BSSM_FC: Optimal Allocation - Minimum Sample Size

In MultAlloc: Optimal Allocation in Stratified Sampling

Description

Allocation of the overall sample size n to the strata for the following purpose:

The total variable survey cost C (c1.n1+c2.n2+...+cH.nH)is minimized, subject to having Coefficients of Variation (CVs) for the estimates of totals of the m survey variables below specified thresholds.

If the unit level survey costs for sampling from the various strata are unknown or are assumed to be the same, then c1,c2,...,cH may all be set to one and the alternative objective function to minimize is n1+n2+...+nH.

Usage

BSSM_FC(Nh,Sh2j,Yj,cvt,nmin,ch,certain)

Arguments

Nh	Vector with total number of population units in each stratum (h=1,...,H)
Sh2j	Matrix (or vector) mxH (m = number of variables and H =number of strata) with Population variance for each variable of the hth stratum
Yj	Vector with population total Yj for the jth survey variable
cvt	Vector with target cvs asociated with survey variables
nmin	Smallest possible sample size in any stratum
ch	Vector with the unit level survey costs for sampling from stratum h
certain	if (nH=NH) => certain=TRUE else certain=FALSE

Details

Function that uses an integer programming formulation

Value

n	Sample size
nh	Sample of size by stratum
cvs	Coefficients of variation for the estimators of totals of the survey variables considered
time_cpu	Time consumed by the algorithm (seconds)

Author(s)

Jose Brito ([e-mail]), Pedro Silva, Gustavo Semaan and Nelson Maculan

References

Brito, J.A.M, Silva, P.L.N.,Semaan, G.S. and Maculan, N. (2015). Integer Programming Formulations Applied to Optimal Allocation in Stratified Sampling. Survey Methodology, 41, No.2, pp.427-442.

See Also

BSSM_FD

Examples

#Example1 - Number of survey variables (m=2) and seven strata (H=7)
Nh<-c(49,78,20,39,73,82,89)
Yj<-c(542350,56089251)
Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505),
            c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806))
cvt<-c(0.02,0.02)
result<-BSSM_FC(Nh,Sh2j,Yj,cvt)

#Example2
#nmin>2
Nh<-c(49,78,20,39,73,82,89)
Yj<-c(542350,56089251)
Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505),
            c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806))
cvt<-c(0.1,0.1)
nmin<-20
result<-BSSM_FC(Nh,Sh2j,Yj,cvt,nmin)

#Example3
#certain=TRUE
Nh<-c(49,78,20,39,73,82,89)
Yj<-c(542350,56089251)
Sh2j<-rbind(c(4436978,5581445,33454902,5763294,8689167,3716130,13938505),
            c(11034299660,40919330279,33519355946,18228286901,74247764986,49062224184,5783096806))
cvt<-c(0.1,0.1)
result<-BSSM_FC(Nh,Sh2j,Yj,cvt,certain=TRUE)


#Example4
#Number of survey variables m=1
Nh<-c(49,78,20,39,73,82,89)
Yj<-542350
Sh2j<-c(4436978,5581445,33454902,5763294,8689167,3716130,13938505)
cvt<-0.1
result<-BSSM_FC(Nh,Sh2j,Yj,cvt)

MultAlloc documentation built on May 2, 2019, 3:59 p.m.