sampling/0000755000176200001440000000000014517474042012074 5ustar liggesuserssampling/NAMESPACE0000644000176200001440000000014514516451542013312 0ustar liggesusersuseDynLib(sampling) import(MASS,lpSolve,stats,graphics) # Export all names exportPattern(".") sampling/data/0000755000176200001440000000000014515723503013002 5ustar liggesuserssampling/data/MU284.rda0000644000176200001440000003702614516451542014263 0ustar liggesusersRDX2 X  MU284   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !8FB < 50O;1&* ! A  Y   tv )  k   B  6( 8<   F1   Q#i" M$.0  1.  $1d   #.   J v #  v   3.   X)& ^<  8 TJ  C'  4>6 2(+N67$'   >!\   lw * l!   >  4* 6<   C0   K&f# J!+%  //   "2j  #- !   I  v &  v  /. ! U+ %]<  5 JH  @#   o`wdS7"aJ?o%A%Y<Q6:&DN'EwI;\hK1)LqZOg:vfa8EIV5iQM+Qzq[rNNHF /Cz*=BWR?AH@}vB#+5RZ>MD4_%#'.;,iWB>J9SJ?m%i&RL?V[dy?ZO2yW5K$RT<.p5ZBdM4<dL1iWFV\1?^|E5[5*2( :=<#iP7."{)6@2'?     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The sample size must be small with respect to the population size; otherwise, the selection time can be very long. } \seealso{\code{\link{UPsampfordpi2}} } \references{ Sampford, M. (1967), On sampling without replacement with unequal probabilities of selection, \emph{Biometrika}, 54:499-513. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) s=UPsampford(pik) #the sample is which(s==1) } \keyword{survey} sampling/man/balancedstratification.Rd0000644000176200001440000000440314516451542017633 0ustar liggesusers\name{balancedstratification} \alias{balancedstratification} \title{Balanced stratification} \description{ Selects a stratified balanced sample (a vector of 0 and 1). Firstly, the flight phase is applied in each stratum. Secondly, the strata are aggregated and the flight phase is applied on the whole population. Finally, the landing phase is applied on the whole population. } \usage{balancedstratification(X,strata,pik,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{strata}{vector of integers that specifies the stratification.} \item{pik}{vector of inclusion probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}} } \examples{ ############ ## Example 1 ############ # variable of stratification (3 strata) strata=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # Vector of inclusion probabilities. # the sample has its size equal to 9. pik=rep(3/5,times=15) # selection of a stratified sample s=balancedstratification(X,strata,pik,comment=TRUE) # the sample is (1:length(pik))[s==1] ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84) strata=MU284$REG pik=inclusionprobabilities(MU284$P75,80) s=balancedstratification(X,strata,pik,TRUE) #the selected units are MU284$LABEL[s==1] } \keyword{survey} \encoding{latin1} sampling/man/UPmultinomial.Rd0000644000176200001440000000161514516451542015737 0ustar liggesusers\name{UPmultinomial} \alias{UPmultinomial} \title{Multinomial sampling} \description{ Uses the Hansen-Hurwitz method to select a sample of units (unequal probabilities, with replacement, fixed sample size). } \usage{ UPmultinomial(pik) } \arguments{ \item{pik}{vector of the inclusion probabilities.} } \value{ Returns a vector of size N, the population size. Each element k of this vector indicates the number of replicates of unit k in the sample. } \references{ Hansen, M. and Hurwitz, W. (1943), On the theory of sampling from finite populations. \emph{Annals of Mathematical Statistics}, 14:333-362. } \examples{ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPmultinomial(pik) #the selected units are which(s!=0) #with the number of replicates s[s!=0] #or use rep((1:length(pik))[s!=0],s[s!=0]) } \keyword{survey} sampling/man/fastflightcube.Rd0000644000176200001440000000337514516451542016137 0ustar liggesusers\name{fastflightcube} \alias{fastflightcube} \title{Fast flight phase for the cube method} \description{Executes the fast flight phase of the cube method (algorithm of Chauvet and Till, 2005, 2006). The data are sorted following the argument \code{order}. Inclusion probabilities equal to 0 or 1 are tolerated. } \usage{fastflightcube(X,pik,order=1,comment=TRUE)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pik}{vector of inclusion probabilities.} \item{order}{ 1, the data are randomly arranged,\cr 2, no change in data order,\cr 3, the data are sorted in decreasing order. } \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}} } \examples{ # Matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1,2,3,4,5,6,7,8,9)) # Vector of inclusion probabilities. # The sample size is 3. pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # pikstar is almost a balanced sample and is ready for the landing phase pikstar=fastflightcube(X,pik,order=1,comment=TRUE) pikstar } \keyword{survey} \encoding{latin1} sampling/man/samplecube.Rd0000644000176200001440000001057114516451542015261 0ustar liggesusers\name{samplecube} \alias{samplecube} \title{Sample cube method} \description{ Selects a balanced sample (a vector of 0 and 1) or an almost balanced sample. Firstly, the flight phase is applied. Next, if needed, the landing phase is applied on the result of the flight phase. } \usage{samplecube(X,pik,order=1,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pik}{vector of inclusion probabilities.} \item{order}{ 1, the data are randomly arranged,\cr 2, no change in data order,\cr 3, the data are sorted in decreasing order. } \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{ 1, for a landing phase by linear programming,\cr 2, for a landing phase by suppression of variables.} } \seealso{ \code{\link{landingcube}}, \code{\link{fastflightcube}} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \examples{ ############ ## Example 1 ############ # matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1.1,2.2,3.1,4.2,5.1,6.3,7.1,8.1,9.1)) # vector of inclusion probabilities # the sample size is 3. pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # selection of the sample s=samplecube(X,pik,order=1,comment=TRUE) # The selected sample (1:length(pik))[s==1] ############ ## Example 2 ############ # 2 strata and 2 auxiliary variables # we verify the values of the inclusion probabilities by simulations X=rbind(c(1,0,1,2),c(1,0,2,5),c(1,0,3,7),c(1,0,4,9), c(1,0,5,1),c(1,0,6,5),c(1,0,7,7),c(1,0,8,6),c(1,0,9,9), c(1,0,10,3),c(0,1,11,3),c(0,1,12,2),c(0,1,13,3), c(0,1,14,6),c(0,1,15,8),c(0,1,16,9),c(0,1,17,1), c(0,1,18,2),c(0,1,19,3),c(0,1,20,4)) pik=rep(1/2,times=20) ppp=rep(0,times=20) sim=10 #for accurate results increase this value for(i in (1:sim)) ppp=ppp+samplecube(X,pik,1,FALSE) ppp=ppp/sim print(ppp) print(pik) ############ ## Example 3 ############ # unequal probability sampling by cube method # one auxiliary variable equal to the inclusion probability N=100 pik=runif(N) pikfin=samplecube(array(pik,c(N,1)),pik,1,TRUE) ############ ## Example 4 ############ # p auxiliary variables generated randomly N=100 p=7 x=rnorm(N*p,10,3) # random inclusion probabilities pik= runif(N) X=array(x,c(N,p)) X=cbind(cbind(X,rep(1,times=N)),pik) pikfin=samplecube(X,pik,1,TRUE) ############ ## Example 5 ############ # strata and an auxiliary variable N=100 a=rep(1,times=N) b=rep(0,times=N) V1=c(a,b,b) V2=c(b,a,b) V3=c(b,b,a) X=cbind(V1,V2,V3) pik=rep(2/10,times=3*N) pikfin=samplecube(X,pik,1,TRUE) ############ ## Example 6 ############ # Selection of a balanced sample using the MU284 population, # Monte Carlo simulation and variance comparison with # unequal probability sampling of fixed sample size. ############ data(MU284) # inclusion probabilities, sample size 50 pik=inclusionprobabilities(MU284$P75,50) # matrix of balancing variables X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84,MU284$REV84) # Horvitz-Thompson estimator for a balanced sample s=samplecube(X,pik,1,FALSE) HTestimator(MU284$RMT85[s==1],pik[s==1]) # Horvitz-Thompson estimator for an unequal probability sample s=samplecube(matrix(pik),pik,1,FALSE) HTestimator(MU284$RMT85[s==1],pik[s==1]) # Monte Carlo simulation; for a better accuracy, increase the value 'sim' sim=5 res1=rep(0,times=sim) res2=rep(0,times=sim) for(i in 1:sim) { cat("Simulation number ",i,"\n") s=samplecube(X,pik,1,FALSE) res1[i]=HTestimator(MU284$RMT85[s==1],pik[s==1]) s=samplecube(matrix(pik),pik,1,FALSE) res2[i]=HTestimator(MU284$RMT85[s==1],pik[s==1]) } # summary and boxplots summary(res1) summary(res2) ss=cbind(res1,res2) colnames(ss) = c("balanced sampling","uneq prob sampling") boxplot(data.frame(ss), las=1) } \keyword{survey} \encoding{latin1} sampling/man/UPbrewer.Rd0000644000176200001440000000166414516451542014677 0ustar liggesusers\name{UPbrewer} \alias{UPbrewer} \title{Brewer sampling} \description{ Uses the Brewer's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPbrewer(pik,eps=1e-06) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{the control value, by default equal to 1e-06; it is used to control pik (pik>eps & pik < 1-eps).} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \seealso{\code{\link{UPsystematic}} } \references{ Brewer, K. (1975), A simple procedure for $pi$pswor, \emph{Australian Journal of Statistics}, 17:166-172. } \examples{ #define the inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPbrewer(pik) #the sample is which(s==1) } \keyword{survey} sampling/man/UPmidzuno.Rd0000644000176200001440000000225314516451542015071 0ustar liggesusers\name{UPmidzuno} \alias{UPmidzuno} \title{Midzuno sampling} \description{ Uses the Midzuno's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPmidzuno(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPtille}} } \references{ Midzuno, H. (1952), On the sampling system with probability proportional to sum of size. \emph{ Annals of the Institute of Statistical Mathematics}, 3:99-107.\cr Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPmidzuno(pik) #the sample is which(s==1) } \keyword{survey} \encoding{latin1} sampling/man/cleanstrata.Rd0000644000176200001440000000113114516451542015432 0ustar liggesusers\name{cleanstrata} \alias{cleanstrata} \title{ Clean strata} \description{Renumbers a variable of stratification (categorical variable). The strata receive a number from 1 to the last stratum number. The empty strata are suppressed. This function is used in `balancedstratification'. } \usage{ cleanstrata(strata) } \arguments{ \item{strata}{vector of stratum numbers.} } \seealso{\code{\link{balancedstratification}}} \examples{ # definition of the stratification variable strata=c(-2,3,-2,3,4,4,4,-2,-2,3,4,0,0,0) # renumber the strata cleanstrata(strata) } \keyword{survey} sampling/man/UPpivotal.Rd0000644000176200001440000000232014516451542015055 0ustar liggesusers\name{UPpivotal} \alias{UPpivotal} \title{Pivotal sampling} \description{ Selects an unequal probability sample using the pivotal method (unequal probabilities, without replacement, fixed sample size). } \usage{ UPpivotal(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value eps is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPrandompivotal}} } \references{ Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{to appear in Computational Statistics}.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPpivotal(pik) #the sample is which(s==1) } \keyword{survey} \encoding{latin1} sampling/man/srswr.Rd0000644000176200001440000000116714516451542014322 0ustar liggesusers\name{srswr} \alias{srswr} \title{Simple random sampling with replacement} \description{ Draws a simple random sampling with replacement of size n (equal probabilities, fixed sample size, with replacement). } \usage{ srswr(n,N) } \value{ Returns a vector of size N, the population size. Each element k of this vector indicates the number of replicates of unit k in the sample. } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \seealso{\code{\link{UPmultinomial}} } \examples{ s=srswr(3,10) #the selected units are which(s!=0) #with the number of replicates s[s!=0] } \keyword{survey} sampling/man/inclusionprobabilities.Rd0000644000176200001440000000212614516451542017712 0ustar liggesusers\name{inclusionprobabilities} \alias{inclusionprobabilities} \title{Inclusion probabilities} \description{Computes the first-order inclusion probabilities from a vector of positive numbers (for a probability proportional-to-size sampling design). Their sum is equal to n, the sample size. } \usage{inclusionprobabilities(a,n)} \arguments{ \item{a}{vector of positive numbers.} \item{n}{sample size.} } \seealso{ \code{\link{inclusionprobastrata}} } \examples{ ############ ## Example 1 ############ # a vector of positive numbers a=1:20 # inclusion probabilities for a sample size n=12 inclusionprobabilities(a,12) ############ ## Example 2 ############ # Computation of the inclusion probabilities proportional to the number # of inhabitants in each municipality of the Belgian municipalities data. data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) # the first-order inclusion probabilities for each municipality data.frame(pik=pik,name=belgianmunicipalities$Commune) # the sum is equal to the sample size sum(pik) } \keyword{survey} sampling/man/cluster.Rd0000644000176200001440000000511314516451542014616 0ustar liggesusers\name{cluster} \alias{cluster} \title{Cluster sampling} \description{Cluster sampling with equal/unequal probabilities.} \usage{cluster(data, clustername, size, method=c("srswor","srswr","poisson", "systematic"),pik,description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is N, the population size.} \item{clustername}{the name of the clustering variable.} \item{size}{sample size.} \item{method}{method to select clusters; the following methods are implemented: simple random sampling without replacement (srswor), simple random sampling with replacement (srswr), Poisson sampling (poisson), systematic sampling (systematic); if the method is not specified, by default the method is "srswor".} \item{pik}{vector of inclusion probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson, systematic). If an auxiliary information is provided, the function uses the \link{inclusionprobabilities} function for computing these probabilities.} \item{description}{a message is printed if its value is TRUE; the message gives the number of selected clusters, the number of units in the population and the number of selected units. By default, the value is FALSE.} } \value{ The function returns a data set with the following information: the selected clusters, the identifier of the units in the selected clusters, the final inclusion probabilities for these units (they are equal for the units included in the same cluster). If method is "srswr", the number of replicates is also given. } \seealso{ \code{\link{mstage}}, \code{\link{strata}}, \code{\link{getdata}}} \examples{ ############ ## Example 1 ############ # Uses the swissmunicipalities data to draw a sample of clusters data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as clustering variable # the sample size is 3; the method is simple random sampling without replacement cl=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial database getdata(swissmunicipalities, cl) ############ ## Example 2 ############ # the same data as in Example 1 # the sample size is 3; the method is systematic sampling # the pik vector is randomly generated using the U(0,1) distribution cl_sys=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="systematic", pik=runif(7)) # extracts the observed data getdata(swissmunicipalities,cl_sys) } \keyword{survey} sampling/man/calib.Rd0000644000176200001440000001137514516740253014216 0ustar liggesusers\name{calib} \alias{calib} \title{g-weights of the calibration estimator} \description{Computes the g-weights of the calibration estimator. The g-weights should lie in the specified bounds for the truncated and logit methods. } \usage{calib(Xs,d,total,q=rep(1,length(d)),method=c("linear","raking","truncated", "logit"),bounds=c(low=0,upp=10),description=FALSE,max_iter=500)} \arguments{ \item{Xs}{matrix of calibration variables.} \item{d}{vector of initial weights.} \item{total}{vector of population totals.} \item{q}{vector of positive values accounting for heteroscedasticity; the variation of the g-weights is reduced for small values of q.} \item{method}{calibration method (linear, raking, logit, truncated).} \item{bounds}{vector of bounds for the g-weights used in the truncated and logit methods; 'low' is the smallest value and 'upp' is the largest value.} \item{description}{if description=TRUE, summary of initial and final weights are printed, and their boxplots and histograms are drawn; by default, its value is FALSE.} \item{max_iter}{maximum number of iterations in the Newton's method.} } \value{Returns the vector of g-weights.} \references{ Cassel, C.-M., Srndal, C.-E., and Wretman, J. (1976). Some results on generalized difference estimation and generalized regression estimation for finite population.\emph{Biometrika}, 63:615--620. \cr Deville, J.-C. and Srndal, C.-E. (1992). Calibration estimators in survey sampling. \emph{Journal of the American Statistical Association}, 87:376--382.\cr Deville, J.-C., Srndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. \emph{Journal of the American Statistical Association}, 88:1013--1020.\cr } \details{The argument \emph{method} implements the methods given in the paper of Deville and Srndal(1992).} \seealso{ \code{\link{checkcalibration}}, \code{\link{calibev}}, \code{\link{gencalib}} } \examples{ ############ ## Example 1 ############ # matrix of sample calibration variables Xs=cbind( c(1,1,1,1,1,0,0,0,0,0), c(0,0,0,0,0,1,1,1,1,1), c(1,2,3,4,5,6,7,8,9,10) ) # inclusion probabilities piks=rep(0.2,times=10) # vector of population totals total=c(24,26,290) # the g-weights using the truncated method g=calib(Xs,d=1/piks,total,method="truncated",bounds=c(0.75,1.2)) # the calibration estimator of X is equal to 'total' vector t(g/piks)\%*\%Xs # the g-weights are between lower and upper bounds range(g) ############ ## Example 2 ############ # Example of g-weights (linear, raking, truncated, logit), # with the data of Belgian municipalities as population. # Firstly, a sample is selected by means of Poisson sampling. # Secondly, the g-weights are calculated. data(belgianmunicipalities) attach(belgianmunicipalities) # matrix of calibration variables for the population X=cbind( Men03/mean(Men03), Women03/mean(Women03), Diffmen, Diffwom, TaxableIncome/mean(TaxableIncome), Totaltaxation/mean(Totaltaxation), averageincome/mean(averageincome), medianincome/mean(medianincome)) # selection of a sample with expectation size equal to 200 # by means of Poisson sampling # the inclusion probabilities are proportional to the average income pik=inclusionprobabilities(averageincome,200) N=length(pik) # population size s=UPpoisson(pik) # sample Xs=X[s==1,] # sample matrix of calibration variables piks=pik[s==1] # sample inclusion probabilities n=length(piks) # expected sample size # vector of population totals of the calibration variables total=c(t(rep(1,times=N))\%*\%X) # computation of the g-weights # by means of different calibration methods g1=calib(Xs,d=1/piks,total,method="linear") g2=calib(Xs,d=1/piks,total,method="raking") g3=calib(Xs,d=1/piks,total,method="truncated",bounds=c(0.5,1.5)) g4=calib(Xs,d=1/piks,total,method="logit",bounds=c(0.5,1.5)) # in some cases, the calibration is not possible, # particularly when bounds are used. # if the calibration is possible, the calibration estimator of X is printed if(checkcalibration(Xs,d=1/piks,total,g1)$result) print(c((g1/piks) \%*\% Xs)) else print("error") if(!is.null(g2)) if(checkcalibration(Xs,d=1/piks,total,g2)$result) if(!is.null(g3)) if(checkcalibration(Xs,d=1/piks,total,g3)$result & all(g3<=1.5) & all(g3>=0.5)) print(c((g3/piks) \%*\% Xs)) else print("error") if(!is.null(g4)) if(checkcalibration(Xs,d=1/piks,total,g4)$result & all(g4<=1.5) & all(g4>=0.5)) print(c((g4/piks) \%*\% Xs)) else print("error") detach(belgianmunicipalities) ############ ## Example 3 ############ # Example of calibration and adjustment for nonresponse in the 'calibration' vignette # vignette("calibration", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/UPmidzunopi2.Rd0000644000176200001440000000173214516451542015505 0ustar liggesusers\name{UPmidzunopi2} \alias{UPmidzunopi2} \title{Joint inclusion probabilities for Midzuno sampling} \description{ Computes the joint (second-order) inclusion probabilities for Midzuno sampling. } \usage{ UPmidzunopi2(pik) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. } \seealso{\code{\link{UPmidzuno}} } \references{ Midzuno, H. (1952), On the sampling system with probability proportional to sum of size. \emph{ Annals of the Institute of Statistical Mathematics}, 3:99-107. