PracTools: clusOpt3fixedPSU – R documentation

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clusOpt3fixedPSU

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. (2013, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples. New York: Springer.

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

Tools for Designing and Weighting Survey Samples

v1.2.2

GPL (>= 2)

Authors