BSSM_FC {MultAlloc}

Optimal Allocation - Minimum Sample Size

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)