| Title: | Probabilistic Sampling Design and Strategies |
|---|---|
| Description: | It allows the user to determine sample sizes, select probabilistic samples, make estimates of different parameters for the total finite population and in studio domains, using the main design drawings. |
| Authors: | Jorge Barón [aut, cre, cph], Guillermo Martínez [aut] |
| Maintainer: | Jorge Barón <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 2.0 |
| Built: | 2024-12-18 06:27:11 UTC |
| Source: | CRAN |
This package provides functions for selecting a sample and estimating parameters such as total, mean, proportion and ratio; through the main sampling designs.
Index of help topics:
BER Bernoulli Sampling Design
CONGL Conglomerate Sampling
ESTRAT Stratified Sampling
M.MET Multi-Stage Sampling
MAS Simple Random Sampling Design without
Replacement
MCR Simple Random Sampling Design with Replacement
PPT Sampling Design with Replacement and Size
Proportional Selection Probabilities
PiPT Sampling Design without Replacement with
Proportional Inclusion Probabilities for Sizes
ProbSamplingI-package Design and Sampling Strategies for Parameter
Estimation and Sample Size Determination.
R.SIS R-Systematic Sampling Design
WHICH1 Positions of the components of a vector with
respect to another vector
n.ESTMAS Sample Size Through Stratified Sampling
n.MAS Sample Size Using Simple Random Sampling Design
Without Replacement
n.MASC Sample size using simple random sampling design
without conglomerate replacement.
Application of probabilistic sampling
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Maintainer: Jorge Alberto Barón Cárdenas <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
The BER function selects a random sample or estimates an interest parameter under a Bernoulli design.
BER(N,Pi,yk=NULL,zk=NULL,dk=NULL,type="selec",parameter="total", Nc=0.95,Ek=NULL) # To selectionar: BER(N,Pi) # To estimate: BER(yk,Pi,type="estm",parameter="total") # To estimate in domains: BER(yk,Pi,type="estm.Ud",parameter="total")BER(N,Pi,yk=NULL,zk=NULL,dk=NULL,type="selec",parameter="total", Nc=0.95,Ek=NULL) # To selectionar: BER(N,Pi) # To estimate: BER(yk,Pi,type="estm",parameter="total") # To estimate in domains: BER(yk,Pi,type="estm.Ud",parameter="total")
N |
Size of the population. |
Pi |
Probability of inclusion. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if "type" is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will perform the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case the type is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results using the Bernoulli sampling design, depending on the "type" argument, which indicates whether you want to select a sample ("select") or estimate a parameter ("estm" or "estm.Ud").
If type="select", the function returns a list with two elements:
Ksel |
Vector with the positions of the selected individuals. |
nk |
Selected sample size. |
If type="estm" or type="estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percentage), a confidence interval and the design effect.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
yk<-rnorm(100,10,2) zk<-rnorm(100,10,2) yk.p<-as.factor(ifelse(yk>10,1,0)) selection<-BER(N=100,Pi=0.3,type="selec") BER(yk=yk[selection$Ksel],Pi=0.3,type="estm",parameter="total") BER(Pi=0.3,yk=yk[selection$Ksel],type="estm",parameter="mean") BER(yk=yk.p[selection$Ksel],Pi=0.3,type="estm",parameter="prop") BER(yk=yk[selection$Ksel],zk=zk[selection$Ksel],Pi=0.3, type="estm",parameter="ratio") # Domain Estimates #Sex<-sample(2,100,replace=T) Sex<-rep(1:2,each=50) dk<-factor(Sex,labels=c("Man","Woman")) BER(yk=yk[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="total") BER(yk=yk[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="mean") BER(yk=yk.p[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="prop") BER(yk=yk[selection$Ksel],zk=zk[selection$Ksel], dk=dk[selection$Ksel],Pi=0.3,type="estm.Ud",parameter="ratio")yk<-rnorm(100,10,2) zk<-rnorm(100,10,2) yk.p<-as.factor(ifelse(yk>10,1,0)) selection<-BER(N=100,Pi=0.3,type="selec") BER(yk=yk[selection$Ksel],Pi=0.3,type="estm",parameter="total") BER(Pi=0.3,yk=yk[selection$Ksel],type="estm",parameter="mean") BER(yk=yk.p[selection$Ksel],Pi=0.3,type="estm",parameter="prop") BER(yk=yk[selection$Ksel],zk=zk[selection$Ksel],Pi=0.3, type="estm",parameter="ratio") # Domain Estimates #Sex<-sample(2,100,replace=T) Sex<-rep(1:2,each=50) dk<-factor(Sex,labels=c("Man","Woman")) BER(yk=yk[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="total") BER(yk=yk[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="mean") BER(yk=yk.p[selection$Ksel],dk=dk[selection$Ksel],Pi=0.3, type="estm.Ud",parameter="prop") BER(yk=yk[selection$Ksel],zk=zk[selection$Ksel], dk=dk[selection$Ksel],Pi=0.3,type="estm.Ud",parameter="ratio")
The CONGL function selects a random sample or estimates a parameter of interest under a cluster sampling design
CONGL(Argt,cong,design="MAS",type="selec",parameter="total",yk=NULL, zk=NULL,dk=NULL,Ek=NULL,Nc=0.95) # To select: CONGL(Argt=Argt,design) # To estimate: CONGL(yk,cong,Argt,design,type="estm") # To estimate in domains: CONGL(yk,dk,cong,Argt,design,type="estm.Ud") # If the objective is to select a sample, the Argt argument is constructed as follows: # "MAS": Argt<-list(NI,nI) # "MCR": Argt<-list(NI,mI) # "BER": Argt<-list(NI,PiI) # "PPT": Argt<-list(txkI,mI) # "PiPT": Argt<-list(txkI,nI) # If the objective is to estimate a parameter of interest, the Argt argument is # constructed as follows: # "MAS": Argt<-list(NI,nI) # "MCR": Argt<-list(NI,mI) # "BER": Argt<-list(NI,PiI) # "PPT": Argt<-list(pkI) # "PiPT": Argt<-list(pikI,mpiklI)CONGL(Argt,cong,design="MAS",type="selec",parameter="total",yk=NULL, zk=NULL,dk=NULL,Ek=NULL,Nc=0.95) # To select: CONGL(Argt=Argt,design) # To estimate: CONGL(yk,cong,Argt,design,type="estm") # To estimate in domains: CONGL(yk,dk,cong,Argt,design,type="estm.Ud") # If the objective is to select a sample, the Argt argument is constructed as follows: # "MAS": Argt<-list(NI,nI) # "MCR": Argt<-list(NI,mI) # "BER": Argt<-list(NI,PiI) # "PPT": Argt<-list(txkI,mI) # "PiPT": Argt<-list(txkI,nI) # If the objective is to estimate a parameter of interest, the Argt argument is # constructed as follows: # "MAS": Argt<-list(NI,nI) # "MCR": Argt<-list(NI,mI) # "BER": Argt<-list(NI,PiI) # "PPT": Argt<-list(pkI) # "PiPT": Argt<-list(pikI,mpiklI)
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if "type"" is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will make the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
Argt |
List with the necessary arguments to select or estimate by the design that you want to use. |
cong |
Vector indicating which cluster each individual belongs to. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
design |
Sampling sampling design to be implemented ("BER", "MAS", "MCR", "PPT", "SIS" or "PiPT"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case "type" is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results under the cluster sampling design, depending on the "type" argument, which indicates whether to select a sample ("select") or to estimate an interest parameter ("estm", "estm.Ud"). The results obtained in each case depend on the design implemented, in this way, such results are the same ones obtained for the case of element sampling, but nevertheless in the estimation of the total the intra-sample rate of variance is appended (IVI).
