2.4 3.8 1.1 versicolor
#> 11 6.4 2.7 5.3 1.9 virginica
#> 12 6.4 2.8 5.6 2.1 virginica
#> 13 6.4 3.2 5.3 2.3 virginica
#> 14 6.8 3.2 5.9 2.3 virginica
#> 15 7.2 3.6 6.1 2.5 virginica
# by fraction
sample_iris <- iris %>%
group_by(Species) %>%
sample_frac(size = .15)
sample_iris
#> # A tibble: 24 × 5
#> # Groups: Species [3]
#> Sepal.Length Sepal.Width Petal.Length Petal.Width Species
#> <dbl> <dbl> <dbl> <dbl> <fct>
#> 1 5.5 4.2 1.4 0.2 setosa
#> 2 5 3 1.6 0.2 setosa
#> 3 5.2 4.1 1.5 0.1 setosa
#> 4 4.6 3.1 1.5 0.2 setosa
#> 5 5.1 3.7 1.5 0.4 setosa
#> 6 4.8 3.4 1.9 0.2 setosa
#> 7 5.1 3.3 1.7 0.5 setosa
#> 8 5.5 3.5 1.3 0.2 setosa
#> 9 5 2.3 3.3 1 versicolor
#> 10 5.6 2.9 3.6 1.3 versicolor
#> # ℹ 14 more rows
library(sampler)
# Stratified sample using proportional allocation without replacement
ssamp(df=albania, n=360, strata=qarku, over=0.1)
#> # A tibble: 395 × 45
#> qarku Q_ID bashkia BAS_ID zaz njesiaAdministrative COM_ID qvKod zgjedhes
#> <fct> <int> <fct> <int> <fct> <fct> <int> <fct> <int>
#> 1 Berat 1 Berat 11 ZAZ … "Berat " 1101 "\"3… 558
#> 2 Berat 1 Berat 11 ZAZ … "Berat " 1101 "\"3… 815
#> 3 Berat 1 Berat 11 ZAZ … "Sinje" 1108 "\"3… 419
#> 4 Berat 1 Kucove 13 ZAZ … "Lumas" 1104 "\"3… 237
#> 5 Berat 1 Kucove 13 ZAZ … "Kucove" 1201 "\"3… 562
#> 6 Berat 1 Skrapar 17 ZAZ … "Corovode" 1303 "\"3… 829
#> 7 Berat 1 Berat 11 ZAZ … "Roshnik" 1107 "\"3… 410
#> 8 Berat 1 Ura Vajg… 19 ZAZ … "Ura Vajgurore" 1110 "\"3… 708
#> 9 Berat 1 Kucove 13 ZAZ … "Perondi" 1203 "\"3… 835
#> 10 Berat 1 Kucove 13 ZAZ … "Kucove" 1201 "\"3… 907
#> # ℹ 385 more rows
#> # ℹ 36 more variables: meshkuj <int>, femra <int>, totalSeats <int>,
#> # vendndodhja <fct>, ambienti <fct>, totalVoters <int>, femVoters <int>,
#> # maleVoters <int>, unusedBallots <int>, damagedBallots <int>,
#> # ballotsCast <int>, invalidVotes <int>, validVotes <int>, lsi <int>,
#> # ps <int>, pkd <int>, sfida <int>, pr <int>, pd <int>, pbdksh <int>,
#> # adk <int>, psd <int>, ad <int>, frd <int>, pds <int>, pdiu <int>, …Identify number of missing points by strata between sample and collected data
20.3 Unequal Probability Sampling
UPbrewer()
UPmaxentropy()
UPmidzuno()
UPmidzunopi2()
UPmultinomial()
UPpivotal()
UPrandompivotal()
UPpoisson()
UPsampford()
UPsystematic()
UPrandomsystematic()
UPsystematicpi2()
UPtille()
UPtillepi2()20.4 Balanced Sampling
Purpose: to get the same means in the population and the sample for all the auxiliary variables
Balanced sampling is different from purposive selection
Balancing equations
\[ \sum_{k \in S} \frac{\mathbf{x}_k}{\pi_k} = \sum_{k \in U} \mathbf{x}_k \]
where \(\mathbf{x}_k\) is a vector of auxiliary variables
20.4.2 Stratification
- Try to replicate the population based on the original multivariate histogram