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #matrix of joint inclusion probabilities UPmidzunopi2(pik) } \keyword{survey} sampling/man/regest.Rd0000644000176200001440000000505714516740721014435 0ustar liggesusers\name{regest} \alias{regest} \title{Regression estimator} \description{Computes the regression estimator of the population total, using the design-based approach. The underling regression model is a model without intercept.} \usage{regest(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights)))} \arguments{ \item{formula}{regression model formula (y~x).} \item{Tx}{population total of x, the auxiliary variable.} \item{weights}{vector of the weights; its length is equal to n, the sample size.} \item{pikl}{matrix of joint inclusion probabilities for the sample.} \item{n}{the sample size.} \item{sigma}{vector of positive values accounting for heteroscedasticity.} } \value{The function returns a list with following components: \item{regest}{value of the regression estimator.} \item{coefficients}{vector of estimated beta coefficients.} \item{std_error}{estimated standard error of the estimated coefficients.} \item{t_value}{t-values associated to the coefficients.} \item{p_value}{p-values associated to the coefficients.} \item{cov_mat}{covariance matrix of the estimated coefficients.} \item{weights}{specified weights.} \item{y}{response variable.} \item{x}{model matrix.} } \seealso{ \code{\link{ratioest}},\code{\link{regest_strata}} } \examples{ # uses the MU284 population to draw a systematic sample data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85; sample size 40 pik=inclusionprobabilities(P85,40) # joint inclusion probabilities for systematic sampling pikl=UPsystematicpi2(pik) # draws a systematic sample of size 40 s=UPsystematic(pik) # defines the variable of interest for the selected sample y=RMT85[s==1] # defines the auxiliary information for the selected sample x1=CS82[s==1] x2=SS82[s==1] # joint inclusion probabilities for the selected sample pikls=pikl[s==1,s==1] # first-order inclusion probabilities for the selected sample piks=pik[s==1] # computes the regression estimator with the model y~x1+x2-1 r=regest(formula=y~x1+x2-1,Tx=c(sum(CS82),sum(SS82)),weights=1/piks,pikl=pikls,n=40) # the regression estimator r$regest # the estimated beta coefficients r$coefficients # the regression estimator is the same as the calibration estimator (method="linear") Xs=cbind(x1,x2) total=c(sum(CS82),sum(SS82)) g1=calib(Xs,d=1/piks,total,method="linear") checkcalibration(Xs,d=1/piks,total,g1) calibev(y,Xs,total,pikls,d=1/piks,g1,with=TRUE,EPS=1e-6) detach(MU281) } \keyword{survey} sampling/man/UPmaxentropy.Rd0000644000176200001440000000742614516451542015621 0ustar liggesusers\name{UPmaxentropy} \alias{UPmaxentropy} \alias{UPmaxentropypi2} \alias{UPMEqfromw} \alias{UPMEpikfromq} \alias{UPMEpiktildefrompik} \alias{UPMEsfromq} \alias{UPMEpik2frompikw} \title{Maximum entropy sampling} \description{ Maximum entropy sampling with fixed sample size and unequal probabilities (or Conditional Poisson sampling) is implemented by means of a sequential method (unequal probabilities, without replacement, fixed sample size). } \usage{ UPmaxentropy(pik) UPmaxentropypi2(pik) UPMEqfromw(w,n) UPMEpikfromq(q) UPMEpiktildefrompik(pik,eps=1e-6) UPMEsfromq(q) UPMEpik2frompikw(pik,w) } \arguments{ \item{n}{sample size.} \item{pik}{vector of prescribed inclusion probabilities.} \item{eps}{tolerance in the Newton's method; by default is 1E-6.} \item{q}{matrix of the conditional selection probabilities for the sequential algorithm.} \item{w}{parameter vector of the maximum entropy design.} } \details{ The maximum entropy sampling maximizes the entropy criterion: \deqn{I(p) = - \sum_s p(s)\log[p(s)]}{% I(p) = -\sum_s p(s)log[p(s)].} The main procedure is \code{UPmaxentropy} which selects a sample (a vector of 0 and 1) from a given vector of inclusion probabilities. The procedure \code{UPmaxentropypi2} returns the matrix of joint inclusion probabilities from the first-order inclusion probability vector. The other procedures are intermediate steps. They can be useful to run simulations as shown in the examples below. The procedure \code{UPMEpiktildefrompik} computes the vector of the inclusion probabilities (denoted \code{pikt}) of a Poisson sampling from the vector of the inclusion probabilities of the maximum entropy sampling. The maximum entropy sampling is the conditional design given the fixed sample size. The vector \code{w} can be easily obtained by \code{w=pikt/(1-pikt)}. Once \code{piktilde} and \code{w} are deduced from \code{pik}, a matrix of selection probabilities \code{q} can be derived from the sample size \code{n} and the vector \code{w} via \code{UPMEqfromw}. Next, a sample can be selected from \code{q} using \code{UPMEsfromq}. In order to generate several samples, it is more efficient to compute the matrix \code{q} (which needs some calculation), and then to use the procedure \code{UPMEsfromq}. The vector of the inclusion probabilities can be recomputed from \code{q} using \code{UPMEpikfromq}, which also checks the numerical precision of the algorithm. The procedure \code{UPMEpik2frompikw} computes the matrix of the joint inclusion probabilities from \code{q} and \code{w}. } \references{ Chen, S.X., Liu, J.S. (1997). Statistical applications of the Poisson-binomial and conditional Bernoulli distributions, \emph{Statistica Sinica}, 7, 875-892;\cr Deville, J.-C. (2000). \emph{Note sur l'algorithme de Chen, Dempster et Liu.} Technical report, CREST-ENSAI, Rennes.\cr Matei, A., Till, Y. (2005) Evaluation of variance approximations and estimators in maximum entropy sampling with unequal probability and fixed sample size, \emph{Journal of Official Statistics}, Vol. 21, No. 4, p. 543-570.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ ############ ## Example 1 ############ # Simple example - sample selection pik=c(0.07,0.17,0.41,0.61,0.83,0.91) # First method UPmaxentropy(pik) # Second method by using intermediate procedures n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) UPMEsfromq(q) # Matrix of joint inclusion probabilities # First method: direct computation from pik UPmaxentropypi2(pik) # Second method: computation from pik and w UPMEpik2frompikw(pik,w) ############ ## Example 2 ############ # other examples in the 'UPexamples' vignette # vignette("UPexamples", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/belgianmunicipalities.Rd0000644000176200001440000000323714516451542017503 0ustar liggesusers\name{belgianmunicipalities} \alias{belgianmunicipalities} \docType{data} \title{ The Belgian municipalities population} \description{This data provides information about the Belgian population of July 1, 2004 compared to that of July 1, 2003, and some financial information about the municipality incomes at the end of 2001. } \usage{data(belgianmunicipalities)} \format{ A data frame with 589 observations on the following 17 variables: \describe{ \item{Commune}{municipality name.} \item{INS}{`Institut National de statistique' code.} \item{Province}{province number.} \item{Arrondiss}{administrative division number.} \item{Men04}{number of men on July 1, 2004.} \item{Women04}{number of women on July 1, 2004.} \item{Tot04}{total population on July 1, 2004.} \item{Men03}{number of men on July 1, 2003.} \item{Women03}{number of women on July 1, 2003.} \item{Tot03}{total population on July 1, 2003.} \item{Diffmen}{number of men on July 1, 2004 minus the number of men on July 1, 2003.} \item{Diffwom}{number of women on July 1, 2004 minus the number of women on July 1, 2003.} \item{DiffTOT}{difference between the total population on July 1, 2004 and on July 1, 2003.} \item{TaxableIncome}{total taxable income in euros in 2001.} \item{Totaltaxation}{total taxation in euros in 2001.} \item{averageincome}{average of the income-tax return in euros in 2001.} \item{medianincome}{median of the income-tax return in euros in 2001.} } } \source{http://https://statbel.fgov.be/fr} \examples{ data(belgianmunicipalities) hist(belgianmunicipalities$medianincome) } \keyword{datasets} sampling/man/srswor.Rd0000644000176200001440000000171014516451542014473 0ustar liggesusers\name{srswor} \alias{srswor} \title{Simple random sampling without replacement} \description{ Draws a simple random sampling without replacement of size n (equal probabilities, fixed sample size, without replacement). } \usage{ srswor(n,N) } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \seealso{\code{\link{srswr}}} \examples{ ############ ## Example 1 ############ #select a sample s=srswor(3,10) #the sample is which(s==1) ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune n=200 #select a sample s=srswor(n,length(Tot)) #the sample is which(s==1) #names of the selected units as.vector(name[s==1]) } \keyword{survey} sampling/man/swissmunicipalities.Rd0000644000176200001440000000300114516451542017237 0ustar liggesusers\name{swissmunicipalities} \alias{swissmunicipalities} \docType{data} \title{The Swiss municipalities population} \description{This population provides information about the Swiss municipalities in 2003. } \usage{data(swissmunicipalities)} \format{ A data frame with 2896 observations on the following 22 variables: \describe{ \item{CT}{Swiss canton.} \item{REG}{Swiss region.} \item{COM}{municipality number.} \item{Nom}{municipality name.} \item{HApoly}{municipality area.} \item{Surfacesbois}{wood area.} \item{Surfacescult}{area under cultivation.} \item{Alp}{mountain pasture area.} \item{Airbat}{area with buildings.} \item{Airind}{industrial area.} \item{P00BMTOT}{number of men.} \item{P00BWTOT}{number of women.} \item{Pop020}{number of men and women aged between 0 and 19.} \item{Pop2040}{number of men and women aged between 20 and 39.} \item{Pop4065}{number of men and women aged between 40 and 64.} \item{Pop65P}{number of men and women aged between 65 and over.} \item{H00PTOT}{number of households.} \item{H00P01}{number of households with 1 person.} \item{H00P02}{number of households with 2 persons.} \item{H00P03}{number of households with 3 persons.} \item{H00P04}{number of households with 4 persons.} \item{POPTOT}{total population.} } } \source{Swiss Federal Statistical Office. } \examples{ data(swissmunicipalities) hist(swissmunicipalities$POPTOT) } \keyword{datasets} sampling/man/varest.Rd0000644000176200001440000000347314516451542014450 0ustar liggesusers\name{varest} \alias{varest} \title{Variance estimation using the Deville's method} \description{Computes the variance estimation of an estimator of the population total using the Deville's method.} \usage{varest(Ys,Xs=NULL,pik,w=NULL)} \arguments{ \item{Ys}{vector of the variable of interest; its length is equal to n, the sample size.} \item{Xs}{matrix of the auxiliary variables; for the calibration estimator, this is the matrix of the sample calibration variables.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{w}{vector of the calibrated weights (for the calibration estimator); its length is equal to n, the sample size.} } \details{ The function implements the following estimator: \deqn{\widehat{Var}(\widehat{Ys})=\frac{1}{1-\sum_{k\in s} a_k^2}\sum_{k\in s}(1-\pi_k)\left(\frac{y_k}{\pi_k}-\frac{\sum_{l\in s} (1-\pi_{l})y_l/\pi_l}{\sum_{l\in s} (1-\pi_l)}\right)} where \eqn{a_k=(1-\pi_k)/\sum_{l\in s} (1-\pi_l)}. } \references{ Deville, J.-C. (1993). \emph{Estimation de la variance pour les enqutes en deux phases}. Manuscript, INSEE, Paris. } \seealso{ \code{\link{calibev}} } \examples{ # Belgian municipalities data base data(belgianmunicipalities) attach(belgianmunicipalities) # Computes the inclusion probabilities pik=inclusionprobabilities(Tot04,200) N=length(pik) n=sum(pik) # Defines the variable of interest y=TaxableIncome # Draws a Tille sample of size 200 s=UPtille(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the variance estimation of the Horvitz-Thompson estimator varest(Ys=y[s==1],pik=pik[s==1]) # for an example using calibration estimator, see the 'calibration' vignette # vignette("calibration", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/Hajekstrata.Rd0000644000176200001440000000373114516451542015402 0ustar liggesusers\name{Hajekstrata} \alias{Hajekstrata} \title{The Hajek estimator for a stratified design} \description{Computes the Hjek estimator of the population total or population mean for a stratified design.} \usage{Hajekstrata(y,pik,strata,N=NULL,type=c("total","mean"),description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{N}{vector of population sizes of strata; N is only used for the total estimator; for the mean estimator its value is NULL.} \item{type}{the estimator type: total or mean.} \item{description}{if TRUE, the estimator is printed for each stratum; by default, FALSE.} } \seealso{ \code{\link{HTstrata}} } \examples{ # Swiss municipalities data data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement # (equal probability, without replacement) st=strata(swissmunicipalities,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the swsissmunicipalities data x=getdata(swissmunicipalities, st) # computes the population sizes of strata N=table(swissmunicipalities$REG) N=N[unique(x$REG)] #the strata 1 2 3 4 5 6 7 #corresponds to REG 4 1 3 2 5 6 7 # computes the Hajek estimator of the total of Pop020 Hajekstrata(x$Pop020,x$Prob,x$Stratum,N,type="total",description=TRUE)} \keyword{survey} \encoding{latin1} sampling/man/landingcube.Rd0000644000176200001440000000321414516451542015410 0ustar liggesusers\name{landingcube} \alias{landingcube} \title{Landing phase for the cube method} \description{ Landing phase of the cube method using linear programming. } \usage{landingcube(X,pikstar,pik,comment=TRUE)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{pikstar}{vector obtained at the end of the flight phase.} \item{pik}{vector of inclusion probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} } \references{ Till, Y. (2006), \emph{Sampling Algorithms}, Springer.\cr Chauvet, G. and Till, Y. (2006). A fast algorithm of balanced sampling. \emph{Computational Statistics}, 21/1:53--62. \cr Chauvet, G. and Till, Y. (2005). New SAS macros for balanced sampling. In INSEE, editor, \emph{Journes de Mthodologie Statistique}, Paris.\cr Deville, J.-C. and Till, Y. (2004). Efficient balanced sampling: the cube method. \emph{Biometrika}, 91:893--912.\cr Deville, J.-C. and Till, Y. (2005). Variance approximation under balanced sampling. \emph{Journal of Statistical Planning and Inference}, 128/2:411--425. } \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}} } \examples{ # matrix of balancing variables X=cbind(c(1,1,1,1,1,1,1,1,1),c(1.1,2.2,3.1,4.2,5.1,6.3,7.1,8.1,9.1)) # the sample size is 3 # vector of inclusion probabilities pik=c(1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3,1/3) # pikstar is almost a balanced sample and is ready for the landing phase pikstar=fastflightcube(X,pik,order=1,comment=TRUE) # selection of the sample s=landingcube(X,pikstar,pik,comment=TRUE) round(s) } \keyword{survey} \encoding{latin1} sampling/man/UPtille.Rd0000644000176200001440000000244714516451542014522 0ustar liggesusers\name{UPtille} \alias{UPtille} \title{Tille sampling} \description{ Uses the Till's method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPtille(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value eps is used to control pik (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPsystematic}} } \references{ Till, Y. (1996), An elimination procedure of unequal probability sampling without replacement, \emph{Biometrika}, 83:238-241.\cr Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89-101. } \examples{ ############ ## Example 1 ############ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPtille(pik) #the sample is which(s==1) ############ ## Example 2 ############ # see in the 'UPexamples' vignette # vignette("UPexamples", package="sampling") } \keyword{survey} \encoding{latin1} sampling/man/ratioest.Rd0000644000176200001440000000217014516740115014764 0ustar liggesusers\name{ratioest} \alias{ratioest} \title{Ratio estimator} \description{Computes the ratio estimator of the population total.} \usage{ratioest(y,x,Tx,pik)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{x}{vector of auxiliary information; its length is equal to n, the sample size.} \item{Tx}{population total of x.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} } \value{The function returns the value of the ratio estimator.} \seealso{ \code{\link{regest}} } \examples{ # population data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85; sample size 120 pik=inclusionprobabilities(P85,120) # defines the variable of interest y=RMT85 # defines the auxiliary information x=CS82 # draws a systematic sample of size 120 s=UPsystematic(pik) # computes the ratio estimator of the total of RMT85 ratioest(y[s==1],x[s==1],sum(x),pik[s==1]) detach(MU281) } \keyword{survey}sampling/man/UPsystematicpi2.Rd0000644000176200001440000000170614516451542016206 0ustar liggesusers\name{UPsystematicpi2} \alias{UPsystematicpi2} \title{Joint inclusion probabilities for systematic sampling} \description{ Computes the joint (second-order) inclusion probabilities for systematic sampling. } \usage{ UPsystematicpi2(pik) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. } \seealso{\code{\link{UPsystematic}} } \references{ Madow, W.G. (1949), On the theory of systematic sampling, II, \emph{Annals of Mathematical Statistics}, 20, 333-354. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #matrix of joint inclusion probabilities UPsystematicpi2(pik) } \keyword{survey} sampling/man/ratioest_strata.Rd0000644000176200001440000000656514516740046016361 0ustar liggesusers\name{ratioest_strata} \alias{ratioest_strata} \title{Ratio estimator for a stratified design} \description{Computes the ratio estimator of the population total for a stratified design. The ratio estimator of a total is the sum of ratio estimator in each stratum.} \usage{ratioest_strata(y,x,TX_strata,pik,strata,description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{x}{vector of auxiliary information; its length is equal to n, the sample size.} \item{TX_strata}{vector of population x-total in each stratum; its length is equal to the number of strata.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{description}{if TRUE, the ratio estimator in each stratum is printed; by default, it is FALSE.} } \value{The function returns the value of the ratio estimator.