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
yk<-rnorm(120,10,2) zk<-rnorm(120,12,2) yk.p<-as.factor(ifelse(yk>10,1,0)) cong<-rep(1:12,each=10);cong Sex<-rep(1:2,each=60) dk<-factor(Sex,labels=c("Man","Woman")) tyi<-tapply(yk,cong,sum) txkI<-runif(12,0.95,1.1)*tyi cor(tyi,txkI) D1<-data.frame(cong,yk,yk.p,zk,dk) # MAS-CONGLOMERATE Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="MAS", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm", parameter="prop") #MCR-CONGLOMERATE Argt<-list(NI=10,mI=3) selection<-CONGL(Argt=Argt,design="MCR") D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:3,Ni) CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="MCR",type="estm") CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="MCR",type="estm",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=cong.s,Argt=Argt,design="MCR",type="estm", parameter="ratio") CONGL(yk=D.sel$yk.p,cong=cong.s,Argt=Argt,design="MCR",type="estm",parameter="prop") #BER-CONGLOMERATE Argt<-list(NI=10,PiI=0.4) selection<-CONGL(Argt=Argt,design="BER") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="BER",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="BER",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="BER", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="BER",type="estm", parameter="prop") #PPT-CONGLOMERATE Argt<-list(txkI=txkI,mI=4) selection<-CONGL(Argt=Argt,design="PPT") ;selection Argt<-list(pkI=selection$pksel) D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:4,Ni) CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="PPT",type="estm") CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="PPT",type="estm",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=cong.s,Argt=Argt,design="PPT",type="estm", parameter="ratio") CONGL(yk=D.sel$yk.p,cong=cong.s,Argt=Argt,design="PPT",type="estm",parameter="prop") #PiPT-CONGLOMERATE Argt<-list(txkI=txkI,nI=4) selection<-CONGL(Argt=Argt,design="PiPT") Argt<-list(pikI=selection$piksel,mpiklI=selection$mpikl.s) D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="PiPT", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm", parameter="prop") # Domain Estimate # MAS-CONGLOMERATE Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="prop") # Domain Estimate # MCR-CONGLOMERATE Argt<-list(NI=10,mI=3) selection<-CONGL(Argt=Argt,design="MCR") D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:3,Ni) CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=cong.s,Argt=Argt, design="MCR",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=cong.s,Argt=Argt,design="MCR", type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,dk=D.sel$dk,cong=cong.s,Argt=Argt, design="MCR",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=cong.s,Argt=Argt,design="MCR", type="estm.Ud",parameter="prop") # Domain Estimate # BER-CONGLOMERATE Argt<-list(NI=10,PiI=0.4) selection<-CONGL(Argt=Argt,design="BER") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,dk=D.sel$dk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="prop")yk<-rnorm(120,10,2) zk<-rnorm(120,12,2) yk.p<-as.factor(ifelse(yk>10,1,0)) cong<-rep(1:12,each=10);cong Sex<-rep(1:2,each=60) dk<-factor(Sex,labels=c("Man","Woman")) tyi<-tapply(yk,cong,sum) txkI<-runif(12,0.95,1.1)*tyi cor(tyi,txkI) D1<-data.frame(cong,yk,yk.p,zk,dk) # MAS-CONGLOMERATE Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="MAS", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="MAS",type="estm", parameter="prop") #MCR-CONGLOMERATE Argt<-list(NI=10,mI=3) selection<-CONGL(Argt=Argt,design="MCR") D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:3,Ni) CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="MCR",type="estm") CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="MCR",type="estm",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=cong.s,Argt=Argt,design="MCR",type="estm", parameter="ratio") CONGL(yk=D.sel$yk.p,cong=cong.s,Argt=Argt,design="MCR",type="estm",parameter="prop") #BER-CONGLOMERATE Argt<-list(NI=10,PiI=0.4) selection<-CONGL(Argt=Argt,design="BER") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="BER",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="BER",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="BER", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="BER",type="estm", parameter="prop") #PPT-CONGLOMERATE Argt<-list(txkI=txkI,mI=4) selection<-CONGL(Argt=Argt,design="PPT") ;selection Argt<-list(pkI=selection$pksel) D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:4,Ni) CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="PPT",type="estm") CONGL(yk=D.sel$yk,cong=cong.s,Argt=Argt,design="PPT",type="estm",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=cong.s,Argt=Argt,design="PPT",type="estm", parameter="ratio") CONGL(yk=D.sel$yk.p,cong=cong.s,Argt=Argt,design="PPT",type="estm",parameter="prop") #PiPT-CONGLOMERATE Argt<-list(txkI=txkI,nI=4) selection<-CONGL(Argt=Argt,design="PiPT") Argt<-list(pikI=selection$piksel,mpiklI=selection$mpikl.s) D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm") CONGL(yk=D.sel$yk,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm", parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt,design="PiPT", type="estm",parameter="ratio") CONGL(yk=D.sel$yk.p,cong=D.sel$cong,Argt=Argt,design="PiPT",type="estm", parameter="prop") # Domain Estimate # MAS-CONGLOMERATE Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="MAS",type="estm.Ud",parameter="prop") # Domain Estimate # MCR-CONGLOMERATE Argt<-list(NI=10,mI=3) selection<-CONGL(Argt=Argt,design="MCR") D.sel<-D1[WHICH1(selection$Ksel,cong),] Ni<-table(cong)[selection$Ksel] cong.s<-rep(1:3,Ni) CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=cong.s,Argt=Argt, design="MCR",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=cong.s,Argt=Argt,design="MCR", type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,zk=D.sel$zk,dk=D.sel$dk,cong=cong.s,Argt=Argt, design="MCR",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=cong.s,Argt=Argt,design="MCR", type="estm.Ud",parameter="prop") # Domain Estimate # BER-CONGLOMERATE Argt<-list(NI=10,PiI=0.4) selection<-CONGL(Argt=Argt,design="BER") D.sel<-D1[WHICH1(selection$Ksel,cong),] CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud") CONGL(yk=D.sel$yk,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="mean") CONGL(yk=D.sel$yk,dk=D.sel$dk,zk=D.sel$zk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="ratio") CONGL(yk=D.sel$yk.p,dk=D.sel$dk,cong=D.sel$cong,Argt=Argt, design="BER",type="estm.Ud",parameter="prop")
The ESTRAT function selects a random sample or estimates an interest parameter under a stratified sampling.
