| Title: | Optimal Allocation in Stratified Sampling |
|---|---|
| Description: | Integer Programming Formulations Applied to Univariate and Multivariate Allocation Problems. |
| Authors: | Jose Brito, Pedro Silva, Nelson Maculan and Gustavo Semaan |
| Maintainer: | Jose Brito <[email protected]> |
| License: | GPL-2 |
| Version: | 1.2 |
| Built: | 2025-01-26 19:16:07 UTC |
| Source: | https://github.com/cranhaven/cranhaven.r-universe.dev |
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.
BSSM_FC(Nh,Sh2j,Yj,cvt,nmin,ch,certain)BSSM_FC(Nh,Sh2j,Yj,cvt,nmin,ch,certain)
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 |
Function that uses an integer programming formulation
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) |
Jose Brito ([email protected]), Pedro Silva, Gustavo Semaan and Nelson Maculan
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.
BSSM_FD
#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)#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)
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.
BSSM_FD(Nh,Sh2j,Yj,Cust,nmin,ch,w,certain)BSSM_FD(Nh,Sh2j,Yj,Cust,nmin,ch,w,certain)
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 |
Function that uses an integer programming formulation
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) |
Jose Brito ([email protected]), Pedro Silva, Gustavo Semaan and Nelson Maculan
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.
BSSM_FC
#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)#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)