} \seealso{ \code{\link{ratioest}} } \examples{ ########### # Example 1 ########### # uses MU284 data as population with the 'REG' variable for stratification data(MU284) # there are 3 outliers which are deleted from the population MU281=MU284[MU284$RMT85<=3000,] attach(MU281) # computes the inclusion probabilities using the variable P85 # sample size 120 pik=inclusionprobabilities(P85,120) # defines the variable of interest y=RMT85 # defines the auxiliary information x=CS82 # computes the population stratum sizes table(REG) # not run # 1 2 3 4 5 6 7 8 # 24 48 32 37 55 41 15 29 # a sample is drawn in each region # the sample stratum sizes are given by size=c(4,10,8,4,6,4,6,7) s=strata(MU281,c("REG"),size=c(4,10,8,4,6,4,6,7), method="systematic",pik=P85) # extracts the observed data MU281sample=getdata(MU281,s) # computes the population x-totals in each stratum TX_strata=as.vector(tapply(CS82,list(REG),FUN=sum)) # computes the ratio estimator ratioest_strata(MU281sample$RMT85,MU281sample$CS82,TX_strata, MU281sample$Prob,MU281sample$Stratum) detach(MU281) ########### # Example 2 ########### # this is an artificial example (see Example 1 in the 'strata' function) # there are 4 columns: state, region, income and aux # 'income' is the variable of interest, and 'aux' is the auxiliary information # which is correlated to the income data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") attach(data) aux=income+rnorm(length(income),0,1) data=cbind.data.frame(data,aux) # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values; one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data xx=getdata(data,s) # computes the population x-total for each stratum TX_strata=na.omit(as.vector(tapply(aux,list(region,state),FUN=sum))) # computes the ratio estimator ratioest_strata(xx$income,xx$aux,TX_strata,xx$Prob,xx$Stratum,description=TRUE) } \keyword{survey} sampling/man/poststrata.Rd0000644000176200001440000000264614516451542015351 0ustar liggesusers\name{poststrata} \alias{poststrata} \title{Postratification} \description{Poststratification using several criteria.} \usage{poststrata(data, postnames = NULL)} \arguments{ \item{data}{data frame or data matrix; its number of rows is n, the sample size.} \item{postnames}{vector of poststratification variables.} } \value{ \item{The function}{produces an object, which contains the following information:} \item{data}{the final data frame with a new column ('poststratum') containg the unit poststratum.} \item{npost}{the number of poststrata.} } \seealso{ \code{\link{postest}}} \examples{ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # postratification using two criteria: state and region poststrata(data,postnames=c("state","region")) } \keyword{survey} sampling/man/balancedtwostage.Rd0000644000176200001440000000362214516451542016447 0ustar liggesusers\name{balancedtwostage} \alias{balancedtwostage} \title{Balanced two-stage sampling} \description{ Selects a balanced two-stage sample.} \usage{balancedtwostage(X,selection,m,n,PU,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{selection}{1, for simple random sampling without replacement at each stage,\cr 2, for self-weighting two-stage selection.} \item{m}{number of primary sampling units to be selected.} \item{n}{number of second-stage sampling units to be selected.} \item{PU}{vector of integers that defines the primary sampling units.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \value{The function returns a matrix whose columns are the following five vectors: the selected second-stage sampling units (0 - unselected, 1 - selected), the final inclusion probabilities, the selected primary sampling units, the inclusion probabilities of the first stage, the inclusion probabilities of the second stage.} \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}}, \code{\link{balancedstratification}}, \code{\link{balancedcluster}} } \examples{ ############ ## Example 1 ############ # definition of the primary units (3 primary units) PU=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # selection of 2 primary sampling units and 4 second-stage sampling units # sample and inclusion probabilities s=balancedtwostage(X,1,2,4,PU,comment=TRUE) s ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$ME84) N=dim(X)[1] PU=MU284$CL m=20 n=60 # sample and inclusion probabilities s=balancedtwostage(X,1,m,n,PU,TRUE) s } \keyword{survey} sampling/man/UPrandomsystematic.Rd0000644000176200001440000000207714516451542016776 0ustar liggesusers\name{UPrandomsystematic} \alias{UPrandomsystematic} \title{Random systematic sampling} \description{ Selects a sample using the systematic method, when the order of the population units is random (unequal probabilities, without replacement, fixed sample size). } \usage{ UPrandomsystematic(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps and pik<1-eps). } \seealso{\code{\link{UPsystematic}} } \references{ Madow, W.G. (1949), On the theory of systematic sampling, II, \emph{Annals of Mathematical Statistics}, 20, 333-354. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPrandomsystematic(pik) #the sample is (1:length(pik))[s==1] } \keyword{survey} sampling/man/UPminimalsupport.Rd0000644000176200001440000000244214516451542016467 0ustar liggesusers\name{UPminimalsupport} \alias{UPminimalsupport} \title{Minimal support sampling} \description{ Uses the minimal support method to select a sample of units (unequal probabilities, without replacement, fixed sample size). } \usage{ UPminimalsupport(pik) } \arguments{ \item{pik}{vector of the inclusion probabilities.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \references{ Deville, J.-C., Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika }, 85, 89-101.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ ############ ## Example 1 ############ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #selects a sample s=UPminimalsupport(pik) #the sample is which(s==1) ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune pik=inclusionprobabilities(Tot,200) #selects a sample s=UPminimalsupport(pik) #the sample is which(s==1) #names of the selected units as.vector(name[s==1]) } \keyword{survey} \encoding{latin1} sampling/man/checkcalibration.Rd0000644000176200001440000000272414516451542016427 0ustar liggesusers\name{checkcalibration} \alias{checkcalibration} \title{Check calibration} \description{Checks the validity of the calibration. In some cases, the computed g-weights do not allow calibration and the calibration estimators do not exist.} \value{ The function returns the following three objects: \item{message}{a message concerning the calibration,} \item{result}{TRUE if the calibration is possible and FALSE, otherwise.} \item{value}{value of max(abs(tr-total)/total, which is used as criterium to validate the calibration, where tr=crossprod(Xs, g*d). If the \code{total} vector contains zeros, the value is max(abs(tr-total)).} } \usage{checkcalibration(Xs, d, total, g, EPS=1e-6)} \arguments{ \item{Xs}{matrix of calibration variables.} \item{d}{vector of initial weights.} \item{total}{vector of population totals.} \item{g}{vector of g-weights.} \item{EPS}{control value used to check the calibration, by default equal to 1e-6.} } \details{In the case where calibration is not possible, the 'value' indicates the difference in obtaining the calibration.} \seealso{ \code{\link{calib}} } \examples{ # matrix of auxiliary variables Xs=cbind(c(1,1,1,1,1,0,0,0,0,0),c(0,0,0,0,0,1,1,1,1,1),c(1,2,3,4,5,6,7,8,9,10)) # inclusion probabilities pik=rep(0.2,times=10) # vector of totals total=c(24,26,280) # g-weights g=calib(Xs,d=1/pik,total,method="raking") # check if the calibration is possible checkcalibration(Xs,d=1/pik,total,g) } \keyword{survey} sampling/man/UPrandompivotal.Rd0000644000176200001440000000221614516451542016262 0ustar liggesusers\name{UPrandompivotal} \alias{UPrandompivotal} \title{Random pivotal sampling} \description{ Selects a sample using the pivotal method, when the order of the population units is random (unequal probabilities, without replacement, fixed sample size). } \usage{ UPrandompivotal(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). The value 'eps' is used to control pik (pik>eps and pik<1-eps). } \seealso{\code{\link{UPpivotal}} } \references{ Deville, J.-C. and Till, Y. (1998), Unequal probability sampling without replacement through a splitting method, \emph{Biometrika}, 85:89--101.\cr Till, Y. (2006), \emph{Sampling Algorithms}, Springer. } \examples{ #define the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #select a sample s=UPrandompivotal(pik) #the sample is which(s==1) } \keyword{survey} \encoding{latin1} sampling/man/varHT.Rd0000644000176200001440000000354114516451542014164 0ustar liggesusers\name{varHT} \alias{varHT} \title{Variance estimators of the Horvitz-Thompson estimator} \description{Computes variance estimators of the Horvitz-Thompson estimator of the population total.} \usage{varHT(y,pikl,method)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pikl}{matrix of joint inclusion probabilities; its dimension is nxn.} \item{method}{if 1, an unbiased variance estimator is computed; if 2, the Sen-Yates-Grundy variance estimator for fixed sample size is computed; be default, the method is 1.} } \details{ If method is 1, the following estimator is implemented \deqn{\widehat{Var}(\widehat{Y}_{HT})_1=\sum_{k\in s}\sum_{\ell\in s} \frac{y_k y_\ell}{\pi_{k\ell} \pi_k \pi_\ell}(\pi_{k\ell} - \pi_k \pi_\ell)} If method is 2, the following estimator is implemented \deqn{\widehat{Var}(\widehat{Y}_{HT})_2=\frac{1}{2}\sum_{k\in s}\sum_{\ell\in s} \left(\frac{y_k}{\pi_k} - \frac{y_\ell}{\pi_\ell}\right)^2 \frac{\pi_k \pi_\ell-\pi_{k\ell}}{\pi_{k\ell}}}} \seealso{ \code{\link{HTestimator}} } \examples{ pik=c(0.2,0.7,0.8,0.5,0.4,0.4) N=length(pik) n=sum(pik) # Defines the variable of interest y=rnorm(N,10,2) # Draws a Poisson sample of expected size n s=UPpoisson(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the joint inclusion prob. for Poisson sampling pikl=outer(pik,pik,"*") diag(pikl)=pik # Computes the variance estimator (method=1, the sample size is not fixed) varHT(y[s==1],pikl[s==1,s==1],1) # Draws a Tille sample of size n s=UPtille(pik) # Computes the Horvitz-Thompson estimator HTestimator(y[s==1],pik[s==1]) # Computes the joint inclusion prob. for Tille sampling pikl=UPtillepi2(pik) # Computes the variance estimator (method=2, the sample size is fixed) varHT(y[s==1],pikl[s==1,s==1],2) } \keyword{survey}sampling/man/MU284.Rd0000644000176200001440000000237214516451542013720 0ustar liggesusers\name{MU284} \alias{MU284} \docType{data} \title{ The MU284 population } \description{ This data is from Srndal et al (1992), see Appendix B, p. 652. } \usage{data(MU284)} \format{ A data frame with 284 observations on the following 11 variables. \describe{ \item{LABEL}{identifier number from 1 to 284.} \item{P85}{1985 population (in thousands).} \item{P75}{1975 population (in thousands).} \item{RMT85}{revenues from 1985 municipal taxation (in millions of kronor).} \item{CS82}{number of Conservative seats in municipal council.} \item{SS82}{number of Social-Democratic seats in municipal council.} \item{S82}{total number of seats in municipal council.} \item{ME84}{number of municipal employees in 1984.} \item{REV84}{real estate values according to 1984 assessment (in millions of kronor).} \item{REG}{geographic region indicator.} \item{CL}{cluster indicator (a cluster consists of a set of neighboring).} } } \references{ Srndal, C.-E., Swensson, B., and Wretman, J. (1992), \emph{Model Assisted Survey Sampling}, Springer Verlag, New York. } \source{ http://lib.stat.cmu.edu/datasets/mu284 } \examples{ data(MU284) hist(MU284$RMT85) } \keyword{datasets} \encoding{latin1} sampling/man/postest.Rd0000644000176200001440000001021314516745421014635 0ustar liggesusers\name{postest} \alias{postest} \title{Poststratified estimator} \description{Computes the poststratified estimator of the population total.} \usage{postest(data, y, pik, NG, description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is n, the sample size.} \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{NG}{vector of population frequency in each group G; for stratified sampling with poststratification, NG is a matrix of population frequency in each cell GH.} \item{description}{if TRUE, the estimator is printed for each poststratum; by default, FALSE.} } \seealso{ \code{\link{poststrata}}} \examples{ ############ ## Example 1 ############ #stratified sampling and poststratification data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # Computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement st=strata(swissmunicipalities,stratanames=c("REG"), size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial data x=getdata(swissmunicipalities, st) px=poststrata(x,"REG") #computes the population frequency in each group ct=unique(px$data$REG) yy=table(swissmunicipalities$REG)[ct] postest(px$data,y=px$data$Pop020,pik=px$data$Prob,NG=diag(yy)) HTstrata(x$Pop020,x$Prob,x$Stratum) #the two estimators are equal ############ ## Example 2 ############ # systematic sampling and poststratification data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune pik=inclusionprobabilities(Tot,200) #selects a sample s=UPsystematic(pik) #the sample is which(s==1) # extracts the observed data b=getdata(belgianmunicipalities,s) pb=poststrata(b,"Province") #computes the population frequency in each group ct=unique(pb$data$Province) yy=table(belgianmunicipalities$Province)[ct] postest(pb$data,y=pb$data$TaxableIncome,pik=pik[s==1],NG=yy,description=TRUE) HTestimator(pb$data$TaxableIncome,pik=pik[s==1]) ############ ## Example 3 ############ #cluster sampling and postratification data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as clustering variable # the sample size is 3; the method is simple random sampling without replacement cl=cluster(swissmunicipalities,clustername=c("REG"),size=3,method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial data c=getdata(swissmunicipalities, cl) pc=poststrata(c,"CT") #computes the population frequency in each group ct=unique(pc$data$CT) yy=table(swissmunicipalities$CT)[ct] postest(pc$data,y=pc$data$Pop020,pik=pc$data$Prob,NG=yy,description=TRUE) ############ ## Example 4 ############ #postratification with two criteria #artificial data data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 #selects a sample of size 10 s=srswor(10,nrow(data)) # postratification using region and state ps=poststrata(data[s==1,],c("region","state")) #computes the population frequency in each group ct=unique(ps$data$poststratum) yy=numeric(length(ct)) for(i in 1:length(ct)) { xy=ps$data[ps$data$poststratum==ct[i],] xstate=unique(xy$state) ystate=unique(xy$region) xx=data[data$state==xstate & data$region==ystate,] yy[i]=nrow(xx) } postest(ps$data,y=ps$data$income,pik=rep(10/nrow(data),10),NG=yy,description=TRUE) } \keyword{survey} sampling/man/calibev.Rd0000644000176200001440000000736514516740303014551 0ustar liggesusers\name{calibev} \alias{calibev} \title{Calibration estimator and its variance estimation} \description{Computes the calibration estimator of the population total and its variance estimation using the residuals' method. } \usage{calibev(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)),with=FALSE,EPS=1e-6)} \arguments{ \item{Ys}{vector of interest variable; its size is n, the sample size.} \item{Xs}{matrix of sample calibration variables.} \item{total}{vector of population totals for calibration.} \item{pikl}{matrix of joint inclusion probabilities of the sample units.} \item{d}{vector of initial weights of the sample units.} \item{g}{vector of g-weights; its size is n, the sample size.} \item{q}{vector of positive values accounting for heteroscedasticity; its size is n, the sample size.} \item{with}{if TRUE, the variance estimation takes into account the initial weights d; otherwise, the final weights w=g*d are taken into account; by default, its value is FALSE.} \item{EPS}{tolerance in checking the calibration; by default, its value is 1e-6.} } \value{ The function returns two values: \item{cest}{the calibration estimator,} \item{evar}{its estimated variance.} } \details{ If with is TRUE, the following formula is used \deqn{\widehat{Var}(\widehat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(d_ke_k)(d_\ell e_\ell)}{\hat{Var}(\hat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(d_ke_k)(d_\ell e_\ell)} else \deqn{\widehat{Var}(\widehat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(w_ke_k)(w_\ell e_\ell)}{\hat{Var}(\hat{Ys})=\sum_{k\in s}\sum_{\ell\in s}((\pi_{k\ell}-\pi_k\pi_{\ell})/\pi_{k\ell})(w_ke_k)(w_\ell e_\ell)} where \eqn{e_k} denotes the residual of unit k. } \references{ Deville, J.-C. and Srndal, C.-E. (1992). Calibration estimators in survey sampling. \emph{Journal of the American Statistical Association}, 87:376--382.\cr Deville, J.-C., Srndal, C.-E., and Sautory, O. (1993). Generalized raking procedure in survey sampling. \emph{Journal of the American Statistical Association}, 88:1013--1020.\cr } \seealso{ \code{\link{calib}} } \examples{ ############ ## Example ############ # Example of g-weights (linear, raking, truncated, logit), # with the data of Belgian municipalities as population. # Firstly, a sample is selected by means of systematic sampling. # Secondly, the g-weights are calculated. data(belgianmunicipalities) attach(belgianmunicipalities) # matrix of calibration variables for the population X=cbind( Men03/mean(Men03), Women03/mean(Women03), Diffmen, Diffwom, TaxableIncome/mean(TaxableIncome), Totaltaxation/mean(Totaltaxation), averageincome/mean(averageincome), medianincome/mean(medianincome)) # selection of a sample of size 200 # using systematic sampling # the inclusion probabilities are proportional to the average income pik=inclusionprobabilities(averageincome,200) N=length(pik) # population size s=UPsystematic(pik) # draws a sample s using systematic sampling Xs=X[s==1,] # matrix of sample calibration variables piks=pik[s==1] # sample inclusion probabilities n=length(piks) # sample size # vector of population totals of the calibration variables total=c(t(rep(1,times=N))\%*\%X) g1=calib(Xs,d=1/piks,total,method="linear") # computes the g-weights pikl=UPsystematicpi2(pik) # computes the matrix of joint inclusion probabilities pikls=pikl[s==1,s==1] # the same matrix for the units in the sample Ys=Tot04[s==1] # the variable of interest is Tot04 (sample level) calibev(Ys,Xs,total,pikls,d=1/piks,g1,with=FALSE,EPS=1e-6) detach(belgianmunicipalities) } \keyword{survey} \encoding{latin1} sampling/man/disjunctive.Rd0000644000176200001440000000105214516451542015462 0ustar liggesusers\name{disjunctive} \alias{disjunctive} \title{Disjunctive combination} \description{ Transforms a categorical variable into a matrix of indicators. The values of the categorical variable are integer numbers (positive or negative). } \usage{disjunctive(strata)} \arguments{ \item{strata}{vector of integer numbers.} } \seealso{\code{ \link{balancedstratification}} } \examples{ # definition of the variable of stratification strata=c(-2,3,-2,3,4,4,4,-2,-2,3,4,0,0,0) # computation of the matrix disjunctive(strata) } \keyword{survey} sampling/man/HTstrata.Rd0000644000176200001440000000305714516451542014674 0ustar liggesusers\name{HTstrata} \alias{HTstrata} \title{The Horvitz-Thompson estimator for a stratified design} \description{Computes the Horvitz-Thompson estimator of the population total for a stratified design.} \usage{HTstrata(y,pik,strata,description=FALSE)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities for the sampled units; its length is equal to n, the sample size.} \item{strata}{vector of size n, with elements indicating the unit stratum.} \item{description}{if TRUE, the estimator is printed for each stratum; by default, FALSE.} } \seealso{ \code{\link{HTestimator}} } \examples{ # Swiss municipalities data base data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # the method is simple random sampling without replacement # (equal probability, fixed sample size, without replacement) st=strata(swissmunicipalities,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data # the order of the columns is different from the order in the initial data x=getdata(swissmunicipalities, st) # computes the HT estimator of the total of Pop020 HTstrata(x$Pop020,x$Prob,x$Stratum,description=TRUE) } \keyword{survey} sampling/man/srswor1.Rd0000644000176200001440000000160314516451542014555 0ustar liggesusers\name{srswor1} \alias{srswor1} \title{Selection-rejection method} \description{ Draws a simple random sampling without replacement of size n using the selection-rejection method (equal probabilities, fixed sample size, without replacement). } \usage{ srswor1(n,N) } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \arguments{ \item{n}{sample size.