ESTRAT(strata,designs,nh,xk=NULL,yk=NULL,zk=NULL,dk=NULL,type="selec", Argt,parameter="total",rh=NULL,Ek=NULL,Nc=0.95) # To select: ESTRAT(strata,nh,designs,xk,rh) # To estimate: ESTRAT(yk,zk,strata,designs,type="estm",Argt,parameter) # To estimate in domains: ESTRAT(yk,zk,dk,strata,designs,type="estm",Argt,parameter)ESTRAT(strata,designs,nh,xk=NULL,yk=NULL,zk=NULL,dk=NULL,type="selec", Argt,parameter="total",rh=NULL,Ek=NULL,Nc=0.95) # To select: ESTRAT(strata,nh,designs,xk,rh) # To estimate: ESTRAT(yk,zk,strata,designs,type="estm",Argt,parameter) # To estimate in domains: ESTRAT(yk,zk,dk,strata,designs,type="estm",Argt,parameter)
strata |
Vector indicating which stratum each individual belongs to. |
nh |
Vector that indicates the number of individuals to select in each stratum. This argument is required if the type argument is equal to "select". |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
xk |
Vector of observations of the auxiliary variable. This vector is only necessary if it is desired to select in any stratum by means of a probability selection or inclusion probability proportional to size design. |
dk |
Factor that indicates the individuals that belong to each domain of interest, is only necessary if type is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will perform the estimation of the indicated parameter and if it is equal to "estm.Ud" will make an estimate in domain. |
designs |
Vector indicating the design to be used in each stratum ("BER", "MAS", "MCR", "PPT", "SIS" or "PiPT"). |
parameter |
This argument indicates the parameter to be estimated ("total", "average", "prop" or "reason"). |
Argt |
It is a list with the necessary arguments for the estimates under the respective designs used in the strata. |
rh |
Vector of size equal to the number of strata, necessary if it is desired to select under an r-sistematic design, which will have the number of starts to be used in the corresponding strata and zeros in the rest of the positions where this design is not used. |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case the type is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to population size. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results under the stratified sampling design depending on the "type" argument, which indicates whether to select ("select") or estimate ("estm", "estm.Ud"). If type is equal to "select" the function returns a list with two elements, the first is a data frame (Sample) in which one of its columns indicates the position of the selected individuals in each stratum and the second (Rtdos.h ) is a list with the results obtained in each stratum which are necessary when making a certain estimate. If type is equal to "est" or "estm.Ud", the function returns a list with two data frames with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percentage) and a confidence interval assuming normality; by stratum and in general.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
yk<-rnorm(1000,10,2) xk<-rnorm(1000,10,3) zk<-rnorm(1000,12,3) yk.p<-factor(ifelse(yk>10,"A","B")) strata<-rep(1:5,each=200) Sex<-rep(1:2,length=1000) dk<-factor(Sex,labels=c("Man","Woman")) nh<-c(60,40,40,60,80) designs<-c("MAS","MAS","MAS","MAS","MAS") select<-ESTRAT(strata=strata,designs=designs,nh=nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-as.factor(yk.p[select$Sample$IND]) zksel<-zk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="total") ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="mean") ESTRAT(yk=yk.psel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="prop") ESTRAT(yk=yksel,zk=zksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="ratio") designs<-c("PiPT","PPT","MAS","MCR","BER") select<-ESTRAT(xk=xk,strata=strata,designs=designs,nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-yk.p[select$Sample$IND] zksel<-zk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="total") ESTRAT(yk=yk.psel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="prop") ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="mean") ESTRAT(yk=yksel,zk=zksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="ratio") # Estimates in Domains designs<-c("MAS","MAS","MAS","MAS","MAS") select<-ESTRAT(strata=strata,designs=designs,nh=nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-yk.p[select$Sample$IND] zksel<-zk[select$Sample$IND] dksel<-dk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="total") ESTRAT(yk=yksel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="mean") ESTRAT(yk=yk.psel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="prop") ESTRAT(yk=yksel,zk=zksel,strata=Strata,dk=dksel,designs=designs, Argt=Argt,type="estm.Ud",parameter="ratio")yk<-rnorm(1000,10,2) xk<-rnorm(1000,10,3) zk<-rnorm(1000,12,3) yk.p<-factor(ifelse(yk>10,"A","B")) strata<-rep(1:5,each=200) Sex<-rep(1:2,length=1000) dk<-factor(Sex,labels=c("Man","Woman")) nh<-c(60,40,40,60,80) designs<-c("MAS","MAS","MAS","MAS","MAS") select<-ESTRAT(strata=strata,designs=designs,nh=nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-as.factor(yk.p[select$Sample$IND]) zksel<-zk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="total") ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="mean") ESTRAT(yk=yk.psel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="prop") ESTRAT(yk=yksel,zk=zksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="ratio") designs<-c("PiPT","PPT","MAS","MCR","BER") select<-ESTRAT(xk=xk,strata=strata,designs=designs,nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-yk.p[select$Sample$IND] zksel<-zk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="total") ESTRAT(yk=yk.psel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="prop") ESTRAT(yk=yksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="mean") ESTRAT(yk=yksel,zk=zksel,strata=Strata,designs=designs,Argt=Argt, type="estm",parameter="ratio") # Estimates in Domains designs<-c("MAS","MAS","MAS","MAS","MAS") select<-ESTRAT(strata=strata,designs=designs,nh=nh) Argt<-select$Rtdos.h Strata<-strata[select$Sample$IND] yksel<-yk[select$Sample$IND] yk.psel<-yk.p[select$Sample$IND] zksel<-zk[select$Sample$IND] dksel<-dk[select$Sample$IND] ESTRAT(yk=yksel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="total") ESTRAT(yk=yksel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="mean") ESTRAT(yk=yk.psel,strata=Strata,dk=dksel,designs=designs,Argt=Argt, type="estm.Ud",parameter="prop") ESTRAT(yk=yksel,zk=zksel,strata=Strata,dk=dksel,designs=designs, Argt=Argt,type="estm.Ud",parameter="ratio")
The M.MET function selects a random sample or estimates an interest parameter under multi-stage sampling (up to four stages).
M.MET(F.UM,designs,list.arg,p,type="selec",parameter="total",yk=NULL, zk=NULL,xk=NULL,dk=NULL,r=NULL,Nc=0.95) # To select: M.MET(F.UM=F.UM,p=p,designs) # To estimate: M.MET(yk,F.UM,p,designs,list.arg,type="estm",parameter)M.MET(F.UM,designs,list.arg,p,type="selec",parameter="total",yk=NULL, zk=NULL,xk=NULL,dk=NULL,r=NULL,Nc=0.95) # To select: M.MET(F.UM=F.UM,p=p,designs) # To estimate: M.MET(yk,F.UM,p,designs,list.arg,type="estm",parameter)
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
xk |
Vector of observations of the auxiliary variable. This vector is only necessary if you want to select using a layout that uses an auxiliary variable. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if type is equal to "estm.Ud". |
F.UM |
Data.frame that contains columns indicating which sampling unit each individual belongs to within each stage. |
p |
Vector indicating the proportion of individuals to be selected at each sampling stage. This argument is necessary if the type is equal to "select". |
designs |
Vector indicating the design to be used in each stage ("BER", "MAS", "MCR", "R.SIS", "PPT", "PiPT"). |
list.arg |
List of arguments required for the estimate |
r |
Number of starts, this argument is only necessary if a r-systematic design is used in the last step. |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will perform the estimation of the indicated parameter and if it is equal to "estm.Ud" will make an estimate in domain. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop" or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case the type is equal to "estm" or "estm.Ud". |
This function returns two types of results through the multi-stage sampling strategy that needs to be implemented, depending on the "type" argument, which indicates whether you want to select a sample ("select") or estimate a parameter ("estm" or "estm.Ud").
