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

## Description

Compute the optimum number of sample elements per primary sampling unit (PSU) for a fixed set of PSUs

## Usage

 1 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. (2013, sect. 9.3.3). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

clusOpt2, clusOpt3, clusOpt3fixedPSU

## Examples

 1 2 3 4 5 6  # 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) 

### Example output



C1 = 500
C2 = 100
m = 100
delta = 0.05
unit relvar = 2
k = 1
cost = 1e+05, 5e+05, 1e+06
n = 5, 45, 95
CV = 0.0693, 0.0377, 0.0346

Warning message:
In if (n < 0) stop(paste("n is negative. Check inputs. n=", n, "\n")) :
the condition has length > 1 and only the first element will be used

C1 = 500, 1000, 5000
C2 = 100
delta = 0.05
m = 100
unit relvar = 2
k = 1
cost = 176666.7, 226666.7, 626666.7
n = 12.7
CV = 0.05


PracTools documentation built on June 13, 2018, 9:03 a.m.