} \item{N}{population size.} } \references{Fan, C.T., Muller, M.E., Rezucha, I. (1962), Development of sampling plans by using sequential (item by item) selection techniques and digital computer, \emph{Journal of the American Statistical Association}, 57, 387--402. } \seealso{\code{\link{srswor}}} \examples{ s=srswor1(3,10) #the sample is which(s==1) } \keyword{survey} sampling/man/rhg.Rd0000644000176200001440000000325714516451542013724 0ustar liggesusers\name{rhg} \alias{rhg} \title{Response homogeneity groups} \description{Computes the response homogeneity groups and the response probability for each unit in these groups. } \usage{rhg(X,selection)} \arguments{ \item{X}{sample data frame; it should contain the columns 'ID_unit' and 'status'; 'ID_unit' denotes the unit identifier (a number); 'status' is a 1/0 variable denoting the response/non-response of a unit.} \item{selection}{vector of variable names in X used to construct the groups.} } \details{ Into a response homogeneity group, the reponse probability is the same for all units. Data are missing at random within groups, conditionally on the selected sample. } \value{ The initial sample data frame and also the following components: \item{rhgroup}{the response homogeneity group for each unit.} \item{prob_response}{the response probability for each unit; for the units with status=0, this probability is 0.} } \references{ Srndal, C.-E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling. \emph{Springer} } \seealso{ \code{\link{rhg_strata}}, \code{\link{calib}} } \examples{ # defines the inclusion probabilities for the population pik=c(0.2,0.7,0.8,0.5,0.4,0.4) # X is the population data frame X=cbind.data.frame(pik,c("A","B","A","A","C","B")) names(X)=c("Prob","town") # selects a sample using systematic sampling s=UPsystematic(pik) # Xs is the sample data frame Xs=getdata(X,s) # adds the status column to Xs (1 - sample respondent, 0 otherwise) Xs=cbind.data.frame(Xs,status=c(1,0,1)) # creates the response homogeneity groups using the 'town' variable rhg(Xs,selection="town") } \keyword{survey} \encoding{latin1} sampling/man/strata.Rd0000644000176200001440000001055214516451542014436 0ustar liggesusers\name{strata} \alias{strata} \title{Stratified sampling} \description{Stratified sampling with equal/unequal probabilities.} \usage{strata(data, stratanames=NULL, size, method=c("srswor","srswr","poisson", "systematic"), pik,description=FALSE)} \arguments{ \item{data}{data frame or data matrix; its number of rows is N, the population size.} \item{stratanames}{vector of stratification variables.} \item{size}{vector of stratum sample sizes (in the order in which the strata are given in the input data set).} \item{method}{method to select units; the following methods are implemented: simple random sampling without replacement (srswor), simple random sampling with replacement (srswr), Poisson sampling (poisson), systematic sampling (systematic); if "method" is missing, the default method is "srswor".} \item{pik}{vector of inclusion probabilities or auxiliary information used to compute them; this argument is only used for unequal probability sampling (Poisson and systematic). If an auxiliary information is provided, the function uses the \link{inclusionprobabilities} function for computing these probabilities. } \item{description}{a message is printed if its value is TRUE; the message gives the number of selected units and the number of the units in the population. By default, the value is FALSE.} } \value{ The function produces an object, which contains the following information: \item{ID_unit}{the identifier of the selected units.} \item{Stratum}{the unit stratum.} \item{Prob}{the unit inclusion probability.} } \details{The data should be sorted in ascending order by the columns given in the stratanames argument before applying the function. Use, for example, data[order(data$state,data$region),]. } \seealso{ \code{\link{getdata}}, \code{\link{mstage}}} \examples{ ############ ## Example 1 ############ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the sampling frame is stratified by region within state. # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values # one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data getdata(data,s) # see the result using a contigency table table(s$region,s$state) ############ ## Example 2 ############ # The same data as in Example 1 # the method is 'systematic' (unequal probability, without replacement) # the selection probabilities are computed using the variable 'income' s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="systematic",pik=data$income) # extracts the observed data getdata(data,s) # see the result using a contigency table table(s$region,s$state) ############ ## Example 3 ############ # Uses the 'swissmunicipalities' data as population for drawing a sample of units data(swissmunicipalities) # the variable 'REG' has 7 categories in the population # it is used as stratification variable # Computes the population stratum sizes table(swissmunicipalities$REG) # do not run # 1 2 3 4 5 6 7 # 589 913 321 171 471 186 245 # sort the data to obtain the same order of the regions in the sample data=swissmunicipalities data=data[order(data$REG),] # the sample stratum sizes are given by size=c(30,20,45,15,20,11,44) # 30 units are drawn in the first stratum, 20 in the second one, etc. # the method is simple random sampling without replacement # (equal probability, without replacement) st=strata(data,stratanames=c("REG"),size=c(30,20,45,15,20,11,44), method="srswor") # extracts the observed data getdata(data, st) # see the result using a contingency table table(st$REG) } \keyword{survey} sampling/man/Hajekestimator.Rd0000644000176200001440000000231614516451542016111 0ustar liggesusers\name{Hajekestimator} \alias{Hajekestimator} \title{The Hajek estimator} \description{Computes the Hjek estimator of the population total or population mean.} \usage{Hajekestimator(y,pik,N=NULL,type=c("total","mean"))} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} \item{N}{population size; N is only used for the total estimator; for the mean estimator its value is NULL.} \item{type}{the estimator type: total or mean.} } \seealso{ \code{\link{HTestimator}} } \examples{ # Belgian municipalities data data(belgianmunicipalities) # Computes the inclusion probabilities pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) # Defines the variable of interest y=belgianmunicipalities$TaxableIncome # Draws a Poisson sample of expected size 200 s=UPpoisson(pik) # Computes the Hajek estimator of the population mean Hajekestimator(y[s==1],pik[s==1],type="mean") # Computes the Hajek estimator of the population total Hajekestimator(y[s==1],pik[s==1],N=N,type="total") } \keyword{survey} \encoding{latin1} sampling/man/UPtillepi2.Rd0000644000176200001440000000211414516451542015124 0ustar liggesusers\name{UPtillepi2} \alias{UPtillepi2} \title{Joint inclusion probabilties for Tille sampling} \description{ Computes the joint (second-order) inclusion probabilities for Till sampling. } \usage{ UPtillepi2(pik,eps=1e-6) } \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} \item{eps}{control value, by default equal to 1e-6.} } \value{ Returns a NxN matrix of the following form: the main diagonal contains the first-order inclusion probabilities for each unit k in the population; elements (k,l) are the joint inclusion probabilities of units k and l, with k not equal to l. N is the population size. The value \code{eps} is used to control \code{pik} (pik>eps & pik < 1-eps). } \seealso{\code{\link{UPtille}} } \references{ Till, Y. (1996), An elimination procedure of unequal probability sampling without replacement, \emph{Biometrika}, 83:238-241. } \examples{ #defines the prescribed inclusion probabilities pik=c(0.2,0.7,0.8,0.5,0.4,0.4) #matrix of joint inclusion probabilities UPtillepi2(pik) } \keyword{survey} \encoding{latin1} sampling/man/regest_strata.Rd0000644000176200001440000000323614516451542016010 0ustar liggesusers\name{regest_strata} \alias{regest_strata} \title{Regression estimator for a stratified design} \description{Computes the regression estimator of the population total for a stratified sampling, using the design-based approach. The same regression model is used for all strata. The underling regression model is a model without intercept.} \usage{regest_strata(formula,weights,Tx_strata,strata,pikl, sigma=rep(1,length(weights)),description=FALSE)} \arguments{ \item{formula}{regression model formula (y~x).} \item{weights}{vector of the weights; its length is equal to n, the sample size.} \item{Tx_strata}{population total of x, the auxiliary variable.} \item{strata}{vector of stratum identificator.} \item{pikl}{joint inclusion probabilities for the sample.} \item{sigma}{vector of positive values accounting for heteroscedasticity.} \item{description}{if TRUE, the following components are printed for each stratum: the Horvitz-Thompson estimator, the estimated beta coefficients, their estimated standard error, t_values, p_values, and the covariance matrix. By default, FALSE.} } \value{ The function returns the value of the regression estimator computed as the sum of the stratum estimators. } \seealso{ \code{\link{regest}} } \examples{ # generates artificial data y=rgamma(10,3) x=y+rnorm(10) Stratum=c(1,1,2,2,2,3,3,3,3,3) # population size N=200 # sample size n=10 # assume proportional allocation, nh/Nh=n/N # joint inclusion probabilities (for the sample) pikl=matrix(n*(n-1)/(N*(N-1)),n,n) diag(pikl)=n/N regest_strata(formula=y~x-1,weights=rep(N/n,n),Tx_strata=c(50,30,40), strata=Stratum,pikl,description=TRUE) } \keyword{survey} sampling/man/balancedcluster.Rd0000644000176200001440000000337614516451542016301 0ustar liggesusers\name{balancedcluster} \alias{balancedcluster} \title{Balanced cluster} \description{ Selects a balanced cluster sample. } \usage{balancedcluster(X,m,cluster,selection=1,comment=TRUE,method=1)} \arguments{ \item{X}{matrix of auxiliary variables on which the sample must be balanced.} \item{m}{number of clusters to be selected.} \item{cluster}{vector of integers that defines the clusters.} \item{selection}{1, selection of the clusters with probabilities proportional to size,\cr 2, selection of the clusters with equal probabilities.} \item{comment}{a comment is written during the execution if \code{comment} is \code{TRUE}.} \item{method}{the used method in the function \code{samplecube}.} } \value{Returns a matrix containing the vector of inclusion probabilities and the selected sample.} \seealso{ \code{\link{samplecube}}, \code{\link{fastflightcube}}, \code{\link{landingcube}} } \examples{ ############ ## Example 1 ############ # definition of the clusters; there are 15 units in 3 clusters cluster=c(1,1,1,1,1,2,2,2,2,2,3,3,3,3,3) # matrix of balancing variables X=cbind(c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15)) # selection of 2 clusters s=balancedcluster(X,2,cluster,2,TRUE) # the sample of clusters with the inclusion probabilities of the clusters s # the selected clusters unique(cluster[s[,1]==1]) # the selected units (1:length(cluster))[s[,1]==1] # with the probabilities s[s[,1]==1,2] ############ ## Example 2 ############ data(MU284) X=cbind(MU284$P75,MU284$CS82,MU284$SS82,MU284$S82,MU284$ME84) s=balancedcluster(X,10,MU284$CL,1,TRUE) cluster=MU284$CL # the selected clusters unique(cluster[s[,1]==1]) # the selected units (1:length(cluster))[s[,1]==1] # with the probabilities s[s[,1]==1,2] } \keyword{survey} sampling/man/rmodel.Rd0000644000176200001440000000404314516451542014420 0ustar liggesusers\name{rmodel} \alias{rmodel} \title{Response probability using logistic regression} \description{Computes the response probabilities using logistic regression for non-response adjustment. For stratified sampling, the same logistic model is used for all strata.} \usage{rmodel(formula,weights,X)} \arguments{ \item{formula}{regression model formula (y~x).} \item{weights}{vector of weights; its length is equal to n, the sample size.} \item{X}{sample data frame.} } \value{The function returns the sample data frame with a new column 'prob_resp', which contains the response probabilities.} \seealso{ \code{\link{rhg}} } \examples{ # Example from An and Watts (New SAS procedures for Analysis of Sample Survey Data) # generates artificial data (a 235X3 matrix with 3 columns: state, region, income). # the variable "state" has 2 categories ('nc' and 'sc'). # the variable "region" has 3 categories (1, 2 and 3). # the sampling frame is stratified by region within state. # the income variable is randomly generated data=rbind(matrix(rep("nc",165),165,1,byrow=TRUE),matrix(rep("sc",70),70,1,byrow=TRUE)) data=cbind.data.frame(data,c(rep(1,100), rep(2,50), rep(3,15), rep(1,30),rep(2,40)), 1000*runif(235)) names(data)=c("state","region","income") # computes the population stratum sizes table(data$region,data$state) # not run # nc sc # 1 100 30 # 2 50 40 # 3 15 0 # there are 5 cells with non-zero values; one draws 5 samples (1 sample in each stratum) # the sample stratum sizes are 10,5,10,4,6, respectively # the method is 'srswor' (equal probability, without replacement) s=strata(data,c("region","state"),size=c(10,5,10,4,6), method="srswor") # extracts the observed data x=getdata(data,s) # generates randomly the 'status' column (1 - respondent, 0 - nonrespondent) status=round(runif(nrow(x))) x=cbind(x,status) # computes the response probabilities rmodel(x$status~x$income+x$Stratum,weights=1/x$Prob,x) # the same example without stratification rmodel(x$status~x$income,weights=1/x$Prob,x) } \keyword{survey} sampling/man/sampling-internal.Rd0000644000176200001440000000034214517464451016564 0ustar liggesusers\name{sampling-internal} \alias{.as_int} \title{Internal sampling Functions} \description{ Internal sampling function } \usage{ .as_int(x) } \details{ These are not to be called by the user. } \keyword{internal} sampling/man/UPopips.Rd0000644000176200001440000000204114516451542014531 0ustar liggesusers\name{UPopips} \alias{UPopips} \title{Order pips sampling} \description{ Implements order \eqn{\pi ps} sampling (unequal probabilities, without replacement, fixed sample size). } \usage{ UPopips(lambda,type=c("pareto","uniform","exponential")) } \arguments{ \item{lambda}{vector of working inclusion probabilities or target ones.} \item{type}{the type of order sampling (pareto, uniform, exponential).} } \value{ Returns a vector of the selected units; its length is equal to the sample size. } \seealso{\code{\link{inclusionprobabilities}} } \references{ Rosn, B. (1997), Asymptotic theory for order sampling, \emph{Journal of Statistical Planning and Inference}, 62:135-158.\cr Rosn, B. (1997), On sampling with probability proportional to size, \emph{Journal of Statistical Planning and Inference}, 62:159-191.\cr } \examples{ #define the working inclusion probabilities lambda=c(0.2,0.7,0.8,0.5,0.4,0.4) #draw a Pareto sample s=UPopips(lambda, type="pareto") #the sample is s } \keyword{survey} \encoding{latin1} sampling/man/HTestimator.Rd0000644000176200001440000000146714516740504015407 0ustar liggesusers\name{HTestimator} \alias{HTestimator} \title{The Horvitz-Thompson estimator} \description{Computes the Horvitz-Thompson estimator of the population total.} \usage{HTestimator(y,pik)} \arguments{ \item{y}{vector of the variable of interest; its length is equal to n, the sample size.} \item{pik}{vector of the first-order inclusion probabilities; its length is equal to n, the sample size.} } \seealso{ \code{\link{UPtille}} } \examples{ data(belgianmunicipalities) attach(belgianmunicipalities) # inclusion probabilities pik=inclusionprobabilities(Tot04,200) N=length(pik) n=sum(pik) # draws a Poisson sample of expected size 200 s=UPpoisson(pik) # Horvitz-Thompson estimator of the total of TaxableIncome HTestimator(TaxableIncome[s==1],pik[s==1]) detach(belgianmunicipalities) } \keyword{survey}sampling/man/inclusionprobastrata.Rd0000644000176200001440000000134314516451542017404 0ustar liggesusers\name{inclusionprobastrata} \alias{inclusionprobastrata} \title{Inclusion probabilities for a stratified design} \description{Computes the inclusion probabilities for a stratified design. The inclusion probabilities are equal in each stratum.} \usage{inclusionprobastrata(strata,nh)} \arguments{ \item{strata}{vector that defines the strata.} \item{nh}{vector of the number of selected units in each stratum.} } \seealso{ \code{\link{balancedstratification}} } \examples{ # the strata strata=c(1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,3) # sample size in each stratum nh=c(2,3,3) # inclusion probabilities for each stratum pik=inclusionprobastrata(strata,nh) #check for each stratum cbind(strata, pik) } \keyword{survey} sampling/man/UPpoisson.Rd0000644000176200001440000000210014516451542015065 0ustar liggesusers\name{UPpoisson} \alias{UPpoisson} \title{Poisson sampling} \description{ Draws a Poisson sample using a prescribed vector of first-order inclusion probabilities (unequal probabilities, without replacement, random sample size). } \usage{UPpoisson(pik)} \arguments{ \item{pik}{vector of the first-order inclusion probabilities.} } \value{ Returns a vector (with elements 0 and 1) of size N, the population size. Each element k of this vector indicates the status of unit k (1, unit k is selected in the sample; 0, otherwise). } \seealso{ \code{\link{inclusionprobabilities}} } \examples{ ############ ## Example 1 ############ # inclusion probabilities pik=c(1/3,1/3,1/3) # selects a sample s=UPpoisson(pik) #the sample is which(s==1) ############ ## Example 2 ############ data(belgianmunicipalities) Tot=belgianmunicipalities$Tot04 name=belgianmunicipalities$Commune n=200 pik=inclusionprobabilities(Tot,n) # select a sample s=UPpoisson(pik) #the sample is which(s==1) # names of the selected units getdata(name,s) } \keyword{survey} sampling/DESCRIPTION0000644000176200001440000000113414517474042013601 0ustar liggesusersPackage: sampling Version: 2.10 Date: 2023-10-27 Title: Survey Sampling Author: Yves Tillé , Alina Matei Maintainer: Alina Matei Description: Functions to draw random samples using different sampling schemes are available. Functions are also provided to obtain (generalized) calibration weights, different estimators, as well some variance estimators. Imports: MASS, lpSolve License: GPL (>= 2) Encoding: UTF-8 NeedsCompilation: yes Packaged: 2023-10-29 14:17:06 UTC; MateiA Repository: CRAN Date/Publication: 2023-10-29 15:20:02 UTC sampling/build/0000755000176200001440000000000014517464542013177 5ustar liggesuserssampling/build/vignette.rds0000644000176200001440000000051014517464542015532 0ustar liggesusersQO0 (DԄ_ B,nla3$koc1VgaPc^ \ YӞ7t+|6"#h!A%XV/琈#$r z;~i%=żw\dȻ|MgJ`&a\-yZ,I jMdŽ"I u&Iője\21Gx^"z]捬)h?Tvm9 AN "AX} {}wy{=̐bqAM%7voGwV 6=sampling/src/0000755000176200001440000000000014517464542012667 5ustar liggesuserssampling/src/init.c0000644000176200001440000000066214516451542013775 0ustar liggesusers#include // for NULL #include /* FIXME: Check these declarations against the C/Fortran source code. */ /* .C calls */ extern void str(void *, void *, void *, void *); static const R_CMethodDef CEntries[] = { {"str", (DL_FUNC) &str, 4}, {NULL, NULL, 0} }; void R_init_sampling(DllInfo *dll) { R_registerRoutines(dll, CEntries, NULL, NULL, NULL); R_useDynamicSymbols(dll, FALSE); } sampling/src/str.c0000644000176200001440000000021014516451542013627 0ustar liggesusersvoid str(double *st, int *h, int *n, double *s) { int i; for(i = 0; i < *n; i++) {s[i]=0; if(st[i]==*h) s[i] = 1; } } sampling/vignettes/0000755000176200001440000000000014517464542014110 5ustar liggesuserssampling/vignettes/calibration.Snw0000644000176200001440000003675414515742162017102 0ustar liggesusers\documentclass[a4paper]{article} \usepackage{pdfpages} %\VignetteIndexEntry{calibration and adjustment for nonresponse} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Calibration and generalized calibration} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ \section{Example 1} Example of using the \verb@calib@ function for calibration and nonresponse adjustment (with response homogeneity groups). @ \noindent We create the following population data frame (the population size is $N=250$): \begin{itemize} \item there are four variables: \verb@state@, \verb@region@, \verb@income@ and \verb@sex@; \item the \verb@state@ variable has 2 categories: 'A' and 'B'; the \verb@region@ variable has 3 categories: 1, 2, 3 (regions within states); \item the \verb@income@ and \verb@sex@ variables are randomly generated using the uniform distribution. \end{itemize} <>= data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), matrix(rep("B", 100), 100, 1, byrow = TRUE)) data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), 1000 * runif(250)) sex = runif(nrow(data)) for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 data = cbind.data.frame(data, sex) names(data) = c("state", "region", "income", "sex") summary(data) @ \noindent We compute the population stratum sizes: <>= table(data$state) @ We select a stratified sample. The \verb@state@ variable is used as a stratification variable. The sample stratum sizes are 25 and 20, respectively. The method is 'srswor' (equal probability, without replacement). <>= s=strata(data,c("state"),size=c(25,20), method="srswor") @ We obtain the observed data: <>= s=getdata(data,s) @ The \verb@status@ variable is used in the \verb@rhg_strata@ function. The \verb@status@ column is added to $s$ (1 - sample respondent, 0 otherwise); it is randomly generated using the uniform distribution U(0,1). The response probability for all units is 0.3. <>= status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) @ We compute the response homeogeneity groups using the \verb@region@ variable: <>= s=rhg_strata(s,selection="region") @ We select only the sample respondents: <>= sr=s[s$status==1,] @ We create the population data frame of sex and region indicators: <>= X=cbind(disjunctive(data$sex),disjunctive(data$region)) @ We compute the population totals for each sex and region: <>= total=c(t(rep(1,nrow(data)))%*%X) @ The first method consists in calibrating with all strata. