# clusOpt2fixedPSU: Optimal number of sample elements per PSU in a two-stage... In PracTools: Tools for Designing and Weighting Survey Samples

 clusOpt2fixedPSU R Documentation

## 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

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. (2018, sect. 9.3.3). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.

clusOpt2, clusOpt3, clusOpt3fixedPSU

### Examples

    # 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)


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