23.4 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

23.4.1 Cube

• flight phase

• landing phase

samplecube()
fastflightcube()
landingcube()

23.4.2 Stratification

• Try to replicate the population based on the original multivariate histogram

library(survey)
data("api")
srs_design <- svydesign(data = apistrat,
                        weights = ~pw, 
                        fpc = ~fpc, 
                        strata = ~stype,
                        id = ~1)

balancedstratification()

23.4.3 Cluster

library(survey)
data("api")
srs_design <- svydesign(data = apiclus1,
                        weights = ~pw, 
                        fpc = ~fpc, 
                        id = ~dnum)

balancedcluster()

23.4.4 Two-stage

library(survey)
data("api")
srs_design <- svydesign(data = apiclus2, 
                        fpc = ~fpc1 + fpc2, 
                        id = ~ dnum + snum)

balancedtwostage()