-If type="select", the function will return a list with two elements:
Sample |
Data frame with the location of the selected individuals |
Results |
List with the results obtained in each stage, which are necessary when making a certain estimate. |
-If type = "estm" or type = "estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percent) and a confidence interval.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
#Selection and estimation using a 4-stage sampling F.UPM<-rep(1:5,each=1000) F.USM<-rep(1:5,each=200,length=5000) F.UTM<-rep(1:10,each=20,length=5000) F.UCM<-rep(1:20,length=5000) F.UM<-data.frame(F.UPM,F.USM,F.UTM,F.UCM) p<-c(0.3,0.3,0.3,0.2) y<-rnorm(5000,10,2) z<-rnorm(5000,12,2) y.p<-as.factor(ifelse(y>10,"A","B")) Sex<-rep(1:2,length=5000) d<-factor(Sex,labels=c("Man","Woman")) designs<-c("MAS","MAS","MAS","MAS") select<-M.MET(F.UM=F.UM,p=p,designs=designs) F.UM.s<-select$Sample[6:8] yk<-y[select$Sample$IND] yk.p<-y.p[select$Sample$IND] zk<-z[select$Sample$IND] dk<-d[select$Sample$IND] list<-select$Results M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="total") M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="mean") M.MET(yk=yk.p,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="prop") M.MET(yk=yk,zk=zk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="ratio") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="total") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="mean") M.MET(yk=yk.p,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="prop") M.MET(yk=yk,zk=zk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="ratio") xk<-rnorm(5000,10,2) designs<-c("PiPT","MAS","PiPT","MAS") select2<-M.MET(xk=xk,F.UM=F.UM,p=p,designs=designs) F.UM.s<-select2$Sample[6:8] yk<-y[select2$Sample$IND] yk.p<-y.p[select2$Sample$IND] zk<-z[select2$Sample$IND] dk<-d[select2$Sample$IND] list<-select2$Results M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="total") M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="mean") M.MET(yk=yk.p,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="prop") M.MET(yk=yk,zk=zk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="ratio") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="total") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="mean") M.MET(yk=yk.p,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="prop") M.MET(yk=yk,zk=zk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="ratio")#Selection and estimation using a 4-stage sampling F.UPM<-rep(1:5,each=1000) F.USM<-rep(1:5,each=200,length=5000) F.UTM<-rep(1:10,each=20,length=5000) F.UCM<-rep(1:20,length=5000) F.UM<-data.frame(F.UPM,F.USM,F.UTM,F.UCM) p<-c(0.3,0.3,0.3,0.2) y<-rnorm(5000,10,2) z<-rnorm(5000,12,2) y.p<-as.factor(ifelse(y>10,"A","B")) Sex<-rep(1:2,length=5000) d<-factor(Sex,labels=c("Man","Woman")) designs<-c("MAS","MAS","MAS","MAS") select<-M.MET(F.UM=F.UM,p=p,designs=designs) F.UM.s<-select$Sample[6:8] yk<-y[select$Sample$IND] yk.p<-y.p[select$Sample$IND] zk<-z[select$Sample$IND] dk<-d[select$Sample$IND] list<-select$Results M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="total") M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="mean") M.MET(yk=yk.p,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="prop") M.MET(yk=yk,zk=zk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="ratio") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="total") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="mean") M.MET(yk=yk.p,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="prop") M.MET(yk=yk,zk=zk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="ratio") xk<-rnorm(5000,10,2) designs<-c("PiPT","MAS","PiPT","MAS") select2<-M.MET(xk=xk,F.UM=F.UM,p=p,designs=designs) F.UM.s<-select2$Sample[6:8] yk<-y[select2$Sample$IND] yk.p<-y.p[select2$Sample$IND] zk<-z[select2$Sample$IND] dk<-d[select2$Sample$IND] list<-select2$Results M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="total") M.MET(yk=yk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="mean") M.MET(yk=yk.p,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="prop") M.MET(yk=yk,zk=zk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm",parameter="ratio") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="total") M.MET(yk=yk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="mean") M.MET(yk=yk.p,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="prop") M.MET(yk=yk,zk=zk,dk=dk,F.UM=F.UM.s,p=p,designs=designs,list.arg=list, type="estm.Ud",parameter="ratio")
The MAS function selects a random sample or estimates a parameter of interest under a simple random sampling design without replacement.
MAS(N,n,yk=NULL,zk=NULL,dk=NULL,type="selec",method="fmuller", parameter="total",Nc=0.95,Ek=NULL) # To select: MAS(N,n,method="fmuller") # To estimate: MAS(yk,N,n,type="estm",parameter="total") # To estimate in domains: MAS(yk,dk,N,n,type="estm.Ud",parameter="total")MAS(N,n,yk=NULL,zk=NULL,dk=NULL,type="selec",method="fmuller", parameter="total",Nc=0.95,Ek=NULL) # To select: MAS(N,n,method="fmuller") # To estimate: MAS(yk,N,n,type="estm",parameter="total") # To estimate in domains: MAS(yk,dk,N,n,type="estm.Ud",parameter="total")
N |
Size of the population |
n |
Sample size. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if "type"" is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will make the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
method |
Indicates the method or selection mechanism. If Method is equal to "fmuller" the function uses the Fan-Muller method or if it is equal to "cnegative" the function uses the negative coordinate method. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case "type" is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results using the simple random sample design without replacement depending on the "type" argument, which indicates whether to select a sample ("select") or to estimate a parameter ("estm" or "estm.Ud").
If type="select", the function returns a list with a vector (Ksel) with the selected individuals' positions.
