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

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

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

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.

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

Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

References

Valliant, R., Dever, J., Kreuter, F. (2013, sect. 9.3.3). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

See Also

clusOpt2, clusOpt3, clusOpt3fixedPSU

Examples

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    # 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)

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