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created. The initial weights using the inclusion prob. and the response probabilities are computed. <>= Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) @ We compute the g-weights using the linear method: <>= g = calib(Xs, d, total, method = "linear") summary(g) @ The final weights are: <>= w=d*g summary(w) @ We check the calibration: <>= checkcalibration(Xs, d, total, g) @ The second method consists in calibrating in each stratum. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created in each stratum. The initial weights using the inclusion prob. and response probabilities are computed in each stratum. <>= cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) @ <>= <> <> <> <> <> <> <> <> <> <> <> <> <> <> sampling.newpage() @ \section{Example 2} This is an example for \begin{itemize} \item variance estimation of the calibration estimator (using the \verb@calibev@ and \verb@varest@ functions), \item variance estimator of the Horvitz-Thompson estimator (using the \verb@varest@ and \verb@varHT@ functions). \end{itemize} We generate an artificial population and use Till\'e sampling. The population size is 100, and the sample size is 20. There are three auxiliary variables (two categorical and one continuous; the matrix $X$). The vector $Z=(150, 151, \dots, 249)'$ is used to compute the first-order inclusion probabilities. The variable of interest $Y$ is computed using the model $Y_j=5*Z_j*(\varepsilon_j+\sum_{i=1}^{100} X_{ij}), \varepsilon_j\sim N(0,1/3), iid, j=1,\dots, 100.$ The calibration estimator uses the linear method. Simulations are conducted to estimate the MSE of the two variance estimators of the calibration estimator. Since the linear method is used in calibration, the calibration estimator corresponds to the generalized regression estimator. For the latter an approximate variance can be computed on the population level and used in the bias estimation of the variance estimators. For the Horvitz-Thompson estimator, the variance can be computed on the population level and compared with the simulations' result. Use 10000 simulation runs to obtain accurate results (for time consuming reason, in the following program, the number of runs is only 10). <>= X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") @ <>= <> sampling.newpage() @ \section{Example 3} This is an example of generalized calibration used to handle unit nonresponse with different forms of response probabilities. Consider the population $U$, the sample $s$ and the set of respondents $r$ with $r\subseteq s \subseteq U.$ The response mechanism is given by the distribution $q(r|s)$ such that for every fixed $s$ we have $$q(r|s)\geq 0, \mbox{ for all } r\in \mathcal{R}_s \mbox{ and } \sum_{s\in {\mathcal R}_s} q(r|s)=1,$$ where ${\mathcal R}_s=\{r | r \subseteq s\}.$ The variable of interest $y_k$ is known only for $k\in r.$ Under unit nonresponse we define the response indicator $R_k=1$ if unit $k\in r$ and 0 otherwise and the response probabilities $p_k=Pr(R_k=1| k\in s).$ It is assumed that $R_k$ are independent Bernoulli variables with expected value equal to $p_k.$ We assume that the units respond independently of each other and of $s$ and so $$q(r|s)=\prod_{k\in r} p_k \prod_{k \in \bar{r}} (1-p_k).$$ The nonresponse model can be rewritten as $$q(r|s, \boldsymbol{\gamma})=\prod_{k\in r} F_k^{-1}(\boldsymbol{\gamma}) \prod_{k \in \bar{r}} (1-F^{-1}_k(\boldsymbol{\gamma})).$$ In calibration method it is assumed that $$\sum_{k\in r} \mathbf{x}_kd_kF_k(\boldsymbol{\gamma})=\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{x}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $F_k(\boldsymbol{\gamma})=F(\boldsymbol{\gamma}^T\mathbf{x}_k), p_k=F_k(\boldsymbol{\gamma})^{-1},$ and $d_k$ are the initial weigths. In generalized calibration a different equation is used $$\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{z}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $\mathbf{z}_k$ is not necessary equal to $\mathbf{x}_k,$ but $\mathbf{z}_k$ and $\mathbf{x}_k$ have to be highly correlated. $\mathbf{z}_k$ should be known only for $k\in r.$ The components of $\mathbf{z}_k$ that are not also components of $\mathbf{x}_k$ are often known as \emph{instrumental variables}. Let $w_k$ be the final weights (obtained after applying generalized calibration). It is possible to assume different forms of response probabilities: \begin{itemize} \item Linear weight adjustment (it can be implemented by using the argument \texttt{method="linear"} in gencalib() function or \texttt{method="truncated"} if bounds are allowed): $p_k=1/(1+ {\boldsymbol\gamma}^T\mathbf{z}_k)$ and $w_k=d_k(1+\mathbf{h}^T\mathbf{z}_k),$ where $\mathbf{h}$ is a consistent estimate of ${\boldsymbol\gamma}.$ \item Raking weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)$ and $w_k=d_k \exp(\mathbf{h}^T\mathbf{z}_k).$ \item Logistic weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/(1+\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)), w_k=d_k (1+\exp(\mathbf{h}^T\mathbf{z}_k)),$ but we calibrate on $\sum_{k\in U} \mathbf{x}_k-\sum_{k\in r} \mathbf{x}_k d_k$ instead of $\sum_{k\in U} \mathbf{x}_k.$\item Generalized exponential weight adjustment (Folsom and Singh, 2000; it can be implemented by using the argument \texttt{method="logit"} in gencalib()): $$p_k=1/F(\boldsymbol{\gamma}^T\mathbf{z}_k), w_k=d_kF(\mathbf{h}^T\mathbf{z}_k),$$ $$F(\mathbf{h}^T\mathbf{z}_k)=\frac{L(U-C)+U(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}{(U-C)+(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}\in (L, U),$$ where $A=(U-L)/((C-L)(U-C))$ and $L\geq 0,1C>L,$ ($C=1$ in the paper of Deville and Sarndal, 1992). The g-weights are centered around of $C.$ For $L=1, C=2$ and $U=\infty, F(\mathbf{h}^T\mathbf{z}_k)$ approaches $1+\exp(\mathbf{h}^T\mathbf{z}_k)$ and for $C=1, L=0, U=\infty,$ $\exp(\mathbf{h}^T\mathbf{z}_k).$ \end{itemize} We exemplify the last form of response probabilities (generalized exponential weight adjustment) using artificial data. We generate a population of size $N=400$ and consider the auxiliary information $X$ following a Gamma distribution with parameters 3 and 4. The instrumental variable $Z$ is generated using the model $Z=2X+\varepsilon,$ where $\varepsilon\sim U(0,1).$ The variable of interest is $Y$ generated using the model $Y=3X+\varepsilon_1,$ where $\varepsilon_1\sim N(0,1).$ We consider here that the nonresponse is not missing at random and the response probabilities $p$ depend on the variable of interest $y$ which may be missing. We draw a simple random sampling without replecement of size $n=100$ and generate the set of respondents $r$ using Poisson sampling with the probabilties $p.$ The bounds are fixed to 1 and 5, and the constant $C=1.5.$ Three estimators are computed: \begin{itemize} \item the generalized calibration estimator using $Z$ as instrumental variable, \item the generalized calibration estimator using $Y$ as instrumental variable, \item the generalized calibration estimator using $X$ as instrumental variable, which is the same with the calibration estimator, but the g-weights are centered around $C$. \end{itemize} The convergence of the method is not guaranteed due to the bounds. Thus $g1, g2, g3$ can be null. If it the case, repeat the code (considering another $s$ and $r$). <>= N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= <> sampling.newpage() @ \end{document} sampling/vignettes/UPexamples.Snw0000644000176200001440000001104314515745027016661 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{UP - unequal probability sampling designs} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Unequal probability sampling designs} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ \section{Examples of maximum entropy sampling design and related functions} a) Example 1 @ Consider the Belgian municipalities data set as population, and a sample size n=50 <>= data(belgianmunicipalities) attach(belgianmunicipalities) n=50 @ Compute the inclusion probabilties proportional to the `averageincome' variable <>= pik=inclusionprobabilities(averageincome,n) @ Draw a random sample using the maximum entropy sampling design <>= s=UPmaxentropy(pik) @ The sample is <>= as.character(Commune[s==1]) @ Compute the joint inclusion probabilities <>= pi2=UPmaxentropypi2(pik) @ Check the result <>= rowSums(pi2)/pik/n detach(belgianmunicipalities) @ b) Example 2 @ Selection of samples from Belgian municipalities data set, sample size 50. Once the matrix q (see below) is computed, a sample is quickly selected. Monte Carlo simulation can be used to compare the true inclusion probabilities with the estimated ones. <>= data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) @ Draw a sample using the q matrix <>= UPMEsfromq(q) @ Monte Carlo simulation to check the sample selection; the difference between pik and the estimated inclusion prob. (object tt below) is almost 0. <>= sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) @ \section{Example of unequal probability (UP) sampling designs} Selection of samples from the Belgian municipalities data set, with equal or unequal probabilities, and study of the Horvitz-Thompson estimator accuracy using boxplots. The following sampling schemes are used: Poisson, random systematic, random pivotal, Till\'e, Midzuno, systematic, pivotal, and simple random sampling without replacement. Monte Carlo simulations are used to study the accuracy of the Horvitz-Thompson estimator of a population total. The aim of this example is to demonstrate the effect of using auxiliary information in sampling designs. We use: \begin{itemize} \item some $\pi$ps sampling designs with Horvitz-Thompson estimation, using auxiliary information in a sampling desing (size measurements of population units in 2004); \item simple random sampling without replacement with Horvitz-Thompson estimation, where no auxiliary information is used. \end{itemize} <>= b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) @ Number of simulations (for an accurate result, increase this value to 10000): <>= sim=10 ss=array(0,c(sim,8)) @ Defines the variable of interest: <>= y=belgianmunicipalities$TaxableIncome @ Simulation and computation of the Horvitz-Thompson estimators: <>= ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } @ Boxplots of the estimators: <>= colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/vignettes/HT_Hajek_estimators.Snw0000644000176200001440000001202514515747167020475 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{Horvitz-Thompson estimator and Hajek estimator} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Comparing the Horvitz-Thompson estimator and Hajek estimator} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ Consider a finite population with labels $U=\{1, 2, \dots, N\}.$ Suppose $y_k, k\in U$ are values of the variable of interest in the population. We wish to estimate the total $\sum_{k=1}^N y_k$ using a sample $s$ selected from the population $U.$ Assume that the sample is taken according to a sampling scheme having inclusion probabilities $\pi_k= Pr(k\in s).$ When $\pi_k$ is proportional to a positive quantity $x_k$ available over $U,$ and $s$ has a predetermined sample size $n,$ then $$\pi_k=\frac{nx_k}{\sum_{i=1}^N x_i},$$ and the sampling scheme is said to be probability proportional to size ($\pi$ps). The H\'ajek estimator of the population total is defined as $$\hat{y}_{Hajek}=N\frac{\sum_{k\in s} y_k/\pi_k}{\sum_{k\in s} 1/\pi_k},$$ while the Horvitz-Thompson estimator is $$\hat{y}_{HT}=\sum_{k\in s} y_k/\pi_k.$$ S$\ddot{a}$rndal, Swenson, and Wretman (1992, p. 182) give several cases for considering the H\'ajek estimator as `usually the better estimator' compared to the Horvitz-Thompson estimator when a $\pi$ps sampling design is used: \begin{itemize} \item[a)] the $y_k-\bar{y}_U$ tend to be small, \item[b)] the sample size is not fixed, \item[c)] $\pi_k$ are weakly or negatively correlated with $y_k$. \end{itemize} Monte Carlo simulation is used here to compare the accuracy of both estimators using a sample size (or the expected value of the sample size) equal to 20. Four cases are considered: \begin{itemize} \item[Case 1.] $y_k$ is constant for $k=1, \dots, N$; this case corresponds to the case a) above; \item[Case 2.] Poisson sampling is used to draw a sample $s$; this case corresponds to the case b) above; \item[Case 3.] $y_k$ are generated using the following model: $x_k=k, \pi_k=nx_k/\sum_{i=1}^N x_i, y_k=1/\pi_k;$ this case corresponds to the case c) above; \item[Case 4.] $y_k$ are generated using the following model: $x_k=k, y_k=5(x_k+\epsilon_k),\epsilon_k\sim N(0, 1/3);$ in this case the Horvitz-Thompson estimator should perform better than the H\'ajek estimator. \end{itemize} Till\'e sampling is used in Cases 1, 3 and 4. Poisson sampling is used in Case 2. The \verb@belgianmunicipalities@ dataset is used in Cases 1 and 2 as population, with $x_k=Tot04_k.$ In Case 2, the variable of interest is TaxableIncome. The mean square error (MSE) is computed using simulations for each case and estimator. The H\'ajek estimator should perform better than the Horvitz-Thompson estimator in Cases 1, 2 and 3. <>= data(belgianmunicipalities) attach(belgianmunicipalities) # sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) @ Number of runs (for an accurate result, increase this value to 10000): <>= sim=10 ss=ss1=array(0,c(sim,4)) @ Defines the variables of interest: <>= cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) @ Monte-Carlo simulation and computation of the Horvitz-Thompson and H\'ajek estimators: <>= ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } @ Estimation of the MSE and computation of the ratio $MSE_{HT}/MSE_{Hajek}:$ <>= #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/R/0000755000176200001440000000000014517446631012300 5ustar liggesuserssampling/R/UPrandompivotal.R0000644000176200001440000000031514516451542015542 0ustar liggesusers"UPrandompivotal" <- function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") N=length(pik) v=sample.int(N,N) s=numeric(N) s[v]=UPpivotal(pik[v],eps) s } sampling/R/regest_strata.r0000644000176200001440000000241214516451542015325 0ustar liggesusersregest_strata<-function(formula,weights,Tx_strata,strata,pikl,sigma=rep(1,length(weights)),description=FALSE) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) x <- model.matrix(mt, mf, contrasts) str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s sample.size = length(y) h = unique(strata) s1 = 0 for (i in 1:length(h)) { s=str(strata, h[i], sample.size) ys=y[s==1] xs=x[s==1,] r=regest(ys~xs-1,Tx=Tx_strata[h[i]],weights=weights[s==1],pikl=pikl[s==1,s==1],n=length(s[s==1]),sigma[s==1]) est=r$regest s1 = s1 + est if(description) {cat("Stratum ",h[i],", the regression estimator is:",est,"\n") cat("Number of units:",sum(s),"\n") cat("Beta coefficient(s):", r$coefficients,"\n") cat("Std. error:", r$std_error,"\n") cat("t-value:", r$t_value, "\n") cat("p_value:",r$p_value,"\n") cat("cov_matrix:\n") print(r$cov_matrix) } } if(description) cat("The regression estimator is:\n") s1 } sampling/R/UPsampford.R0000644000176200001440000000117014516451542014476 0ustar liggesusersUPsampford<-function(pik,eps=1e-6,max_iter=500) { if(any(is.na(pik))) stop("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list= pik>eps & pik < 1-eps pikb=pik[list] n=sum(pikb) N=length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { sb=rep(2,N) y=pikb/(1-pikb)/sum(pikb/(1-pikb)) step=0 while(sum(sb<=1)!=N & step<=max_iter) { sb=as.vector(rmultinom(1,1,pikb/sum(pikb))+rmultinom(1,.as_int(n-1),y)) step=step+1 } if(sum(sb<=1)==N) s[list]=sb else stop("Too many iterations. The algorithm was stopped.") } s } sampling/R/vartaylor_ratio.r0000644000176200001440000000154514516451542015705 0ustar liggesusersvartaylor_ratio=function(Ys,Xs,pikls) { if (any(is.na(pikls))) stop("there are missing values in pikls") if(nrow(pikls)!