If type="estm" or type="estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percent) and an interval of trust.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martinez Florez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
zk<-rnorm(200,15,2) yk<-rnorm(200,10,3) yk.p<-as.factor(ifelse(yk>10,"A","B")) Sex<-rep(1:2,length=200) dk<-factor(Sex,labels=c("Man","Woman")) selection<-MAS(N=200,n=40,type="selec",method="fmuller") MAS(N=200,n=40,type="selec",method="cnegativo") MAS(yk=yk[selection$K],N=200,n=40,type="estm",parameter="total") MAS(yk=yk[selection$K],N=200,n=40,type="estm",parameter="mean") MAS(yk=yk.p[selection$K],N=200,n=40,type="estm",parameter="prop") MAS(yk=yk[selection$K],zk=zk[selection$K],N=200,n=40,type="estm", parameter="ratio") # Domain Estimate MAS(yk=yk[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="total") MAS(yk=yk[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="mean") MAS(yk=yk.p[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="prop") MAS(yk=yk[selection$K],zk=zk[selection$K],dk=dk[selection$K],N=200,n=40, type="estm.Ud",parameter="ratio")zk<-rnorm(200,15,2) yk<-rnorm(200,10,3) yk.p<-as.factor(ifelse(yk>10,"A","B")) Sex<-rep(1:2,length=200) dk<-factor(Sex,labels=c("Man","Woman")) selection<-MAS(N=200,n=40,type="selec",method="fmuller") MAS(N=200,n=40,type="selec",method="cnegativo") MAS(yk=yk[selection$K],N=200,n=40,type="estm",parameter="total") MAS(yk=yk[selection$K],N=200,n=40,type="estm",parameter="mean") MAS(yk=yk.p[selection$K],N=200,n=40,type="estm",parameter="prop") MAS(yk=yk[selection$K],zk=zk[selection$K],N=200,n=40,type="estm", parameter="ratio") # Domain Estimate MAS(yk=yk[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="total") MAS(yk=yk[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="mean") MAS(yk=yk.p[selection$K],dk=dk[selection$K],N=200,n=40,type="estm.Ud", parameter="prop") MAS(yk=yk[selection$K],zk=zk[selection$K],dk=dk[selection$K],N=200,n=40, type="estm.Ud",parameter="ratio")
The MCR function selects a random sample or estimates an interest parameter under a simple random sampling design without replacement.
MCR(N,m,yk=NULL,zk=NULL,dk=NULL,type="selec",parameter="total", Ek=NULL,Nc=0.95) # To select: MCR(N,m) # To estimate: MCR(yk,N,m,type="estm",parameter) # To domain estimate: MCR(yk,dk,N,m,type="est.Ud",parameter)MCR(N,m,yk=NULL,zk=NULL,dk=NULL,type="selec",parameter="total", Ek=NULL,Nc=0.95) # To select: MCR(N,m) # To estimate: MCR(yk,N,m,type="estm",parameter) # To domain estimate: MCR(yk,dk,N,m,type="est.Ud",parameter)
N |
Size of the population. |
m |
Sample size. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if type is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will make the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case the type is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results using the simple random sample design with replacement, depending on the "type" argument with which it is indicated to select a sample ("select") or to estimate a parameter ("estm" or "estm.Ud").
If type="select", the function returns a list with two elements:
Ksel |
Vector with the positions of the selected individuals. |
pksel |
Vector with the probabilities of selection of individuals. |
If type="estm" or type="estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percentage), a confidence interval and the design effect.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
yk<-rnorm(200,10,2) zk<-rnorm(200,15,3) yk.p<-as.factor(ifelse(yk>10,1,0)) selection<-MCR(N=200,m=40) MCR(yk=yk[selection$Ksel],N=200,m=40,type="estm",parameter="total") MCR(yk=yk[selection$Ksel],N=200,m=40,type="estm",parameter="mean") MCR(yk=yk.p[selection$Ksel],N=200,m=40,type="estm",parameter="prop") MCR(yk=yk[selection$Ksel],zk=zk[selection$Ksel],N=200,m=40, type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=200) dk<-factor(Sex,labels=c("Man","Woman")) MCR(yk=yk[selection$K],dk=dk[selection$K],N=200,m=40,type="estm.Ud") MCR(yk=yk[selection$K],dk=dk[selection$K],N=200,m=40,type="estm.Ud", parameter="mean") MCR(yk=yk.p[selection$Ksel],dk=dk[selection$K],N=200,m=40, type="estm.Ud",parameter="prop") MCR(yk=yk[selection$Ksel],zk=zk[selection$Ksel],dk=dk[selection$K], N=100,m=40,type="estm.Ud",parameter="ratio")yk<-rnorm(200,10,2) zk<-rnorm(200,15,3) yk.p<-as.factor(ifelse(yk>10,1,0)) selection<-MCR(N=200,m=40) MCR(yk=yk[selection$Ksel],N=200,m=40,type="estm",parameter="total") MCR(yk=yk[selection$Ksel],N=200,m=40,type="estm",parameter="mean") MCR(yk=yk.p[selection$Ksel],N=200,m=40,type="estm",parameter="prop") MCR(yk=yk[selection$Ksel],zk=zk[selection$Ksel],N=200,m=40, type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=200) dk<-factor(Sex,labels=c("Man","Woman")) MCR(yk=yk[selection$K],dk=dk[selection$K],N=200,m=40,type="estm.Ud") MCR(yk=yk[selection$K],dk=dk[selection$K],N=200,m=40,type="estm.Ud", parameter="mean") MCR(yk=yk.p[selection$Ksel],dk=dk[selection$K],N=200,m=40, type="estm.Ud",parameter="prop") MCR(yk=yk[selection$Ksel],zk=zk[selection$Ksel],dk=dk[selection$K], N=100,m=40,type="estm.Ud",parameter="ratio")
The n.ESTMAS function determines the sample size with its corresponding allocation by stratum, using a stratified sampling strategy, where a simple random sampling design with no replacement (ESTMAS) is applied in each stratum; taking into account whether the parameter of interest is the average (or total) or a proportion.
