Compute optimal sample sizes for a three-stage sample

Description

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

Usage

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clusOpt3(unit.cost, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL, tot.cost=NULL, cal.sw)

Arguments

unit.cost

vector with three components for unit costs: C1 = unit cost per primary sampling unit (PSU); C2 = unit cost per secondary sampling unit (SSU); C3 = unit cost per element

delta1

homogeneity measure among elements within PSUs

delta2

homogeneity measure among elements within SSUs

unit.rv

population unit relvariance

k1

ratio of B^2 + W^2 to the population unit relvariance

k2

ratio of W_{2}^2 + W_{3}^2 to the population 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

clusOpt3 will compute m_{opt}, \bar{n}_{opt}, and \bar{\bar{q}}_{opt} for a three-stage sample which uses simple random sampling at each stage or ppswr at the first stage and srs at the second and third stages.

Value

List with values:

C1

unit cost per PSU

C2

unit cost per SSU

C3

unit cost per element

delta1

homogeneity measure among elements within PSUs

delta2

homogeneity measure among elements within SSUs

unit relvar

unit relvariance

k1

ratio of B^2 + W^2 to the population unit relvariance

k2

ratio of W_{2}^2 + W_{3}^2 to the population unit relvariance

cost

total budget for variable costs if cal.sw=1; or computed cost if cal.sw=2

m.opt

optimum number of sample PSUs

n.opt

optimum number of sample SSUs per PSU

q.opt

optimum number of sample elements per SSU

CV

achieved 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, p. 225). Sample Survey Methods and Theory, Vol.II. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2013, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

See Also

clusOpt2, clusOpt2fixedPSU, clusOpt3fixedPSU

Examples

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    # optima for a fixed total budget
clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1,
       k1=1, k2=1, tot.cost=100000,cal.sw=1)
    # optima for a target CV
clusOpt3(unit.cost=c(500, 100, 120), delta1=0.01, delta2=0.10, unit.rv=1,
       k1=1, k2=1, CV0=0.01,cal.sw=2)

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