=ncol(pikls)) stop("pikls is not a square matrix") if (any(is.na(Ys))) stop("there are missing values in y") if (any(is.na(Xs))) stop("there are missing values in x") if (length(Ys) != nrow(pikls) | length(Xs) != nrow(pikls) | length(Xs) != length(Ys)) stop("y, x and pikls have different sizes") pik=diag(pikls) n=length(pik) xhat=sum(Xs/pik) yhat=sum(Ys/pik) r=yhat/xhat z=(Ys-r*Xs)/xhat delta=matrix(0,nrow=nrow(pikls),ncol=ncol(pikls)) for(i in 1:(n-1)) {for(j in (i+1):n) delta[i,j]=delta[j,i]=(1-pik[i]*pik[j]/pikls[i,j])*z[i]*z[j]/(pik[i]*pik[j]) delta[i,i]=(1-pik[i])*z[i]^2/pik[i]^2} delta[n,n]=(1-pik[n])*z[n]^2/pik[n]^2 list(ratio=r, estvar=sum(delta)) } sampling/R/fastflightcube.R0000644000176200001440000000601014516451542015406 0ustar liggesusers"fastflightcube" <- function(X,pik,order=1,comment=TRUE) { EPS = 1e-11 "algofastflightcube" <- function(X,pik) { "jump" <- function(X,pik){ N = length(pik) p = round(length(X)/length(pik)) X<-array(X,c(N,p)) X1=cbind(X,rep(0,times=N)) kern<-svd(X1)$u[,p+1] listek=abs(kern)>EPS buff1<-(1-pik[listek])/kern[listek] buff2<- -pik[listek]/kern[listek] la1<-min( c(buff1[(buff1>0)] , buff2[(buff2>0)]) ) pik1<- pik+la1*kern buff1<- -(1-pik[listek])/kern[listek] buff2<- pik[listek]/kern[listek] la2<-min(c(buff1[(buff1>0)] , buff2[(buff2>0)])) pik2<- pik-la2*kern q<-la2/(la1+la2) if (runif(1)(1-EPS) | psikEPS & pik<(1-EPS))])==(p+1)) psik <- jump(B,psik) pik[ind]=psik pik } "reduc" <- function(X) { EPS=1e-11 N=dim(X)[1] Re=svd(X) array(Re$u[,(Re$d>EPS)] , c(N,sum(as.integer(Re$d>EPS)))) } N = length(pik); p = round(length(X)/length(pik)) X<-array(X,c(N,p)) if (order==1) o<-sample.int(N,N) else { if(order==2) o<-seq(1,N,1) else o<-order(pik,decreasing=TRUE) } liste<-o[(pik[o]>EPS & pik[o]<(1-EPS))] if(comment==TRUE){ cat("\nBEGINNING OF THE FLIGHT PHASE\n") cat("The matrix of balanced variable has",p," variables and ",N," units\n") cat("The size of the inclusion probability vector is ",length(pik),"\n") cat("The sum of the inclusion probability vector is ",sum(pik),"\n") cat("The inclusion probability vector has ",length(liste)," non-integer elements\n") } pikbon<-pik[liste]; Nbon=length(pikbon); Xbon<-array(X[liste,] ,c(Nbon,p)) pikstar<-pik flag=0 if(Nbon>p){if(comment==TRUE) cat("Step 1 ") pikstarbon<-algofastflightcube(Xbon,pikbon) pikstar[liste]=pikstarbon flag=1 } liste<-o[(pikstar[o]>EPS & pikstar[o]<(1-EPS))] pikbon<-pikstar[liste] Nbon=length(pikbon) Xbon<-array(X[liste,] ,c(Nbon,p)) pbon=dim(Xbon)[2] if(Nbon>0){ Xbon=reduc(Xbon) pbon=dim(Xbon)[2] } k=2 while(Nbon>pbon & Nbon>0){ if(comment==TRUE) cat("Step ",k,", ") k=k+1 pikstarbon<-algofastflightcube(Xbon/pik[liste]*pikbon,pikbon) pikstar[liste]=pikstarbon liste<-o[(pikstar[o]>EPS & pikstar[o]<(1-EPS))] pikbon<-pikstar[liste] Nbon=length(pikbon) Xbon<-array(X[liste,] ,c(Nbon,p)) if(Nbon>0) { Xbon=reduc(Xbon) pbon=dim(Xbon)[2] } flag=1 } if(comment==TRUE) if(flag==0) cat("NO FLIGHT PHASE") if(comment==TRUE) cat("\n") pikstar } sampling/R/UPminimalsupport.R0000644000176200001440000000114214516451542015745 0ustar liggesusers"UPminimalsupport" <- function(pik) { if(any(is.na(pik))) stop("there are missing values in the pik vector") basicsplit<-function(pik) { N=length(pik) n=sum(pik) A=(1:N)[pik==0] B=(1:N)[pik==1] C=setdiff(setdiff(1:N,A),B) D=C[sample.int(length(C), round(n-length(B)))] s1v=rep(0,times=N) s1v[c(B,D)]=1 alpha=min(1-max(pik[setdiff(C,D)]),min(pik[D])) pikb= (pik-alpha*s1v)/(1-alpha) if(runif(1,0,1) 0 & pik < 1] N = length(pik1) Vk = cumsum(pik1) Vk1=Vk%%1 if(Vk1[N]!=0) Vk1[N]=0 r = c(sort(Vk1), 1) cent = (r[1:N] + r[2:(N + 1)])/2 p = r[2:(N + 1)] - r[1:N] A = matrix(c(0, Vk), nrow = N + 1, ncol = N) - t(matrix(cent,nrow = N, ncol = N + 1)) A = A%%1 M = matrix(as.integer(A[1:N, ] > A[2:(N + 1), ]), N, N) pi21 = M %*% diag(p) %*% t(M) pi2 = pik %*% t(pik) pi2[pik > 0 & pik < 1, pik > 0 & pik < 1] = pi21 pi2 } sampling/R/landingcube.R0000644000176200001440000000354614516451542014702 0ustar liggesusers"landingcube" <- function(X,pikstar,pik,comment=TRUE) # landing phase of the cube method ###################################################### { # extraction of the non-integer values for the landing phase EPS=1e-11 p=dim(X)[2] N=dim(X)[1] liste=(pikstar>EPS & pikstar<(1-EPS)) pikland=pikstar[liste] Nland=length(pikland) Xland=array(X[liste,] ,c(Nland,p)) nland=sum(pikland) FLAGI=(abs(nland-round(nland))EPS,]/pik[pik>EPS] cost=rep(0,times=lll) for(i in 1:lll) cost[i]=t(Asmp[,i]) %*% ginv(t(A) %*% A) %*% Asmp[,i] # linear programming V = t(cbind(SSS,rep(1,times=lll))) b=c(pikland,1) constdir=rep("==",times=(Nland+1)) x=lp("min",cost,V,constdir,b)$solution # choice of the sample u=runif(1,0,1) i=0 ccc=0 while(ccc= C || bounds[1] > bounds[2]) stop("The conditions low bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - c(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] Zs1 = Zs[list, ] d1 = d[list] q1 = q[list] list1 = list } } t1 = c(t(d1) %*% Xs1) lambda1 = ginv(t(Xs1 * d1 * q1) %*% Zs1, tol = EPS) %*% (t2 - t1) if (length(list1) > 1) g1 = 1 + q1 * c(Zs1 %*% lambda1) else if (length(list1) == 1) { g1 = 1 + q1 * c(as.vector(Zs1) %*% as.vector(lambda1)) } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("No convergence in", max_iter, "iterations with the given bounds. \n") cat("The bounds for the g-weights are:", min(g), " and ", max(g), "\n") g=NULL } } else if (method == "raking") { lambda = as.matrix(rep(0, ncol(Xs))) w1 = as.vector(d * exp(Zs %*% lambda * q)) T = t(Xs) for (l in 1:max_iter) { phi = t(Xs) %*% w1 - total T1 = t(Xs * w1) phiprim = T1 %*% Zs lambda = lambda - ginv(phiprim, tol = EPS) %*% phi w1 = as.vector(d * exp(Zs %*% lambda * q)) if (any(is.na(w1)) | any(is.infinite(w1)) | any(is.nan(w1))) { warning("No convergence") g = NULL der = g l = max_iter break } tr = crossprod(Xs, w1) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1) break } if (l == max_iter) { warning("No convergence") g = NULL der = g } else {g = w1/d; der=g} } else if (method == "logit") if (missing(bounds)) stop("Specify the bounds") else { if (bounds[2] <= C || bounds[1] >= C || bounds[1] > bounds[2]) stop("The conditions low EPS1 | any(g < bounds[1]) | any(g > bounds[2])) { lambda1 = rep(0, ncol(Xs)) list = 1:length(g) t2 = total Xs1 = Xs d1 = d Zs1 = Zs g1 = g q1 = q list1 = 1:length(g) for (l in 1:max_iter) { if (any(g < bounds[1]) | any(g > bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - c(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] Zs1 = Zs[list, ] d1 = d[list] q1 = q[list] list1 = list } else break } if (is.vector(Xs1)) { warning("no convergence") g1 = g = NULL break } t1 = c(t(d1) %*% Xs1) phi = t(Xs1) %*% as.vector(d1 * g1) T = t(Xs1 * as.vector(d1 * g1)) phiprime = T %*% Zs1 lambda1 = lambda1 - ginv(phiprime, tol = EPS) %*% (as.vector(phi) - t2) u = exp(A * (Zs1 %*% lambda1 * q1)) F = g1 = (bounds[1] * (bounds[2] - C) + bounds[2] * (C - bounds[1]) * u)/(bounds[2] - C + (C - bounds[1]) * u) if (any(is.na(g1))) { warning("no convergence") g1 = g = NULL break } g[list1] = g1 der = g-1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("no convergence in", max_iter, "iterations with the given bounds. \n") cat("the bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") g = NULL der = g } } } if (description && !is.null(g)) { par(mfrow = c(3, 2), pty = "s") hist(g) boxplot(g, main = "Boxplot of g") hist(d) boxplot(d, main = "Boxplot of d") hist(g * d) boxplot(g * d, main = "Boxplot of w=g*d") if (method %in% c("truncated", "raking", "logit")) cat("number of iterations ", l, "\n") cat("summary - initial weigths d\n") print(summary(d)) cat("summary - final weigths w=g*d\n") print(summary(as.vector(g * d))) } g } sampling/R/srswor.R0000644000176200001440000000011314516451542013751 0ustar liggesusers"srswor" <- function(n,N) {s<-rep(0,times=N);s[sample.int(N,n)]<-1;s} sampling/R/srswor1.R0000644000176200001440000000016614516451542014042 0ustar liggesusers"srswor1" <- function(n,N) {j=0 s=numeric(N) for(k in 1:N) if(runif(1)<(n-j)/(N-k+1)) {j=j+1;s[k]=1;} s } sampling/R/cluster.r0000644000176200001440000001365114516451542014146 0ustar liggesuserscluster<-function (data, clustername, size, method = c("srswor", "srswr", "poisson", "systematic"), pik, description = FALSE) { if (size == 0) stop("the size is zero") if (missing(method)) { warning("the method is not specified; by default, the method is srswor") method = "srswor" } if (!(method %in% c("srswor", "srswr", "poisson", "systematic"))) stop("the name of the method is wrong") if (method %in% c("poisson", "systematic") & missing(pik)) stop("the vector of probabilities is missing") if (method %in% c("poisson", "systematic") & !missing(pik)) if(!is.vector(pik)) pik=as.vector(pik) data = data.frame(data) index = 1:nrow(data) if (missing(clustername)) { if (method == "srswor") result = data.frame(index[srswor(size, nrow(data)) == 1], rep(size/nrow(data), size)) if (method == "srswr") { s = srswr(size, nrow(data)) st = s[s != 0] l = length(st) result = data.frame(index[s != 0]) result = cbind.data.frame(result, st, prob = rep(1-(1-1/nrow(data))^size,l)) colnames(result) = c("ID_unit", "Replicates", "Prob") } if (method == "poisson") { pikk = inclusionprobabilities(pik, size) s = (UPpoisson(pikk) == 1) if (length(s) > 0) result = data.frame(index[s], pikk[s]) if (description) cat("\nNumber of units in the population and number of selected units:", nrow(data), length(s), "\n") } if (method == "systematic") { pikk = inclusionprobabilities(pik, size) s = (UPsystematic(pikk) == 1) result = data.frame(index[s], pikk[s]) } if (method != "srswr") colnames(result) = c("ID_unit", "Prob") if (description) cat("\nNumber of units in the population and number of selected units:", nrow(data), sum(size), "\n") } else { data = data.frame(data) m = match(clustername, colnames(data)) if (length(m) > 1) stop("there are too many specified variables as clusters") if (is.na(m)) stop("the cluster name is wrong") x1 = factor(data[, m]) result = NULL if (nlevels(x1) == 0) stop("the cluster variable has 0 categories") else { nr_cluster = nlevels(x1) if (method == "srswor") { s = as.data.frame(levels(x1)[srswor(size, nr_cluster) == 1]) names(s) = c("cluster") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") r = merge(r, s, by.x = "cluster", by.y = "cluster", sort = TRUE) result = cbind.data.frame(r, rep(size/nr_cluster, nrow(r))) } if (method == "srswr") { s = srswr(size, nr_cluster) st = cbind.data.frame(levels(x1)[s != 0], s[s != 0]) names(st) = c("cluster", "repl") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") r = merge(r, st, by.x = "cluster", by.y = "cluster") result = cbind.data.frame(r, rep(1-(1-1/nr_cluster)^size, nrow(r))) } if (method == "systematic") { pikk = inclusionprobabilities(pik, size) s = (UPsystematic(pikk) == 1) st = cbind.data.frame(levels(x1)[s], pikk[s]) names(st) = c("cluster", "prob") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") result = merge(r, st, by.x = "cluster", by.y = "cluster") } if (method == "poisson") { pikk = inclusionprobabilities(pik, size) s = (UPpoisson(pikk) == 1) if (any(s)) { st = cbind.data.frame(levels(x1)[s], pikk[s]) names(st) = c("cluster", "prob") r = cbind.data.frame(index, data[, m]) names(r) = c("index", "cluster") result = merge(r, st, by.x = "cluster", by.y = "cluster") if (description) { cat("Number of selected clusters:", sum(s), "\n") cat("\nNumber of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } else { if (description) { cat("Number of selected clusters: 0\n") cat("Population total and number of selected units:", nrow(data), 0, "\n") } result = NULL } } if (method == "srswr") { colnames(result) = c(clustername, "ID_unit", "Replicates", "Prob") if (description) { cat("Number of selected clusters:", length(s[s != 0]), "\n") cat("Number of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } else if (!is.null(result)) colnames(result) = c(clustername, "ID_unit", "Prob") if (description & !(method %in% c("poisson", "srswr"))) { cat("Number of selected clusters:", size, "\n") cat("Number of units in the population and number of selected units:", nrow(data), nrow(result), "\n") } } } result } sampling/R/ratioest.r0000644000176200001440000000064714516451542014320 0ustar liggesusersratioest<-function(y,x,Tx,pik) {if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(y))) stop("there are missing values in y") if (any(is.na(x))) stop("there are missing values in x") if (length(y) != length(pik) | length(x)!=length(pik) | length(x)!=length(y)) stop("y, x and pik have different lengths") sum(y/pik)*Tx/sum(x/pik) } sampling/R/srswr.R0000644000176200001440000000011014516451542013567 0ustar liggesusers"srswr" <- function(n,N) as.vector(rmultinom(1,n,rep(n/N,times=N))) sampling/R/balancedtwostage.R0000644000176200001440000000157414516451542015735 0ustar liggesusers"balancedtwostage" <- function(X,selection,m,n,PU,comment=TRUE,method=1) { N=dim(X)[1] p=dim(X)[2] str=cleanstrata(PU) M=max(PU) res1=balancedcluster(X,m,PU,method,comment) if(selection==2) { pik2=rep(n/N*M/m,times=N); if(n/N*M/m>1) stop("at the second stage, inclusion probabilities larger than 1"); } if(selection==1) { pik2=inclusionprobastrata(str,rep(n/m ,times=max(str))); if(max(pik2)>1) stop("at the second stage, inclusion probabilities larger than 1"); } liste=(res1[,1]==1) sf=rep(0,times=N) sf[liste]=balancedstratification(array(X[liste,]/res1[,2][liste],c(sum(as.integer(liste)),p)),cleanstrata(str[liste]),pik2[liste],comment,method) x=cbind(sf,res1[,2]*pik2,res1[,1],res1[,2],pik2) colnames(x)=c("second_stage","final_pik", "primary","pik_first_stage", "pik_second_stage") x } sampling/R/Hajekestimator.r0000644000176200001440000000107614516451542015435 0ustar liggesusersHajekestimator<-function(y,pik,N=NULL,type=c("total","mean")) { if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") if(missing(type) | is.null(N)) { if(missing(type)) warning("the type estimator is missing") warning("by default the mean estimator is computed") est<-crossprod(y,1/pik)/sum(1/pik)} else if(type=="total") est<-N*crossprod(y,1/pik)/sum(1/pik) est } sampling/R/cleanstrata.R0000644000176200001440000000020714516451542014717 0ustar liggesusers"cleanstrata" <- function(strata) { a=sort(unique(strata)) b=1:length(a) names(b)=a as.vector(b[as.character(strata)]) } sampling/R/UPmidzunopi2.R0000644000176200001440000000017214516451542014764 0ustar liggesusers"UPmidzunopi2" <- function(pik) { N=length(pik) UN=rep(1,times=N) b=1-pik%*%t(UN) 1-b-t(b)+UPtillepi2(1-pik) } sampling/R/UPmultinomial.R0000644000176200001440000000024114516451542015213 0ustar liggesusers"UPmultinomial" <- function(pik) {if(any(is.na(pik))) stop("there are missing values in the pik vector") as.vector(rmultinom(1,sum(pik),pik/sum(pik))) } sampling/R/disjunctive.R0000644000176200001440000000023514516451542014746 0ustar liggesusers"disjunctive" <- function(strata) {ss=cleanstrata(strata) m=matrix(0,length(strata),length(unique(strata))) for(i in 1:length(ss)) m[i,ss[i]]=1 m } sampling/R/UPpoisson.R0000644000176200001440000000022014516451542014350 0ustar liggesusers"UPpoisson" <- function(pik) {if(any(is.na(pik))) stop("there are missing values in the pik vector") as.numeric(runif(length(pik))=eps & a<= 1-eps & b>=eps & b<= 1-eps) if(a+b>1) { if(u<(1-b)/(2-a-b)) {b<-a+b-1;a<-1} else {a<-a+b-1;b<-1} } else{ if(u< b/(a+b)) {b<- a+b;a<-0} else {a<- a+b;b<-0} } if( (a 1-eps)& (k<=N)) {s[i]=a;a=pik[k];i=k;k=k+1;} if( (b 1-eps)& (k<=N) ) {s[j]=b;b=pik[k];j=k;k=k+1;} } u<-runif(1) if(a>=eps & a<= 1-eps & b>=eps & b<= 1-eps) if(a+b>1) { if(u<(1-b)/(2-a-b)) {b<-a+b-1;a<-1} else {a<-a+b-1;b<-1} } else{ if(u< b/(a+b)) {b<-a+b;a<-0} else {a<- a+b;b<-0} } s[i]=a; s[j]=b; s } sampling/R/writesample.R0000644000176200001440000000066414516451542014761 0ustar liggesusers"writesample" <- function(n,N) { if(n==N) samples=rep(1,times=N) else{ x=numeric(N) row=1 for(i in (n+1):N) row=row*i k=1 for(i in 1:(N-n)) k=k*i row=row/k samples=matrix(0,row,N) k=1 sol=0 x[1]=-1 while(k<=N && k>0) { while(x[k]<1) { x[k]=x[k]+1 s=0 for(i in 1:N) s=s+x[i] if(s==n) { sol=sol+1 samples[sol,]=x } else if(keps) { w=(pikt)/(1-pikt) q=UPMEqfromw(w,n) pikt1=pikt+pik-UPMEpikfromq(q) arr=sum(abs(pikt-pikt1)) pikt=pikt1 } pikt } sampling/R/rhg_strata.r0000644000176200001440000000141214516451542014613 0ustar liggesusersrhg_strata<-function(X,selection) { if(is.matrix(X)) X=as.data.frame(X) m=match(selection,names(X),nomatch=0) if(sum(m)==0) stop("the 'selection' should be the name of one the X columns") if(!("Stratum" %in% names(X))) stop("the column 'Stratum' is missing") result=NULL u=unique(X$Stratum) for(i in 1:length(u)) {si=X[X$Stratum==u[i],] x=cbind.data.frame(si$ID_unit,si$status,si[,m]) names(x)=c("ID_unit","status",names(X)[m]) result=rbind.data.frame(result,rhg(x,selection)) } res = NULL mm = match(names(X), names(result), nomatch = 0) index = (1:ncol(X))[mm == 0] if (length(index) > 0) { res = cbind.data.frame(X[X$ID_unit==result$ID_unit, index], result) names(res)[1:length(index)] = names(X)[index] } res } sampling/R/UPsampfordpi2.r0000644000176200001440000000151614516451542015155 0ustar liggesusersUPsampfordpi2<-function(pik) { n=sum(pik) n=.as_int(n) if(n<2) stop("the sample size<2") N=length(pik) p=pik/n pikl=matrix(0,N,N) Lm=rep(0, n) lambda=p/(1-n*p) Lm[1]=1 if(n>=2) for (i in 2:n) { for (r in 1:(i-1)) Lm[i]=Lm[i]+((-1)^(r-1))*sum(lambda^r)*Lm[i-r] Lm[i]=Lm[i]/(i - 1) } if(any(Lm<0)) stop("it is not possible to compute pik2 for this example") t1=(n + 1) - (1:n) Kn=1/sum(t1*Lm/n^t1) Lm2=rep(0, n - 1) t2=(1:(n - 1)) t3=n - t2 for (i in 2:N) { for (j in 1:(i - 1)) { Lm2[1]=1 Lm2[2]=Lm[2] - (lambda[i] + lambda[j]) if(n>3) for (m in 3:(n - 1)) { Lm2[m]=Lm[m] - (lambda[i] + lambda[j]) * Lm2[m -1] - lambda[i] * lambda[j] * Lm2[m - 2] } pikl[i, j]=Kn * lambda[i] * lambda[j] * sum((t2+1-n*(p[i] + p[j]))*Lm2[t3]/n^(t2 - 1)) pikl[j, i]=pikl[i, j] } pikl[i, i]=pik[i] } pikl[1, 1]=pik[1] pikl } sampling/R/poststrata.r0000644000176200001440000000160114516451542014661 0ustar liggesuserspoststrata<-function(data, postnames = NULL) { if (missing(data) | missing(postnames)) stop("incomplete input") data = data.frame(data) if(is.null(colnames(data))) stop("the column names in data are missing") index = 1:nrow(data) m = match(postnames, colnames(data)) if (any(is.na(m))) stop("the names of the poststrata are wrong") data2 = cbind.data.frame(data[, m]) x1 = data.frame(unique(data[, m])) colnames(x1) = postnames nr_post=0 post=numeric(nrow(data)) nh=numeric(nrow(x1)) for(i in 1:nrow(x1)) { expr=rep(FALSE, nrow(data2)) for(j in 1:nrow(data2)) expr[j]=all(data2[j, ]==x1[i, ]) y=index[expr] if(is.matrix(y)) nh[i]=nrow(y) else nh[i]=length(y) post[expr]=i } result=cbind.data.frame(data,post) names(result)=c(names(data),"poststratum") list(data=result, npost=nrow(x1)) } sampling/R/UPbrewer.R0000644000176200001440000000113614516451542014153 0ustar liggesusers"UPbrewer" <- function(pik, eps = 1e-06) { if(any(is.na(pik))) stop("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list = pik > eps & pik < 1 - eps pikb = pik[list] N = length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { sb=rep(0,N) n=sum(pikb) for (i in 1:n) { a = sum(pikb*sb) p = (1-sb)*pikb*((n-a)-pikb)/((n-a)-pikb*(n-i+1)) p = p/sum(p) p = cumsum(p) u=runif(1) for(j in 1:length(p)) if(u .Machine$integer.max)) stop("the input has entries too large to be integer") if(!identical(TRUE, (ax <- all.equal(xo, x)))) warning("the argument is not integer") else x=xo } x } sampling/R/UPMEsfromq.R0000644000176200001440000000022114516451542014410 0ustar liggesusers"UPMEsfromq" <- function(q) { n=ncol(q) N=nrow(q) s=rep(0,times=N) for(k in 1:N) if(n!=0) if(runif(1) eps & pik < 1 - eps pikb = pik[list] N = length(pikb) s=pik if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { n=sum(pikb) sb=rep(1,N) b=rep(1,N) for(i in 1:(N-n)) {a=inclusionprobabilities(pikb,N-i) v=1-a/b b=a p=v*sb p=cumsum(p) u=runif(1) for(j in 1:length(p)) if(u1) stop("pik is not a vector") else pik=unlist(pik) else if(is.matrix(pik)) if(ncol(pik)>1) stop("pik is not a vector") else pik=pik[,1] else if(is.list(pik)) if(length(pik)>1) stop("pik is not a vector") else pik=unlist(pik) n=sum(pik) n=.as_int(n) if(n>=2) { pik2=pik[pik!=1] n=sum(pik2) n=.as_int(n) piktilde=UPMEpiktildefrompik(pik2) w=piktilde/(1-piktilde) q=UPMEqfromw(w,n) s2=UPMEsfromq(q) s=rep(0,times=length(pik)) s[pik==1]=1 s[pik!=1][s2==1]=1 } if(n==0) s=rep(0,times=length(pik)) if(n==1) s=as.vector(rmultinom(1, 1,pik)) s } sampling/R/Hajekstrata.r0000644000176200001440000000231414516451542014720 0ustar liggesusersHajekstrata<-function(y,pik,strata,N=NULL,type=c("total","mean"),description=FALSE) { str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") if (is.matrix(y)) sample.size <- nrow(y) else sample.size <- length(y) if(!is.vector(N)) N <- as.vector(N) h <- unique(strata) if(length(N)!