n.ESTMAS(Nh,Sh,Ch,Ph,Emax.a,Nc=0.95,parameter="mean",Asig="Optima") # n.ESTMAS(Nh,Sh,Ch,Emax.a,Nc=0.95,parameter="mean",Asig="Optima") # n.ESTMAS(Nh,Ph,Ch,Emax.a,Nc=0.95,parameter="prop",Asig="Optima") # n.ESTMAS(Nh,Sh,Emax.a,Nc=0.95,parameter="mean",Asig="Neyman") # n.ESTMAS(Nh,Ph,Emax.a,Nc=0.95,parameter="prop",Asig="Neyman") # n.ESTMAS(Nh,Sh,Emax.a,Nc=0.95,parameter="mean",Asig="Proportional") # n.ESTMAS(Nh,Ph,Emax.a,Nc=0.95,parameter="prop",Asig="Proportional")n.ESTMAS(Nh,Sh,Ch,Ph,Emax.a,Nc=0.95,parameter="mean",Asig="Optima") # n.ESTMAS(Nh,Sh,Ch,Emax.a,Nc=0.95,parameter="mean",Asig="Optima") # n.ESTMAS(Nh,Ph,Ch,Emax.a,Nc=0.95,parameter="prop",Asig="Optima") # n.ESTMAS(Nh,Sh,Emax.a,Nc=0.95,parameter="mean",Asig="Neyman") # n.ESTMAS(Nh,Ph,Emax.a,Nc=0.95,parameter="prop",Asig="Neyman") # n.ESTMAS(Nh,Sh,Emax.a,Nc=0.95,parameter="mean",Asig="Proportional") # n.ESTMAS(Nh,Ph,Emax.a,Nc=0.95,parameter="prop",Asig="Proportional")
Nh |
Numerical vector with the respective sizes of strata. |
Sh |
Numerical vector with the respective standard deviations of the variable of interest of each stratum. This argument is necessary only if the parameter of interest is the mean. |
Ch |
Numerical vector with the costs of sampling an element within each stratum. This argument is only necessary if the allocation by stratum is the optimal allocation. |
Ph |
Numerical vector with estimated proportions within each stratum. |
Emax.a |
Absolute maximum error. |
parameter |
Type of parameter to be estimated, either the mean or a proportion ("mean", "prop"). |
Nc |
Confidence level (between 0 and 1) that you want to set. |
Asig |
Assignment by stratum ("Optima", "Neyman" or "Proportional") |
This function returns the sample size and the allocation by stratum, through the conditions established in the arguments.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
Nc<-0.95 E<-0.3 Nh<-c(400,220,380) Sh<-sqrt(c(0.7521,1.4366,1.1361)) Ph<-c(0.4,0.2,0.6) Ch<-c(1000,1200,1500) # Optimal Assignment n.ESTMAS(Nh=Nh,Sh=Sh,Ch=Ch,E=E,Nc=0.95,parameter="mean",Asig="Optima") n.ESTMAS(Nh=Nh,Ph=Ph,Ch=Ch,E=E,Nc=0.95,parameter="prop",Asig="Optima") # Neyman Assignment n.ESTMAS(Nh=Nh,Sh=Sh,E=E,Nc=0.95,parameter="mean",Asig="Neyman") n.ESTMAS(Nh=Nh,Ph=Ph,E=E,Nc=0.95,parameter="prop",Asig="Neyman") # Proportional Assignment n.ESTMAS(Nh=Nh,Sh=Sh,E=E,Nc=0.95,parameter="mean",Asig="Proportional") n.ESTMAS(Nh=Nh,Ph=Ph,E=E,Nc=0.95,parameter="prop",Asig="Proportional")Nc<-0.95 E<-0.3 Nh<-c(400,220,380) Sh<-sqrt(c(0.7521,1.4366,1.1361)) Ph<-c(0.4,0.2,0.6) Ch<-c(1000,1200,1500) # Optimal Assignment n.ESTMAS(Nh=Nh,Sh=Sh,Ch=Ch,E=E,Nc=0.95,parameter="mean",Asig="Optima") n.ESTMAS(Nh=Nh,Ph=Ph,Ch=Ch,E=E,Nc=0.95,parameter="prop",Asig="Optima") # Neyman Assignment n.ESTMAS(Nh=Nh,Sh=Sh,E=E,Nc=0.95,parameter="mean",Asig="Neyman") n.ESTMAS(Nh=Nh,Ph=Ph,E=E,Nc=0.95,parameter="prop",Asig="Neyman") # Proportional Assignment n.ESTMAS(Nh=Nh,Sh=Sh,E=E,Nc=0.95,parameter="mean",Asig="Proportional") n.ESTMAS(Nh=Nh,Ph=Ph,E=E,Nc=0.95,parameter="prop",Asig="Proportional")
The n.MAS function determines the sample size by a simple random sample design without replacement, taking into account whether the parameter of interest is the mean (or total) or a proportion.
n.MAS(N,Argt,Nc=0.95,opc=2) # n.MAS(N,Argt=c(S,Emax.a),opc=1,Nc=0.95) # n.MAS(N,Argt=c(Cve,Emax.r),opc=2,Nc=0.95) # n.MAS(N,Argt=c(p,Emax.a),opc=3,Nc=0.95) # n.MAS(N,Argt=c(p,Emax.r),opc=4,Nc=0.95)n.MAS(N,Argt,Nc=0.95,opc=2) # n.MAS(N,Argt=c(S,Emax.a),opc=1,Nc=0.95) # n.MAS(N,Argt=c(Cve,Emax.r),opc=2,Nc=0.95) # n.MAS(N,Argt=c(p,Emax.a),opc=3,Nc=0.95) # n.MAS(N,Argt=c(p,Emax.r),opc=4,Nc=0.95)
N |
Population size. |
opc |
Numeric value from 1 to 4, which indicates the option to choose. |
Argt |
Vector of length two, in which its components depends on the chosen option ("opc"). If option 1, (opc = 1) is chosen, the components of the Argt vector are in their order, the standard deviation of the variable of interest and the respective absolute maximum error that can be admitted; If option 2 (opc = 2) is chosen, the components of the Argt vector are respectively the estimated coefficient of variation and the relative maximum error to be controlled; If option 3 (opc = 3) is chosen, the components are the estimated proportion and absolute maximum error that can be admitted; And if option 4 (opc = 4) is chosen, the components are the estimated ratio and the relative maximum error respectively. |
Nc |
Confidence level (between 0 and 1) that you want to set. |
This function returns the sample size through the conditions set in the arguments.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
# Sample size for the mean (or total) when you want to control the absolute maximum error. Nc<-0.95 S<-sqrt(6.0590) Emax.a<-0.2 N<-10000 n.MAS(N=N,Argt=c(S,Emax.a),opc=1) # Sample size for the mean (or total) when you want to control the relative maximum error. Cve<-0.4346 Emax.r<-0.05 N<-10000 n.MAS(N=N,Argt=c(Cve,Emax.r)) # Sample size for proportions when you want to control the absolute maximum error. N<-10000 p<-14/30 Emax.a<-0.04 Nc<-0.9 n.MAS(N=N,Argt=c(p,Emax.a),opc=3,Nc=Nc) # Sample size for proportions when you want to control the relative maximum error. N<-10000 p<- 14/30 Emax.r<-0.1 Nc<-0.9 n.MAS(N=N,Argt=c(p,Emax.r),opc=4,Nc=Nc)# Sample size for the mean (or total) when you want to control the absolute maximum error. Nc<-0.95 S<-sqrt(6.0590) Emax.a<-0.2 N<-10000 n.MAS(N=N,Argt=c(S,Emax.a),opc=1) # Sample size for the mean (or total) when you want to control the relative maximum error. Cve<-0.4346 Emax.r<-0.05 N<-10000 n.MAS(N=N,Argt=c(Cve,Emax.r)) # Sample size for proportions when you want to control the absolute maximum error. N<-10000 p<-14/30 Emax.a<-0.04 Nc<-0.9 n.MAS(N=N,Argt=c(p,Emax.a),opc=3,Nc=Nc) # Sample size for proportions when you want to control the relative maximum error. N<-10000 p<- 14/30 Emax.r<-0.1 Nc<-0.9 n.MAS(N=N,Argt=c(p,Emax.r),opc=4,Nc=Nc)
The n.MASC function determines sample size using a simple random sampling design without replacement of Conglomerates.
