clusOpt2 {PracTools}

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)

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

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.

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

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

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)