clusOpt3fixedPSU {PracTools}

Compute optimal number of sample secondary sampling units (SSUs) and elements per SSU for a fixed set of primary sampling units (PSUs) in 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 when the PSU sample is fixed.

Usage

clusOpt3fixedPSU(unit.cost, m, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL,
         tot.cost=NULL, cal.sw)

Arguments

unit.cost

3-vector of unit costs: C1 = unit cost per PSU; C2 = unit cost per SSU; C3 = unit cost per element

m

number of sample PSUs (fixed)

delta1

homogeneity measure among elements within PSUs

delta2

homogeneity measure among elements within SSUs

unit.rv

unit relvariance

k1

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

k2

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

CV0

target CV

tot.cost

total budget for variable costs, including PSU 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 \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. The set of sample PSUs is assumed to be fixed. "Variable costs" in tot.cost includes the budget for all costs that vary with the number of sample PSUs, SSUs, and elements, i.e., C_{1}m + C_{2}m\bar{n} + C_{3}m\bar{n}\bar{\bar{q}}.

Value

List with values:

C1

unit cost per PSU

C2

unit cost per SSU

C3

unit cost per element

m

number of sample PSUs (fixed)

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 unit relvariance

k2

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

cost

budget constraint, tot.cost if cal.sw=1; computed cost if cal.sw=2

n

optimum number of sample SSUs per PSU

q

optimum number of sample elements per SSU

CV

achieved CV, used if cal.sw=1; or target CV, used if cal.sw=2

CV check

computed CV based on optimal sample sizes; used only 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. (2018, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt2fixedPSU, clusOpt3

Examples

    # optima for a fixed total budget
clusOpt3fixedPSU(unit.cost=c(500, 100, 120), m=100, delta1=0.01, delta2=0.05, unit.rv=1,
     k1=1, k2=1, tot.cost=500000,cal.sw=1)
    # optima for a target CV
clusOpt3fixedPSU(unit.cost=c(500, 100, 120), m=100, delta1=0.01, delta2=0.05, unit.rv=1,
     k1=1, k2=1, CV0=0.05,cal.sw=2)