# 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

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 |

`CV0` |
target CV |

`tot.cost` |
total budget for variable costs |

`cal.sw` |
specify type of optimum:
1 = find optimal |

### 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 |

`cost` |
total budget for variable costs, |

`n` |
optimum number of sample elements per PSU |

`CV` |
computed CV if |

### 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.

### See Also

`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)
``` |