=length(h)) stop("N should be a vector with the length equal to the number of strata") options(warn=-1) s1 <- 0 for (i in 1:length(h)) { s <- str(strata, h[i], sample.size) est <- Hajekestimator(y[s == 1], pik[s == 1], type="mean") s1 <- s1 + est*N[i] if(description) if(type=="mean") cat("For stratum ",i,", the Hajek estimator is:",est,"\n") else cat("For stratum ",i,", the Hajek estimator is:",est*N[i],"\n") } if(description) cat("The Hajek estimator is:\n") if(type=="mean") return(s1/sum(N)) else return(s1) } sampling/R/inclusionprobastrata.R0000644000176200001440000000057514516451542016674 0ustar liggesusersinclusionprobastrata<-function (strata, nh) { N = length(strata) EPS = 1e-6 if (min(unique(strata)) < 1) stop("the stratification variable has incorect values (less than 1)\n") Nh=as.vector(table(strata)) if(any(nh/Nh>1+EPS)) warning("in a stratum the sample size is larger than the population size\n") pik=nh[strata]/Nh[strata] pik } sampling/R/UPrandomsystematic.R0000644000176200001440000000032314516451542016250 0ustar liggesusers"UPrandomsystematic" <- function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") N=length(pik) v=sample.int(N,N) s=numeric(N) s[v]=UPsystematic(pik[v],eps) s } sampling/R/rmodel.r0000644000176200001440000000104114516451542013735 0ustar liggesusersrmodel<-function(formula,weights,X) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) x <- model.matrix(mt, mf, contrasts) prob<-glm(y~x,family="binomial",weights=w)$fitted.values result<-cbind.data.frame(X,prob) names(result)<-c(names(X),"prob_resp") result } sampling/R/samplecube.R0000644000176200001440000000273314516451542014544 0ustar liggesusers"samplecube" <- function(X,pik,order=1,comment=TRUE,method=1) { EPS=1e-11 N=length(pik) if(!is.array(X)) X=array(X,c(N,length(X)/N)) if(method==1) { if (length(pik[pik > EPS & pik < (1 - EPS)]) > 0) pikstar = fastflightcube(X, pik, order, comment) else { if (comment) cat("\nNO FLIGHT PHASE") pikstar = pik } if (length(pikstar[pikstar > EPS & pikstar < (1 - EPS)]) > 0) pikfin = landingcube(X, pikstar, pik, comment) else { if (comment) cat("\nNO LANDING PHASE") pikfin = pikstar } } else { p=length(X)/length(pik) pikstar=pik for(i in 0:(p-1)) { if (length(pikstar[pikstar > EPS & pikstar < (1 - EPS)]) > 0) pikstar = fastflightcube(X[,1:(p-i)]/pik*pikstar, pikstar, order, comment) } pikfin = pikstar for(i in 1:N) if(runif(1) EPS, ]/pik[pik > EPS] TOT = t(A) %*% pik[pik > EPS] EST = t(A) %*% pikfin[pik > EPS] DEV = 100 * (EST - TOT)/TOT cat("\n\nQUALITY OF BALANCING\n") if(is.null(colnames(X))) Vn = as.character(1:length(TOT)) else Vn=colnames(X) for(i in 1:length(TOT)) if(Vn[i]=="") Vn[i]=as.character(i) d = data.frame(TOTALS = c(TOT), HorvitzThompson_estimators = c(EST), Relative_deviation = c(DEV)) rownames(d)<-Vn print(d) } round(pikfin) } sampling/R/mstage.r0000644000176200001440000003300314516451542013736 0ustar liggesusersmstage<-function (data, stage = c("stratified", "cluster", ""), varnames, size, method = c("srswor", "srswr", "poisson", "systematic"), pik, description = FALSE) { if (missing(size)) stop("the size argument is missing") if (!missing(stage) & missing(varnames)) stop("indicate the stage argument") if (!missing(stage)) { number = length(stage) for (i in 1:length(stage)) if (!(stage[i] %in% c("stratified", "cluster", ""))) stop("the stage argument is wrong") } else number = length(size) if (number > 1) { if (!missing(varnames)) { if (!is.list(size)) stop("the size must be a list") size = as.list(size) varnames = as.list(varnames) size1 = size[[1]] varnames1 = varnames[[1]] if (method[[1]] %in% c("systematic", "poisson")) pik1 = pik[[1]] } else { size1 = size[[1]] varnames1 = NULL if (method[[1]] %in% c("systematic", "poisson")) pik1 = pik[[1]] } } else { size1 = size if(missing(method)) method="srswor" else if (method %in% c("systematic", "poisson")) pik1 = pik } if (description) cat("STAGE 1", "\n") if (missing(stage)) { if (missing(varnames)) if (missing(method)) s = strata(data, stratanames = NULL, size = size1, description) else if (method[[1]] %in% c("systematic", "poisson")) s = strata(data, stratanames = NULL, size = size1, method[[1]], pik = pik1, description) else s = strata(data, stratanames = NULL, size = size1, method[[1]], description) else s = strata(data, stratanames = NULL, size1, method[[1]], pik = pik1, description) } else if (stage[1] == "stratified") { s = strata(data, varnames1, size1, method="srswor",description) dimension_st = table(s$Stratum) if(description) cat("Number of strata:",length(dimension_st),"\n") } else { s = cluster(data, varnames1, size1, method[[1]], pik1, description) if (is.null(s)) stop("0 selected units in the first stage") m = match(varnames1, names(s)) nl = nlevels(as.factor(s[, m])) lev = levels(as.factor(s[, m])) if (nl >= 1) { dimension_cl = NULL for (i in 1:nl) if(nrow(subset(s,s[, m] == unique(s[,m])[i]))>0) dimension_cl = c(dimension_cl,nrow(subset(s,s[, m] == unique(s[,m])[i]))) } dimension = dimension_cl } if (is.null(s)) stop("0 selected units in the first stage") if (number > 1) if ((is.element("cluster", stage) & is.element("stratified", stage))) result = getdata(data, s) else result = s res = list() res[[1]] = s if (number >= 2) for (j in 2:number) { if (description) cat("STAGE ", j, "\n") if (!missing(varnames)) { if (stage[[j]] == "cluster") { if (stage[[j - 1]] == "stratified") { k = length(dimension_st) s1 = NULL limit = 0 dimension = list() if (k >= 1) for (ii in 1:k) { r = res[[j - 1]][(limit + 1):(limit + dimension_st[ii]), ] r = getdata(data, r) m = match(varnames[[j]], names(r)) if (method[[j]] %in% c("systematic", "poisson")) { index = res[[j - 1]][(limit + 1):(limit + dimension_st[ii]), ]$ID_unit pikk = pik[[j]][index] if (!is.null(r)) s3 = cluster(r, clustername = varnames[[j]], size = size[[j]][ii], method = method[[j]], pik = pikk, description) else s3 = NULL } else { s3 = cluster(r, clustername = varnames[[j]], size = size[[j]][ii], method = method[[j]], description = description) } limit = limit + dimension_st[ii] if (method[[j]] == "srswr") { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Replicates, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if(!is.null(s3)) { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s3)) { m = match(varnames[[j]], names(s3)) for (l in 1:nlevels(as.factor(s3[, m]))) dimension = c(dimension, table(s3[, m])[l]) s1 = rbind(s1, s3) } } } else if (stage[[j - 1]] == "cluster") { m_cl = match(varnames, names(res[[j-1]]),0) mat=res[[j-1]][, m_cl] nl = nlevels(as.factor(mat)) if (nl >= 1) { dimension_cl =NULL for (i in 1:nl) if(length(subset(mat, mat==unique(mat)[i]))>0) dimension_cl = c(dimension_cl,length(subset(mat, mat==unique(mat)[i]))) k = length(dimension_cl) } else stop("error in the previous stage") s1 = NULL limit = 0 dimension = list() if (k > length(size[[j]])) { warning("the number of selected clusters in the previous stage is larger than the size argument") warning("the size 1 is added") size1 = size[[j]] for (i in 1:(k - length(size[[j]]))) size1 = c(size1, 1) } else size1 = size[[j]] if (k >= 1) for (ii in 1:k) { r = res[[j - 1]][(limit + 1):(limit + dimension_cl[ii]), ] r = getdata(data, r) m = match(varnames[[j]], names(r)) if (method[[j]] %in% c("systematic", "poisson")) { m1 = match(varnames[[j - 1]], names(r)) m2 = match(varnames[[j - 1]], names(data)) mm = match(r[1, m1], levels(factor(data[, m2]))) pikk = as.numeric(pik[[j]][[mm]]) if (!is.null(r)) s3 = cluster(r, clustername = varnames[[j]], size = size1[[ii]], method = method[[j]], pik = pikk, description) else s3 = NULL } else s3 = cluster(r, clustername = varnames[[j]], size = size1[ii], method = method[[j]], pik, description) limit = limit + dimension_cl[ii] if (method[[j]] == "srswr") { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Replicates, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if (!is.null(s3)) { s3 = cbind.data.frame(r[s3$ID_unit, m], r[s3$ID_unit, ]$ID_unit, s3$Prob, r[s3$ID_unit, ]$Prob * s3$Prob) colnames(s3) = c(varnames[[j]], "ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s3)) { m = match(varnames[[j]], names(s3)) for (l in 1:nlevels(as.factor(s3[, m]))) dimension = c(dimension, table(s3[, m])[l]) s1 = rbind(s1, s3) } } } } else if (j > 1) { k = length(dimension) s1 = NULL limit = 0 count = 0 if (k > length(size[[j]])) { warning("the number of selected clusters at the previous stage is larger than the size argument") warning("the size 1 is added") size1 = size[[j]] for (i in 1:(k - length(size[[j]]))) size1 = c(size1,1) } else size1 = size[[j]] if (k >= 1) for (i in 1:k) for (ii in 1:length(dimension[[i]])) { r = res[[j - 1]][(limit + 1):(limit + dimension[[i]][ii]), ] count = count + 1 if (method[[j]] %in% c("systematic", "poisson")) { index = res[[j - 1]][(limit + 1):(limit + dimension[[i]][ii]), ]$ID_unit pikk = pik[[j]][index] if (!is.null(r)) s2 = strata(r, NULL, size = size1[count], method = method[[j]], pik = pikk, description) else s2 = NULL } else s2 = strata(r, NULL, size = size1[count], method = method[[j]], pik, description) limit = limit + dimension[[i]][ii] if (method[[j]] == "srswr") { s2 = cbind.data.frame(r[s2$ID_unit, ]$ID_unit, s2$Replicates, s2$Prob, r[s2$ID_unit, ]$Prob * s2$Prob) colnames(s2) = c("ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else if (!is.null(s2)) { s2 = cbind.data.frame(r[s2$ID_unit, ]$ID_unit, s2$Prob, r[s2$ID_unit, ]$Prob * s2$Prob) colnames(s2) = c("ID_unit", paste("Prob_", j, "_stage"), "Prob") } if (!is.null(s2)) s1 = rbind(s1, s2) } } } else { if (missing(stage)) { if (missing(method)) s1 = strata(result, stratanames = NULL, size = size[[j]], description = description) else if (method[[j]] == "poisson" | method[[j]] == "systematic") s1 = strata(result, stratanames = NULL, size = size[[j]], method = method[[j]], pik = pik[[j]], description = description) else s1 = strata(result, stratanames = NULL, size = size[[j]], method = method[[j]], description = description) if (method[[j]] == "srswr") { s1 = cbind.data.frame(result[s1$ID_unit, ]$ID_unit, s1$Replicates, s1$Prob, result[s1$ID_unit, ]$Prob * s1$Prob) colnames(s1) = c("ID_unit", "Replicates", paste("Prob_", j, "_stage"), "Prob") } else { s1 = cbind.data.frame(result[s1$ID_unit, ]$ID_unit, s1$Prob, result[s1$ID_unit, ]$Prob * s1$Prob) colnames(s1) = c("ID_unit", paste("Prob_", j, "_stage"), "Prob") } } } if (!is.null(s1)) { result = s1 res[[j]] = result } else number = number - 1 } if (!is.null(names(res[[1]]))) { m = match("Prob", names(res[[1]])) names(res[[1]])[m] = "Prob_ 1 _stage" } names(res) = c(1:number) res } sampling/R/strata.r0000644000176200001440000001034314516451542013756 0ustar liggesusersstrata<-function(data, stratanames=NULL, size, method=c("srswor","srswr","poisson","systematic"),pik,description=FALSE) { if(missing(method)) {warning("the method is not specified; by default, the method is srswor") method="srswor" } if(!(method %in% c("srswor","srswr","poisson","systematic"))) stop("the method name is not in the list") if(method %in% c("poisson","systematic") & missing(pik)) stop("the vector of probabilities is missing") if(missing(stratanames)|is.null(stratanames)) { if(length(size)>1) stop("the argument giving stratification variable is missing. The argument size should be a value.") if(method=="srswor") result=data.frame((1:nrow(data))[srswor(size,nrow(data))==1],rep(size/nrow(data),size)) if(method=="srswr") { s=srswr(size,nrow(data)) st=s[s!=0] l=length(st) result=data.frame((1:nrow(data))[s!=0]) result=cbind.data.frame(result,st,prob=rep(1-(1-1/nrow(data))^size,l)) colnames(result)=c("ID_unit","Replicates","Prob") } if(method=="poisson") { pikk=inclusionprobabilities(pik,size) s=(UPpoisson(pikk)==1) if(length(s)>0) result=data.frame((1:nrow(data))[s],pikk[s]) if(description) cat("\nPopulation total and number of selected units:",nrow(data),sum(s),"\n") } if(method=="systematic") { pikk=inclusionprobabilities(pik,size) s=(UPsystematic(pikk)==1) result=data.frame((1:nrow(data))[s],pikk[s]) } if(method!="srswr") colnames(result)=c("ID_unit","Prob") if(description & method!="poisson") cat("\nPopulation total and number of selected units:",nrow(data),sum(size),"\n") } else { data=data.frame(data) index=1:nrow(data) m=match(gsub(" ",".",stratanames),colnames(data)) if(any(is.na(m))) stop("the names of the strata are wrong") data2=cbind.data.frame(data[,m],index) colnames(data2)=c(stratanames,"index") x1=data.frame(unique(data[,m])) colnames(x1)=stratanames result=NULL for(i in 1:nrow(x1)) { if(is.vector(x1[i,])) data3=data2[data2[,1]==x1[i,],] else {as=data.frame(x1[i,]) names(as)=names(x1) data3=merge(data2, as, by = intersect(names(data2), names(as))) } y=sort(data3$index) if(description & method!="poisson") {cat("Stratum" ,i,"\n") cat("\nPopulation total and number of selected units:",length(y),size[i],"\n") } if(method!="srswr" & length(y)=3) for(i in 3:ncol(X1)) x=list(x,unique(X1[,i])) x=expand.grid(x) ng=1 prob=rhgroup=numeric(nrow(X1)) for (i in 1:nrow(x)) { expr=rep(FALSE, nrow(X1)) for(j in 1:nrow(X1)) { expr[j] = all(X1[j,2:ncol(X1)] == x[i, ]) if(expr[j]) rhgroup[j]=ng } if(any(expr)) ng=ng+1 } gr=unique(rhgroup) if(is.data.frame(X1)) X1=cbind.data.frame(X1,rhgroup) else X1=cbind(X1,rhgroup) for(i in 1:length(gr)) {l=nrow(X1[X1[,ncol(X1)]==gr[i],]) lr=nrow(X1[X1[,ncol(X1)]==gr[i] & X1[,1]==1,]) for(j in 1:length(prob)) if(rhgroup[j]==gr[i] & X1[j,1]==1) prob[j]=lr/l } result=cbind.data.frame(X$ID_unit,X1,prob) names(result)=c("ID_unit",names(X1),"prob_resp") res = NULL mm = match(names(X), names(result), nomatch = 0) if(0 %in% mm) {index = (1:ncol(X))[mm == 0] res = cbind.data.frame(X[X$ID_unit==result$ID_unit, index], result) names(res)[1:length(index)] = names(X)[index] } else res=result res } sampling/R/UPsystematic.R0000644000176200001440000000045314516451542015053 0ustar liggesusers"UPsystematic"<-function(pik,eps=1e-6) { if(any(is.na(pik))) stop("there are missing values in the pik vector") list=pik > eps & pik < 1-eps pik1 = pik[list] N = length(pik1) a = (c(0, cumsum(pik1)) - runif(1, 0, 1))%%1 s1 = as.integer(a[1:N] > a[2:(N + 1)]) s = pik s[list] = s1 s } sampling/R/UPMEqfromw.R0000644000176200001440000000067614516451542014432 0ustar liggesusers"UPMEqfromw" <- function(w,n) { N=length(w) expa=array(0,c(N,n)) for(i in 1:N) expa[i,1]= sum(w[i:N]) for(i in (N-n+1):N) expa[i,N-i+1]=exp(sum(log(w[i:N]))) for(i in (N-2):1) for(z in 2:min(N-i,n)) { expa[i,z]=w[i]*expa[i+1,z-1]+expa[i+1,z] } q=array(0,c(N,n)) for(i in N:1) q[i,1]= w[i]/expa[i,1] for(i in N:(N-n+1)) q[i,N-i+1]=1 for(i in (N-2):1) for(z in 2:min(N-i,n)) q[i,z] = w[i]*expa[i+1,z-1]/expa[i,z] q } sampling/R/calib.r0000644000176200001440000001762014516451542013537 0ustar liggesuserscalib<-function (Xs, d, total, q = rep(1, length(d)), method = c("linear", "raking", "truncated", "logit"), bounds = c(low = 0, upp = 10), description = FALSE, max_iter = 500) { if (any(is.na(Xs)) | any(is.na(d)) | any(is.na(total)) | any(is.na(q))) stop("the input should not contain NAs") if (!(is.matrix(Xs) | is.array(Xs))) Xs = as.matrix(Xs) if (is.matrix(Xs)) if (length(total) != ncol(Xs)) stop("Xs and total have different dimensions") if (is.vector(Xs) & length(total) != 1) stop("Xs and total have different dimensions") if (any(is.infinite(q))) stop("there are Inf values in the q vector") if (missing(method)) stop("specify a method") if (!(method %in% c("linear", "raking", "logit", "truncated"))) stop("the specified method is not in the list") if (method %in% c("linear", "raking") & !missing(bounds)) stop("for the linear and raking the bounds are not allowed") EPS = .Machine$double.eps EPS1 = 1e-06 n = length(d) lambda = as.matrix(rep(0, n)) lambda1 = ginv(t(Xs * d * q) %*% Xs, tol = EPS) %*% (total - as.vector(t(d) %*% Xs)) if (method == "linear" | max(abs(lambda1)) < EPS) g = 1 + q * as.vector(Xs %*% lambda1) else if (method == "truncated") { if (!missing(bounds)) { if (bounds[2] <= 1 || bounds[1] >= 1 || bounds[1] > bounds[2]) warning("The conditions low<1 bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - as.vector(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] d1 = d[list] q1 = q[list] list1 = list } } t1 = as.vector(t(d1) %*% Xs1) lambda1 = ginv(t(Xs1 * d1 * q1) %*% Xs1, tol = EPS) %*% (t2 - t1) if (length(list1) > 1) g1 = 1 + q1 * as.vector(Xs1 %*% lambda1) else if (length(list1) == 1) { g1 = 1 + q1 * as.vector(as.vector(Xs1) %*% as.vector(lambda1)) } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("No convergence in", max_iter, "iterations with the given bounds. \n") cat("The bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") } } else if (method == "raking") { lambda = as.matrix(rep(0, ncol(Xs))) w1 = as.vector(d * exp(Xs %*% lambda * q)) for (l in 1:max_iter) { phi = t(Xs) %*% w1 - total T1 = t(Xs * w1) phiprim = T1 %*% Xs lambda = lambda - ginv(phiprim, tol = EPS) %*% phi w1 = as.vector(d * exp(Xs %*% lambda * q)) if (any(is.na(w1)) | any(is.infinite(w1))) { warning("No convergence") g = NULL break } tr = crossprod(Xs, w1) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1) break } if (l == max_iter) { warning("No convergence") g = NULL } else g = w1/d } else if (method == "logit") { if (bounds[2] <= 1 || bounds[1] >= 1 || bounds[1] > bounds[2]) stop("The conditions low<1 EPS1 | any(g < bounds[1]) | any(g > bounds[2])) { lambda1 = rep(0, ncol(Xs)) list = 1:length(g) t2 = total Xs1 = Xs d1 = d g1 = g q1 = q list1 = 1:length(g) for (l in 1:max_iter) { if (any(g < bounds[1]) | any(g > bounds[2])) { g[g < bounds[1]] = bounds[1] g[g > bounds[2]] = bounds[2] list = (1:length(g))[g > bounds[1] & g < bounds[2]] if (length(list) != 0) { g1 = g[list] t2 = total - as.vector(t(g[-list] * d[-list]) %*% Xs[-list, ]) Xs1 = Xs[list, ] d1 = d[list] q1 = q[list] list1 = list } else break } if (is.vector(Xs1)) { warning("no convergence") g1 = g = NULL break } t1 = as.vector(t(d1) %*% Xs1) phi = t(Xs1) %*% as.vector(d1 * g1) - t1 T = t(Xs1 * as.vector(d1 * g1)) phiprime = T %*% Xs1 lambda1 = lambda1 - ginv(phiprime, tol = EPS) %*% (as.vector(phi) - t2 + t1) u = exp(A * (Xs1 %*% lambda1 * q1)) F = g1 = (bounds[1] * (bounds[2] - 1) + bounds[2] * (1 - bounds[1]) * u)/(bounds[2] - 1 + (1 - bounds[1]) * u) if (any(is.na(g1))) { warning("no convergence") g1 = g = NULL break } g[list1] = g1 tr = crossprod(Xs, g * d) expression = max(abs(tr - total)/total) if(any(total==0)) expression = max(abs(tr - total)) if (expression < EPS1 & all(g >= bounds[1] & g <= bounds[2])) break } if (l == max_iter) { cat("no convergence in", max_iter, "iterations with the given bounds. \n") cat("the bounds for the g-weights are:", min(g), " and ", max(g), "\n") cat(" and the g-weights are given by g\n") g = NULL } } } if (description && !is.null(g)) { par(mfrow = c(3, 2), pty = "s") hist(g) boxplot(g, main = "Boxplot of g") hist(d) boxplot(d, main = "Boxplot of d") hist(g * d) boxplot(g * d, main = "Boxplot of w=g*d") if (method %in% c("truncated", "raking", "logit")) cat("number of iterations ", l, "\n") cat("summary - initial weigths d\n") print(summary(d)) cat("summary - final weigths w=g*d\n") print(summary(as.vector(g * d))) } g } sampling/R/HTestimator.R0000644000176200001440000000036214516451542014663 0ustar liggesusersHTestimator<-function(y,pik) { if(any(is.na(pik))) stop("there are missing values in pik") if(any(is.na(y))) stop("there are missing values in y") if(length(y)!=length(pik)) stop("y and pik have different sizes") crossprod(y,1/pik) } sampling/R/UPopips.r0000644000176200001440000000066514516451542014065 0ustar liggesusersUPopips<-function(lambda, type=c("pareto","uniform","exponential")) { if(any(is.na(lambda))) stop("there are missing values in the lambda vector") n=sum(lambda) if(!(type %in% c("pareto","uniform","exponential"))) stop("the type argument is wrong") omega=runif(n) switch(type,pareto=order(omega*(1-lambda)/((1-omega)*lambda))[1:n], uniform=order(omega/lambda)[1:n], exponential=order(log(1-omega)/log(1-lambda)))[1:n] } sampling/R/varHT.r0000644000176200001440000000157314516451542013511 0ustar liggesusersvarHT<-function(y, pikl, method=1) { if(any(is.na(pikl))) stop("there are missing values in pikl") if (any(is.na(y))) stop("there are missing values in y") if(!(is.data.frame(pikl) | is.matrix(pikl))) stop("pikl should be a matrix or a data frame") if(is.data.frame(pikl) | is.matrix(pikl)) if(nrow(pikl)!=ncol(pikl)) stop("pikl is not a square matrix") if (length(y) != nrow(pikl)) stop("y and pik have different sizes") if(!missing(method) & !