# clusOpt3fixedPSU: Compute optimal number of sample secondary sampling units... In PracTools: Tools for Designing and Weighting Survey Samples

 clusOpt3fixedPSU R Documentation

## 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.

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)


PracTools documentation built on Aug. 17, 2022, 5:06 p.m.