clusOpt3: Compute optimal sample sizes for a three-stage sample

In PracTools: Tools for Designing and Weighting Survey Samples

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

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. (2018, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

See Also

clusOpt2, clusOpt2fixedPSU, clusOpt3fixedPSU

Examples

    # 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)

PracTools documentation built on Nov. 9, 2023, 9:06 a.m.