PracTools (version 1.6)

clusOpt2fixedPSU: Optimal number of sample elements per PSU in a two-stage sample when the sample of PSUs is fixed

Description

Compute the optimum number of sample elements per primary sampling unit (PSU) for a fixed set of PSUs

Usage

clusOpt2fixedPSU(C1, C2, m, delta, unit.rv, k=1, CV0=NULL, tot.cost, cal.sw)

Value

List with values:

C1

unit cost per PSU

C2

unit cost per element

m

number of (fixed) sample PSUs

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

n

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 PSU

C2

unit cost per element

m

number of sample PSU's (fixed)

delta

homogeneity measure

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 \(\bar{n}\) for fixed total budget; 2 = find optimal \(\bar{n}\) for target CV0

Author

Richard Valliant, Jill A. Dever, Frauke Kreuter

Details

clusOpt2fixedPSU will compute \(\bar{n}_{opt}\) for a two-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second. The PSU sample is fixed.

References

Valliant, R., Dever, J., Kreuter, F. (2018, sect. 9.3.3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt3, clusOpt3fixedPSU

Examples

    # optima for a vector of budgets
clusOpt2fixedPSU(C1=500, C2=100, m=100, delta=0.05, unit.rv=2, k=1, CV0=NULL,
       tot.cost=c(100000, 500000, 10^6), cal.sw=1)
    # optima for a target CV and vector of PSU costs
clusOpt2fixedPSU(C1=c(500,1000,5000), C2=100, m=100, delta=0.05, unit.rv=2, k=1,
       CV0=0.05, tot.cost=NULL, cal.sw=2)