MultAlloc (version 1.2)

BSSM_FD: Optimal Allocation - Minimum Sum of Relative Variances

Description

Allocation of the overall sample size n to the strata for the following purpose: A weighted sum of variances (or relative variances) of the estimates of totals for the m survey variables is minimized.

Usage

BSSM_FD(Nh,Sh2j,Yj,Cust,nmin,ch,w,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

Cust

Corresponds to the overall variable cost budget for the survey C

nmin

Smallest possible sample size in any stratum

ch

Vector with the unit level survey costs for sampling from stratum h

w

Vector with Variable-specific weights, set a priori to represent the relative importance of the survey variables

certain

if (nH=NH) => certain=TRUE else certain=FALSE

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)

Details

Function that uses an integer programming formulation

References

Brito, J.A.M, Silva, P.L.N.,Semaan, G.Srogramming Formulations Applied to Optimal Allocation in Stratified Sampling. Survey Methodology, 41, No.2, pp.427-442.

See Also

BSSM_FC

Examples

#Example1
#Unit level survey costs for sampling from the strata are assumed to be the same.
#Number of survey variables (m=2) and seven strata (H=7)
#ch=1 ==> Cust = n
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))
n<-200 #sample size
result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n)

#Example2
#Unit level survey costs for sampling from the strata are assumed to be the same.
#ch=1 ==> Cust = n
#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))
nmin<-20
n<-200
result<-BSSM_FD(Nh,Sh2j,Yj,nmin,Cust=n)

#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))
n<-200
result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n,certain=TRUE)


#Example4
#Relative importance of the survey variables is different
w<-c(0.3,0.7)
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))
n<-200
result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n,w=w)


#Example5
#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)
n<-100
result<-BSSM_FD(Nh,Sh2j,Yj,Cust=n)