n.MASC(N,NI,Ni,St,Emax.a,Nc=0.95,n.equal=TRUE) # For clusters with equal sizes. # n.MASC(NI,Ni,St,Emax.a,Nc) # For clusters with different sizes. # n.MASC(N,NI,St,Emax.a,Nc,n.equal=FALSE)n.MASC(N,NI,Ni,St,Emax.a,Nc=0.95,n.equal=TRUE) # For clusters with equal sizes. # n.MASC(NI,Ni,St,Emax.a,Nc) # For clusters with different sizes. # n.MASC(N,NI,St,Emax.a,Nc,n.equal=FALSE)
N |
Size of the population, this argument is only necessary if the size of the conglomerates is different. |
NI |
Number of clusters in the population. |
Ni |
Size of the clusters, this argument is only necessary if the conglomerates have equal size (constant size). |
St |
Standard deviation of conglomerate totals. |
Emax.a |
Absolute maximum error. |
Nc |
Confidence level (between 0 and 1) to be set. |
n.equal |
Logical value indicating whether clusters have the same size |
This function returns the sample size under the conditions set in the arguments, that is, the number of clusters to select.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
# Sample size for populations with clusters of equal size. st<-sqrt(1417.8668) NI<-2000 Ni<-6 e<-2 nc=0.9 n.MASC(St=st,NI=NI,Ni=Ni,Emax.a=e,Nc=nc) # Sample size for populations with clusters of different sizes. st=sqrt(2019760.760) N<-11000 NI<-400 e=10 nc=0.95 n.MASC(St=st,N=N,NI=NI,Emax.a=e,Nc=nc,n.equal=FALSE)# Sample size for populations with clusters of equal size. st<-sqrt(1417.8668) NI<-2000 Ni<-6 e<-2 nc=0.9 n.MASC(St=st,NI=NI,Ni=Ni,Emax.a=e,Nc=nc) # Sample size for populations with clusters of different sizes. st=sqrt(2019760.760) N<-11000 NI<-400 e=10 nc=0.95 n.MASC(St=st,N=N,NI=NI,Emax.a=e,Nc=nc,n.equal=FALSE)
The PiPT function selects a random sample or estimates an interest parameter under a sampling design with proportional inclusion probabilities proportional to size.
PiPT(xk,n,yk=NULL,zk=NULL,pik=NULL,mpikl=NULL,dk=NULL,type="selec", parameter="total",Nc=0.95,Ek=NULL) # To select: PiPT(xk,n) # To estimate: PiPT(yk,pik,mpikl,type="estm",parameter="total") # To estimate in domains # PiPT(yk,pik,mpikl,dk,type="estm",parameter="total")PiPT(xk,n,yk=NULL,zk=NULL,pik=NULL,mpikl=NULL,dk=NULL,type="selec", parameter="total",Nc=0.95,Ek=NULL) # To select: PiPT(xk,n) # To estimate: PiPT(yk,pik,mpikl,type="estm",parameter="total") # To estimate in domains # PiPT(yk,pik,mpikl,dk,type="estm",parameter="total")
xk |
Vector of observations of the auxiliary variable. This vector is only necessary if you wish to select. |
n |
Sample size. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
pik |
Vector of the first-order inclusion probabilities. |
mpikl |
Matrix of second-order inclusion probabilities. |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If type is equal to "select" the function will make a selection, if it is equal to "estm" the function will make the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
dk |
Factor that indicates the individuals that belong to each domain of interest, Only needed if "type"" is equal to "estm.Ud". |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case "type" is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
The PiPT function returns two types of results using a sampling design with inclusion probabilities proportional to size, depending on the argument "type", which indicates whether to select ("select") or estimate ("estm" or "estm.Ud").
If type="select" the function will return a list with three elements:
Ksel |
Vector with the positions of the selected individuals |
piksel |
First order inclusion probability vector of selected individuals |
mpikl.s |
Matrix of the second-order inclusion probabilities |
If type="estm" or type="estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percentage) and a confidence interval.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
set.seed(12265) yk<-rnorm(100,mean=50,sd=5) zk<-rnorm(100,mean=51,sd=5) yk.p<-as.factor(ifelse(yk>50,"A","B")) set.seed(12245) # Información Auxiliar xk<-yk*runif(100,min=0.9,max=1.1) r<-cor(yk,xk) selection<-PiPT(xk=xk,n=10,type="selec") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="total") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="mean") PiPT(yk=yk.p[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="prop") PiPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pik=selection$pik, mpikl=selection$mpikl.s,type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="total") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="mean") PiPT(yk=yk.p[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="prop") PiPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pik=selection$pik, mpikl=selection$mpikl.s,dk=dk[selection$Ksel],type="estm.Ud", parameter="ratio")set.seed(12265) yk<-rnorm(100,mean=50,sd=5) zk<-rnorm(100,mean=51,sd=5) yk.p<-as.factor(ifelse(yk>50,"A","B")) set.seed(12245) # Información Auxiliar xk<-yk*runif(100,min=0.9,max=1.1) r<-cor(yk,xk) selection<-PiPT(xk=xk,n=10,type="selec") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="total") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="mean") PiPT(yk=yk.p[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, type="estm",parameter="prop") PiPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pik=selection$pik, mpikl=selection$mpikl.s,type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="total") PiPT(yk=yk[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="mean") PiPT(yk=yk.p[selection$Ksel],pik=selection$pik,mpikl=selection$mpikl.s, dk=dk[selection$Ksel],type="estm.Ud",parameter="prop") PiPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pik=selection$pik, mpikl=selection$mpikl.s,dk=dk[selection$Ksel],type="estm.Ud", parameter="ratio")
The PPT function selects a random sample or estimates a parameter of interest under a sampling design with proportional proportional selection probabilities (PPT).
PPT(xk,m,yk=NULL,zk=NULL,pk=NULL,dk=NULL,type="selec",parameter="total", method ="acum.total",Nc=0.95,Ek=NULL) # To select: PPT(xk,m,method="acum.total") # To estimate: PPT(yk,pk,type="estm",parameter) # To estimate in domains: PPT(yk,pk,dk,type="estm.Ud",parameter)PPT(xk,m,yk=NULL,zk=NULL,pk=NULL,dk=NULL,type="selec",parameter="total", method ="acum.total",Nc=0.95,Ek=NULL) # To select: PPT(xk,m,method="acum.total") # To estimate: PPT(yk,pk,type="estm",parameter) # To estimate in domains: PPT(yk,pk,dk,type="estm.Ud",parameter)
xk |
Vector of observations of the auxiliary variable. This vector is only necessary if you wish to select. |
m |
Sample size. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
pk |
Vector of the probabilities of selection of individuals. |
dk |
Factor that indicates the individuals that belong to each domain of interest, is only necessary if "type" is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If "type" is equal to "select" the function will make a selection, if it is equal to "estm" the function will perform the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
method |
Indicates the method or selection mechanism. If method is equal to "total cum." The function uses the total cumulative method or if it is equal to "lahiri" the function uses the method of Lahiri. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case the type is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results using the PPT sampling design, depending on the "type" argument with which to select ("select") or estimate ("estm" or "estm.Ud").
