Compute optimal sample sizes for a threestage sample
Description
Compute the sample sizes that minimize the variance of the pwrestimator of a total in a threestage sample.
Usage
1 
Arguments
unit.cost 
vector with three components for unit costs:

delta1 
homogeneity measure among elements within PSUs 
delta2 
homogeneity measure among elements within SSUs 
unit.rv 
population unit relvariance 
k1 
ratio of B^2 + W^2 to the population unit relvariance 
k2 
ratio of W_{2}^2 + W_{3}^2 to the population unit relvariance 
CV0 
target CV 
tot.cost 
total budget for variable costs 
cal.sw 
specify type of optimum:
1 = find optimal 
Details
clusOpt3
will compute m_{opt}, \bar{n}_{opt}, and \bar{\bar{q}}_{opt}
for a threestage sample which uses simple random sampling at each stage or ppswr
at the first stage and srs at the second and third stages.
Value
List with values:
C1 
unit cost per PSU 
C2 
unit cost per SSU 
C3 
unit cost per element 
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 the population unit relvariance 
k2 
ratio of W_{2}^2 + W_{3}^2 to the population unit relvariance 
cost 
total budget for variable costs if 
m.opt 
optimum number of sample PSUs 
n.opt 
optimum number of sample SSUs per PSU 
q.opt 
optimum number of sample elements per SSU 
CV 
achieved CV if 
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.
See Also
clusOpt2
, clusOpt2fixedPSU
, clusOpt3fixedPSU
Examples
1 2 3 4 5 6 
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