PracTools (version 1.6)

clusOpt2: Compute optimal sample sizes for a two-stage sample

Description

Compute the sample sizes that minimize the variance of the pwr-estimator of a total in a two-stage sample.

Usage

clusOpt2(C1, C2, delta, unit.rv, k=1, CV0=NULL, tot.cost=NULL, cal.sw)

Value

List with values:

C1

unit cost per PSU

C2

unit cost per element

delta

homogeneity measure

unit relvar

unit relvariance

k

ratio of \(B^2 + W^2\) to unit relvariance

cost

total budget for variable costs, \(C-C_{0}\) if cal.sw=1; or computed cost if cal.sw=2

m.opt

optimum number of sample PSUs

n.opt

optimum number of sample elements per PSU

CV

computed CV if cal.sw=1; or target CV if cal.sw=2

Arguments

C1

unit cost per primary sampling unit (PSU)

C2

unit cost per element

delta

homogeneity measure \(\delta\)

unit.rv

unit relvariance

k

ratio of \(B^2 + W^2\) to unit relvariance

CV0

target CV

tot.cost

total budget for variable costs

cal.sw

specify type of optimum: 1 = find optimal m.opt for fixed total budget; 2 = find optimal m.opt for target CV0

Author

Richard Valliant, Jill A. Dever, Frauke Kreuter

Details

clusOpt2 will compute \(m_{opt}\) and \(\bar{n}_{opt}\) for a two-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second.

References

Hansen,M.H., Hurwitz,W.N., and Madow,W.G. (1953, chap. 6, sect. 16). Sample Survey Methods and Theory, Vol.I. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.1). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2fixedPSU, clusOpt3, clusOpt3fixedPSU

Examples

    # optimum for a fixed total budget
clusOpt2(C1=750, C2=100, delta=0.05, unit.rv=1, k=1, tot.cost=100000, cal.sw=1)
clusOpt2(C1=750, C2=100, delta=seq(0.05,0.25,0.05), unit.rv=1, k=1, tot.cost=100000, cal.sw=1)
    # optimum for a target CV
clusOpt2(C1=750, C2=100, delta=0.01, unit.rv=1, k=1, CV0=0.05, cal.sw=2)