View source: R/clusOpt3fixedPSU.R
clusOpt3fixedPSU  R Documentation 
Compute the sample sizes that minimize the variance of the pwrestimator of a total in a threestage sample when the PSU sample is fixed.
clusOpt3fixedPSU(unit.cost, m, delta1, delta2, unit.rv, k1=1, k2=1, CV0=NULL, tot.cost=NULL, cal.sw)
unit.cost 
3vector of unit costs:

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 
clusOpt3
will compute \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. 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}}.
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, 
n 
optimum number of sample SSUs per PSU 
q 
optimum number of sample elements per SSU 
CV 
achieved CV, used if 
CV check 
computed CV based on optimal sample sizes; used only if 
Richard Valliant, Jill A. Dever, Frauke Kreuter
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. (2018, sect. 9.3.2). Practical Tools for Designing and Weighting Survey Samples, 2nd edition. New York: Springer.
clusOpt2
, clusOpt2fixedPSU
, clusOpt3
# 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)
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