If type is equal to "select" the function will return a list with two elements:
Ksel |
Vector with the positions of the selected individuals. |
pksel |
Selection probabilities vector of selected individuals. |
-If type="estm" or type="estm.Ud", the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percentage) and a confidence interval.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
set.seed(12265) yk<-rnorm(100,50,5) zk<-rnorm(100,12,4) set.seed(12245) xk<-yk*runif(100,min=0.9,max=1.1) r<-cor(yk,xk) yk.p<-as.factor(ifelse(yk>50,"A","B")) selection<-PPT(xk=xk,m=10,type="selec",method="acum.total") PPT(yk=yk[selection$Ksel],pk=selection$pksel,type="estm",parameter="total") PPT(yk=yk[selection$Ksel],pk=selection$pksel,type="estm",parameter="mean") PPT(yk=yk.p[selection$Ksel],pk=selection$pksel,type="estm",parameter="prop") PPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pk=selection$pksel, type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) PPT(yk=yk[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="total") PPT(yk=yk[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="mean") PPT(yk=yk.p[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="prop") PPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],dk=dk[selection$Ksel], pk=selection$pksel,type="estm.Ud",parameter="ratio")set.seed(12265) yk<-rnorm(100,50,5) zk<-rnorm(100,12,4) set.seed(12245) xk<-yk*runif(100,min=0.9,max=1.1) r<-cor(yk,xk) yk.p<-as.factor(ifelse(yk>50,"A","B")) selection<-PPT(xk=xk,m=10,type="selec",method="acum.total") PPT(yk=yk[selection$Ksel],pk=selection$pksel,type="estm",parameter="total") PPT(yk=yk[selection$Ksel],pk=selection$pksel,type="estm",parameter="mean") PPT(yk=yk.p[selection$Ksel],pk=selection$pksel,type="estm",parameter="prop") PPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],pk=selection$pksel, type="estm",parameter="ratio") # Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) PPT(yk=yk[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="total") PPT(yk=yk[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="mean") PPT(yk=yk.p[selection$Ksel],dk=dk[selection$Ksel],pk=selection$pksel, type="estm.Ud",parameter="prop") PPT(yk=yk[selection$Ksel],zk=zk[selection$Ksel],dk=dk[selection$Ksel], pk=selection$pksel,type="estm.Ud",parameter="ratio")
The R.SIS function selects a random sample or estimates a parameter of interest under a r-systematic sampling design.
R.SIS(N,n,r,yk=NULL,zk=NULL,fact=NULL,dk=NULL,type="selec", parameter="total",Nc=0.95,Ek=NULL) # To select: R.SIS(N,n,r) #To estimate: R.SIS(N,n,r,fact,yk,type="estm",parameter) # To estimate in domains # R.SIS(yk,fact,N,n,r,type="estm.Ud",parameter)R.SIS(N,n,r,yk=NULL,zk=NULL,fact=NULL,dk=NULL,type="selec", parameter="total",Nc=0.95,Ek=NULL) # To select: R.SIS(N,n,r) #To estimate: R.SIS(N,n,r,fact,yk,type="estm",parameter) # To estimate in domains # R.SIS(yk,fact,N,n,r,type="estm.Ud",parameter)
N |
Size of the population. |
n |
Sample size. |
r |
Number of starts. |
yk |
Vector of observations of the characteristic of interest. This vector is only necessary if you want to estimate. |
zk |
Vector of observations of the characteristic of interest of equal length that yk. This vector is necessary if the parameter of interest is the ratio and refers to the variable involved in the denominator of the ratio. |
fact |
Factor indicating that Ur belongs to the observations of the variable of interest and yk. This factor is only necessary if type is equal to "estm" or "estm.Ud". |
dk |
Factor that indicates the individuals that belong to each domain of interest, is only necessary if type is equal to "estm.Ud". |
type |
This argument indicates the procedure that will have the function ("select", "estm" or "estm.Ud"). If "type" is equal to "select" the function will make a selection, if it is equal to "estm" the function will perform the estimation of the indicated parameter and if it is equal to "estm.Ud" it will make an estimate in domain. |
parameter |
This argument indicates the parameter to be estimated ("total", "mean", "prop", or "ratio"). |
Nc |
Confidence level (between 0 and 1), for the confidence interval of the estimator in case "type" is equal to "estm" or "estm.Ud". |
Ek |
Vector of random numbers of length equal to the size of the population. This argument is optional and by default the function generates them from a uniform distribution (0,1). |
This function returns two types of results using the r-systematic sampling design, depending on the "type" argument with which to select ("select") or estimate "estm.Ud").
If type="select", the function returns a list with four elements:
Sel |
Array with r columns that refers to the clusters selected by each boot |
Ksel |
Vector with selected individuals |
fact |
factor indicating which start each selected individual belongs to |
n.s |
Sample size |
If type="estm" or type="estm.Ud" the function returns a data frame with the estimation of the parameter of interest, the estimated variance of the estimator, the standard error, the coefficient of variation (in percent), an interval of confidence, the intraclass correlation coefficient and the intra-sample rate of variance.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
yk<-rnorm(100,40,2) zk<-rnorm(100,12,2) yk.p<-as.factor(ifelse(yk>40,"A","B")) selection<-R.SIS(N=100,n=20,r=3,type="selec") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="total") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="mean") R.SIS(yk=yk.p[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="prop") R.SIS(yk=yk[selection$Ksel],zk=zk[selection$Ksel],fact=selection$fact, N=100,n=20,r=3,type="estm",parameter="ratio") #Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) R.SIS(yk=yk[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="total") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="mean") R.SIS(yk=yk.p[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="prop") R.SIS(yk=yk[selection$Ksel],zk=zk[selection$Ksel],fact=selection$fact, dk=dk[selection$Ksel],N=100,n=20,r=3,type="estm.Ud",parameter="ratio")yk<-rnorm(100,40,2) zk<-rnorm(100,12,2) yk.p<-as.factor(ifelse(yk>40,"A","B")) selection<-R.SIS(N=100,n=20,r=3,type="selec") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="total") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="mean") R.SIS(yk=yk.p[selection$Ksel],fact=selection$fact,N=100,n=20,r=3, type="estm",parameter="prop") R.SIS(yk=yk[selection$Ksel],zk=zk[selection$Ksel],fact=selection$fact, N=100,n=20,r=3,type="estm",parameter="ratio") #Domain Estimate Sex<-rep(1:2,length=100) dk<-factor(Sex,labels=c("Man","Woman")) R.SIS(yk=yk[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="total") R.SIS(yk=yk[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="mean") R.SIS(yk=yk.p[selection$Ksel],fact=selection$fact,dk=dk[selection$Ksel], N=100,n=20,r=3,type="estm.Ud",parameter="prop") R.SIS(yk=yk[selection$Ksel],zk=zk[selection$Ksel],fact=selection$fact, dk=dk[selection$Ksel],N=100,n=20,r=3,type="estm.Ud",parameter="ratio")
The WHICH1 function returns the positions in which the vector components (V1) are located in another vector (V2).
WHICH1(V1,V2)WHICH1(V1,V2)
V1 |
Vector initial. |
V2 |
Vector containing replicates of the components of the initial vector. |
This function is used to extract the positions of all the individuals that are part of the selected clusters, in a cluster sampling.
Jorge Alberto Barón Cárdenas <[email protected]>
Guillermo Martínez Flórez <[email protected]>
Särndal, C. E., J. H. Wretman, and C. M. Cassel (1992). Foundations of Inference in Survey Sampling. Wiley New York.
Cochran, W. G. (1977). Sampling Techniques, 3ra ed. New York: Wiley.
Thompson, S. K. (1945). Wiley Series in Probability and Statistics, Sampling, 1ra ed. United States of America.
cong<-rep(1:12,each=10) Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") WHICH1(selection$Ksel,cong)cong<-rep(1:12,each=10) Argt<-list(NI=12,nI=3) selection<-CONGL(Argt=Argt,design="MAS") WHICH1(selection$Ksel,cong)