(method %in% c(1,2))) stop("the method should be 1 or 2") if(is.data.frame(pikl)) pikl=as.matrix(pikl) pik=diag(pikl) pik1=outer(pik,pik,"*") delta=pikl-pik1 diag(delta)=pik*(1-pik) y1=outer(y,y,"*") if(method==1)return(sum(y1*delta/(pik1*pikl))) if(method==2) {y2=outer(y/pik,y/pik,"-")^2 return(0.5*sum(y2*(pik1-pikl)/pikl)) } } sampling/R/calibev.r0000644000176200001440000000174114516451542014067 0ustar liggesuserscalibev<-function(Ys,Xs,total,pikl,d,g,q=rep(1,length(d)),with=FALSE,EPS=1e-6) { if(any(is.na(g))) stop("There are missing values in g") stopifnot((ns <- length(g)) >= 1) if(min(pikl)==0) {ss=NULL warning("There are zero values in the 'pikl' matrix. The variance estimator can not be computed.\n") } piks=as.vector(diag(pikl)) if(!checkcalibration(Xs,d,total,g,EPS)$result) stop("The calibration is not possible. The calibration estimator is not computed.\n") if(is.data.frame(Xs)) Xs=as.matrix(Xs) if(!is.vector(Ys)) Ys=as.vector(Ys) if(is.matrix(Xs)) n=nrow(Xs) else n=length(Xs) if(ns!=length(Ys) | ns!=length(piks) | ns!=n | ns!=length(d)) stop("The parameters have different sizes.\n") w=g*d wtilde=w*q B=t(Xs*wtilde) beta=ginv(B%*%Xs)%*%B%*%Ys e=Ys-Xs%*%beta if(!with) e=e*w else e=e*d ss=0 for(k in 1:ns) {ss2=0 for(l in 1:ns) ss2=ss2+(1-piks[k]*piks[l]/pikl[k,l])*e[l] ss=ss+e[k]*ss2 } list(calest=sum(w*Ys),evar=as.numeric(ss)) } sampling/R/getdata.r0000644000176200001440000000322214516451542014067 0ustar liggesusersgetdata<-function(data, m) { if (!is.data.frame(data)) data = as.data.frame(data) if (is.null(names(data))) stop("the column names are missing") if (is.vector(m) & !is.list(m)) { res = NULL if (is.null(names(m))) if (all(m %in% c(0, 1))) { res = NULL if (!("ID_unit" %in% names(data))) { res = cbind.data.frame((1:length(m))[m == 1], data[m == 1, ]) names(res) = c("ID_unit", names(data)) } else res = data[m == 1, ] } else res=data[rep(which(m>0),m[m>0]),] } else if (is.data.frame(m)) { res = NULL if (!is.null(names(m))) { mm = match(names(data), names(m), nomatch = 0) index = (1:ncol(data))[mm == 0] if (length(index) > 0) { res = cbind.data.frame(data[m$ID_unit, index], m) names(res)[1:length(index)] = names(data)[index] } else res = m } } else if (is.list(m)) { res = list() if (length(m) >= 1) for (j in 1:length(m)) { mm = match(names(data), names(m[[j]]), nomatch = 0) index = (1:ncol(data))[mm == 0] if (length(index) > 0) { res[[j]] = cbind.data.frame(data[m[[j]]$ID_unit, index], m[[j]]) names(res[[j]])[1:length(index)] = names(data)[index] } } else res = m } res } sampling/R/regest.r0000644000176200001440000000470014516451542013751 0ustar liggesusersregest<-function(formula,Tx,weights,pikl,n,sigma=rep(1,length(weights))) { cl <- match.call() mf <- match.call(expand.dots = FALSE) m <- match(c("formula", "weights"), names(mf), 0) mf <- mf[c(1, m)] mf$drop.unused.levels <- TRUE mf[[1]] <- as.name("model.frame") mf <- eval(mf, parent.frame()) mt <- attr(mf, "terms") y <- model.response(mf, "numeric") w <- as.vector(model.weights(mf)) pik<-1/w if(!identical(sigma,rep(1,length(pik)))) w<-w/sigma^2 x <- model.matrix(mt, mf, contrasts) if(ncol(x)==1) x=as.vector(x) if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(y))) stop("there are missing values in y") if (any(is.na(x))) stop("there are missing values in x") if(is.vector(x)) {if (length(y) != length(pik) | length(x)!=length(pik) | length(x)!=length(y)) stop("y, x and pik have different lengths") } else if(is.matrix(x)) {if (length(y) != length(pik) | nrow(x)!=length(pik) | nrow(x)!=length(y)) stop("y, x and pik have different sizes") if(ncol(x)>2 & length(Tx)!=ncol(x)-1) stop("x and Tx have different sizes") } model<-lm(y~x-1,weights=w) e<-model$residuals beta<-model$coefficient # variance of beta, Sarndal p. 194 delta<-matrix(0,nrow(pikl),ncol(pikl)) for(k in 1:(nrow(delta)-1)) {for(l in (k+1):ncol(delta)) delta[l,k]<-delta[k,l]<-1-pikl[k,k]*pikl[l,l]/pikl[k,l] delta[k,k]<-1-pikl[k,k] } delta[nrow(delta),ncol(delta)]<-1-pikl[nrow(delta),ncol(delta)] j_start<-1 if(is.matrix(x)) { if(all(x[,1]==rep(1,nrow(x)))) j_start<-2 xx<-as.matrix(x[,j_start:ncol(x)]) s<-0 for(i in 1:ncol(xx)) if(j_start==2) s<-s+sum(beta[i+1]*(Tx[i]-HTestimator(xx[,i],pik))) else s<-s+sum(beta[i]*(Tx[i]-HTestimator(xx[,i],pik))) est<-HTestimator(y,pik)+s } else est<-HTestimator(y,pik)+sum(beta*(Tx-HTestimator(x,pik))) V<-t(x*w*e)%*%delta%*%(x*e*w) inv<-ginv(t(x * w) %*% x) var_beta<-inv%*%V%*%inv z<-list() class(z) <- c("regest") z$call <- cl z$formula <- formula z$x <- x z$y <- y z$weights<-w z$regest<-as.numeric(est) z$coefficients<-beta z$std_error<-sqrt(diag(var_beta)) z$t_value<-beta/sqrt(diag(var_beta)) # number of degrees of freedom is number of obs-1 if intercept, and number of obs otherwise if(j_start==1) z$p_value<-2*(1-pt(z$t_value,n-1)) else z$p_value<-2*(1-pt(z$t_value,n)) z$cov_matrix<-var_beta z } sampling/R/varest.r0000644000176200001440000000141714516451542013766 0ustar liggesusersvarest<-function(Ys,Xs=NULL,pik,w=NULL) { if (any(is.na(pik))) stop("there are missing values in pik") if (any(is.na(Ys))) stop("there are missing values in y") if (length(Ys) != length(pik)) stop("y and pik have different sizes") if(!is.null(Xs)) {if(is.data.frame(Xs)) Xs=as.matrix(Xs) if(is.vector(Xs) & (length(Ys)!= length(Xs))) stop("x and y have different sizes") if(is.matrix(Xs) & (length(Ys) != nrow(Xs))) stop("x and y have different sizes") } a=(1-pik)/sum(1-pik) if(is.null(Xs)) {A=sum(a*Ys/pik) var=sum((1-pik)*(Ys/pik-A)^2)/(1-sum(a^2)) } else {B=t(Xs*w) beta=ginv(B%*%Xs)%*%B%*%Ys e=Ys-Xs%*%beta A=sum(a*e/pik) var=sum((1-pik)*(e/pik-A)^2)/(1-sum(a^2)) } var }sampling/R/balancedcluster.R0000644000176200001440000000115614516451542015555 0ustar liggesusers"balancedcluster" <- function(X,m,cluster,selection=1,comment=TRUE,method=1) { cluster=cleanstrata(cluster) if(comment==TRUE) cat("\nSELECTION OF A SAMPLE OF CLUSTERS\n") p=dim(X)[2] N=dim(X)[1] H=max(cluster) XC=array(0,c(H,p)) Ni=rep(0,times=H) for(h in 1:H) { Ni[h]=sum(as.integer(cluster==h)) for(j in 1:p) XC[h,j]=sum(X[cluster==h,j]) } if(selection==1) pik=inclusionprobabilities(Ni,m) else pik=rep(m/H,times=H) s=samplecube(cbind(pik,XC),pik,1,comment,method) res=array(0,c(N,2)) for(h in 1:H) { res[cluster==h,1]=s[h] res[cluster==h,2]=pik[h] } res } sampling/R/postest.r0000644000176200001440000000371714516451542014170 0ustar liggesuserspostest<-function(data, y, pik, NG, description=FALSE) { if (missing(data) | missing(y) | missing(pik) | missing(NG)) stop("incomplete input") str <- function(st, h, n) .C("str", as.double(st), as.integer(h), as.integer(n), s = double(n), PACKAGE = "sampling")$s data=as.data.frame(data) sample.size=nrow(data) t_post=0 if(!is.null(colnames(data))) {m = match("Stratum", colnames(data)) if(!any(is.na(m))) { m = match("poststratum", colnames(data)) if (any(is.na(m))) stop("the column 'poststratum' is missing") h=unique(data$Stratum) g=unique(data$poststratum) for(j in 1:length(g)) {p=str(data$poststratum, g[j], sample.size) Ng=sum(NG[,j]) t1=t2=0 for (i in 1:length(h)) {s = str(data$Stratum, h[i], sample.size) shg=s*p if(!all(shg==0)) { nhg=length(shg[shg==1]) t1=t1+sum(y[shg==1]/pik[shg==1]) t2=t2+sum(1/pik[shg==1]) if(description) {cat("Stratum ",j,", postratum ", i," \n") cat("the postratified estimator is:",Ng*t1/t2,"\n") } t_post=t_post+Ng*t1/t2 } else if(description) cat("Stratum ",j,", postratum ", i," empty intersection set \n") }} } else { g=unique(data$poststratum) for(j in 1:length(g)) {p=str(data$poststratum, g[j], sample.size) Ng=NG[j] t1=Ng*sum(y[p==1]/pik[p==1])/sum(1/pik[p==1]) t_post=t_post+t1 if(description) {cat("postratum ", j," \n") cat("the postratified estimator is:",t1,"\n") } } } } else stop("the column names in data are missing") t_post } sampling/R/inclusionprobabilities.R0000644000176200001440000000145214516451542017175 0ustar liggesusersinclusionprobabilities <- function(a,n) { if(!is.vector(a)) a=as.vector(a) nnull = length(a[a == 0]) nneg = length(a[a < 0]) if (nnull > 0) warning("there are zero values in the initial vector a\n") if (nneg > 0) { warning("there are ", nneg, " negative value(s) shifted to zero\n") a[(a < 0)] = 0 } if(identical(a,rep(0,length(a)))) pik1=a else { pik1 =n * a/sum(a) pik=pik1[pik1>0] list1=pik1>0 list = pik >= 1 l = length(list[list == TRUE]) if(l>0) { l1=0 while (l != l1) { x=pik[!list] x=x/sum(x) pik[!list] = (n - l)*x pik[list] = 1 l1 = l list = (pik >= 1) l = length(list[list == TRUE]) } pik1[list1]=pik } } pik1 } sampling/R/UPtillepi2.R0000644000176200001440000000111614516451542014407 0ustar liggesusers"UPtillepi2" <- function(pik,eps=1e-6) { if(any(is.na(pik))) warning("there are missing values in the pik vector") n=sum(pik) n=.as_int(n) list = pik > eps & pik < 1 - eps pikb = pik[list] N = length(pikb) #ppf=pik%*%t(pik) ppf=matrix(0,length(pik),length(pik)) if(N<1) stop("the pik vector has all elements outside of the range [eps,1-eps]") else { n=sum(pikb) if(N>n) { UN=rep(1,N) b=rep(1,N) pp=1 for(i in 1:(N-n)) { a=inclusionprobabilities(pikb,N-i) vv=1-a/b b=a d=vv %*% t(UN) pp=pp*(1-d-t(d)) } diag(pp)=pikb ppf[list,list]=pp } } ppf } sampling/R/UPmaxentropypi2.R0000644000176200001440000000053314516451542015506 0ustar liggesusers"UPmaxentropypi2" <-function(pik) { n=sum(pik) n=.as_int(n) N=length(pik) M=array(0,c(N,N)) if(n>=2) { pik2=pik[pik>0 & pik<1] pikt=UPMEpiktildefrompik(pik2) w=pikt/(1-pikt) M[pik>0 & pik<1,pik>0 & pik<1]=UPMEpik2frompikw(pik2,w) M[,pik==1]=pik for(k in 1:N) if(pik[k]==1) M[k,]=pik } if(n==1) for(k in 1:N) M[k,k]=pik[k] M } sampling/MD50000644000176200001440000001644014517474042012411 0ustar liggesusers6003ccf87018c224179e077c964ebf46 *DESCRIPTION 8741a4e05231fcb44c4583179eba6161 *NAMESPACE 9da2c0433ff0f277f4dca4edb4e4cc38 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################################################### ### code chunk number 2: entropy1 ################################################### data(belgianmunicipalities) attach(belgianmunicipalities) n=50 ################################################### ### code chunk number 3: entropy2 ################################################### pik=inclusionprobabilities(averageincome,n) ################################################### ### code chunk number 4: entropy3 ################################################### s=UPmaxentropy(pik) ################################################### ### code chunk number 5: entropy4 ################################################### as.character(Commune[s==1]) ################################################### ### code chunk number 6: entropy5 ################################################### pi2=UPmaxentropypi2(pik) ################################################### ### code chunk number 7: entropy6 ################################################### rowSums(pi2)/pik/n detach(belgianmunicipalities) ################################################### ### code chunk number 8: entropy7 ################################################### data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) ################################################### ### code chunk number 9: entropy8 ################################################### UPMEsfromq(q) ################################################### ### code chunk number 10: entropy9 ################################################### sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) ################################################### ### code chunk number 11: up1 ################################################### b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) ################################################### ### code chunk number 12: up2 ################################################### sim=10 ss=array(0,c(sim,8)) ################################################### ### code chunk number 13: up3 ################################################### y=belgianmunicipalities$TaxableIncome ################################################### ### code chunk number 14: up4 ################################################### ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } ################################################### ### code chunk number 15: up5 ################################################### colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) ################################################### ### code chunk number 16: UPexamples.Snw:163-170 (eval = FALSE) ################################################### ## b=data(belgianmunicipalities) ## pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) ## N=length(pik) ## n=sum(pik) ## sim=10 ## ss=array(0,c(sim,8)) ## y=belgianmunicipalities$TaxableIncome ## ht=numeric(8) ## for(i in 1:sim) ## { ## cat("Step ",i,"\n") ## s=UPpoisson(pik) ## ht[1]=HTestimator(y[s==1],pik[s==1]) ## s=UPrandomsystematic(pik) ## ht[2]=HTestimator(y[s==1],pik[s==1]) ## s=UPrandompivotal(pik) ## ht[3]=HTestimator(y[s==1],pik[s==1]) ## s=UPtille(pik) ## ht[4]=HTestimator(y[s==1],pik[s==1]) ## s=UPmidzuno(pik) ## ht[5]=HTestimator(y[s==1],pik[s==1]) ## s=UPsystematic(pik) ## ht[6]=HTestimator(y[s==1],pik[s==1]) ## s=UPpivotal(pik) ## ht[7]=HTestimator(y[s==1],pik[s==1]) ## s=srswor(n,N) ## ht[8]=HTestimator(y[s==1],rep(n/N,n)) ## ss[i,]=ht ## } ## colnames(ss) <- ## c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") ## boxplot(data.frame(ss), las=3) ## ## ## sampling.newpage() sampling/inst/doc/calibration.pdf0000644000176200001440000054276514517474042016623 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 5379 /Filter /FlateDecode /N 91 /First 745 >> stream x\ے}߯7K`Wl8E2EYh=8MÙqpM9@86vc$t]pL$2O&PMרFhF4vB㚠e!i*uaF؀AFF PM#B}nM#|#-HJ]#=+Fud$+F)VҍLlAlF}(7Sx-:-A o:Sh:hxd:\7Fal +wEc@qZ5&(vUxo b Drҡzkd4dmTl"ta ~uh8xm<&@`Sثn-fcV;BrRbƤ ` څVq6%gCQ ] Πg+oE*Q ơg0;B/:i(a^yڴ/ן/_*.wd?:bA' bIC/XuC%;?=g&Ѽ.Y( B:W&:\$FgПl$Њ^67A(ӯ2gq۟6'vT$9vΨ3y1 E>| XOHTs>aΧUp\hK-F){fT`1jÜQ9vpiFe5raFFͨˌZ7gUS} 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The \verb@state@ variable is used as a stratification variable. The sample stratum sizes are 25 and 20, respectively. The method is 'srswor' (equal probability, without replacement). <>= s=strata(data,c("state"),size=c(25,20), method="srswor") @ We obtain the observed data: <>= s=getdata(data,s) @ The \verb@status@ variable is used in the \verb@rhg_strata@ function. The \verb@status@ column is added to $s$ (1 - sample respondent, 0 otherwise); it is randomly generated using the uniform distribution U(0,1). The response probability for all units is 0.3. <>= status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) @ We compute the response homeogeneity groups using the \verb@region@ variable: <>= s=rhg_strata(s,selection="region") @ We select only the sample respondents: <>= sr=s[s$status==1,] @ We create the population data frame of sex and region indicators: <>= X=cbind(disjunctive(data$sex),disjunctive(data$region)) @ We compute the population totals for each sex and region: <>= total=c(t(rep(1,nrow(data)))%*%X) @ The first method consists in calibrating with all strata. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created. The initial weights using the inclusion prob. and the response probabilities are computed. <>= Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) @ We compute the g-weights using the linear method: <>= g = calib(Xs, d, total, method = "linear") summary(g) @ The final weights are: <>= w=d*g summary(w) @ We check the calibration: <>= checkcalibration(Xs, d, total, g) @ The second method consists in calibrating in each stratum. The respondent data frame of \verb@sex@ and \verb@region@ indicators is created in each stratum. The initial weights using the inclusion prob. and response probabilities are computed in each stratum. <>= cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) @ <>= <> <> <> <> <> <> <> <> <> <> <> <> <> <> sampling.newpage() @ \section{Example 2} This is an example for \begin{itemize} \item variance estimation of the calibration estimator (using the \verb@calibev@ and \verb@varest@ functions), \item variance estimator of the Horvitz-Thompson estimator (using the \verb@varest@ and \verb@varHT@ functions). \end{itemize} We generate an artificial population and use Till\'e sampling. The population size is 100, and the sample size is 20. There are three auxiliary variables (two categorical and one continuous; the matrix $X$). The vector $Z=(150, 151, \dots, 249)'$ is used to compute the first-order inclusion probabilities. The variable of interest $Y$ is computed using the model $Y_j=5*Z_j*(\varepsilon_j+\sum_{i=1}^{100} X_{ij}), \varepsilon_j\sim N(0,1/3), iid, j=1,\dots, 100.$ The calibration estimator uses the linear method. Simulations are conducted to estimate the MSE of the two variance estimators of the calibration estimator. Since the linear method is used in calibration, the calibration estimator corresponds to the generalized regression estimator. For the latter an approximate variance can be computed on the population level and used in the bias estimation of the variance estimators. For the Horvitz-Thompson estimator, the variance can be computed on the population level and compared with the simulations' result. Use 10000 simulation runs to obtain accurate results (for time consuming reason, in the following program, the number of runs is only 10). <>= X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") @ <>= <> sampling.newpage() @ \section{Example 3} This is an example of generalized calibration used to handle unit nonresponse with different forms of response probabilities. Consider the population $U$, the sample $s$ and the set of respondents $r$ with $r\subseteq s \subseteq U.$ The response mechanism is given by the distribution $q(r|s)$ such that for every fixed $s$ we have $$q(r|s)\geq 0, \mbox{ for all } r\in \mathcal{R}_s \mbox{ and } \sum_{s\in {\mathcal R}_s} q(r|s)=1,$$ where ${\mathcal R}_s=\{r | r \subseteq s\}.$ The variable of interest $y_k$ is known only for $k\in r.$ Under unit nonresponse we define the response indicator $R_k=1$ if unit $k\in r$ and 0 otherwise and the response probabilities $p_k=Pr(R_k=1| k\in s).$ It is assumed that $R_k$ are independent Bernoulli variables with expected value equal to $p_k.$ We assume that the units respond independently of each other and of $s$ and so $$q(r|s)=\prod_{k\in r} p_k \prod_{k \in \bar{r}} (1-p_k).$$ The nonresponse model can be rewritten as $$q(r|s, \boldsymbol{\gamma})=\prod_{k\in r} F_k^{-1}(\boldsymbol{\gamma}) \prod_{k \in \bar{r}} (1-F^{-1}_k(\boldsymbol{\gamma})).$$ In calibration method it is assumed that $$\sum_{k\in r} \mathbf{x}_kd_kF_k(\boldsymbol{\gamma})=\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{x}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $F_k(\boldsymbol{\gamma})=F(\boldsymbol{\gamma}^T\mathbf{x}_k), p_k=F_k(\boldsymbol{\gamma})^{-1},$ and $d_k$ are the initial weigths. In generalized calibration a different equation is used $$\sum_{k\in r} \mathbf{x}_kd_kF(\boldsymbol{\gamma}^T\mathbf{z}_k)=\sum_{k\in U} \mathbf{x}_k,$$ where $\mathbf{z}_k$ is not necessary equal to $\mathbf{x}_k,$ but $\mathbf{z}_k$ and $\mathbf{x}_k$ have to be highly correlated. $\mathbf{z}_k$ should be known only for $k\in r.$ The components of $\mathbf{z}_k$ that are not also components of $\mathbf{x}_k$ are often known as \emph{instrumental variables}. Let $w_k$ be the final weights (obtained after applying generalized calibration). It is possible to assume different forms of response probabilities: \begin{itemize} \item Linear weight adjustment (it can be implemented by using the argument \texttt{method="linear"} in gencalib() function or \texttt{method="truncated"} if bounds are allowed): $p_k=1/(1+ {\boldsymbol\gamma}^T\mathbf{z}_k)$ and $w_k=d_k(1+\mathbf{h}^T\mathbf{z}_k),$ where $\mathbf{h}$ is a consistent estimate of ${\boldsymbol\gamma}.$ \item Raking weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)$ and $w_k=d_k \exp(\mathbf{h}^T\mathbf{z}_k).$ \item Logistic weight adjustment (it can be implemented by using the argument \texttt{method="raking"} in gencalib()): $p_k=1/(1+\exp(\boldsymbol{\gamma}^T\mathbf{z}_k)), w_k=d_k (1+\exp(\mathbf{h}^T\mathbf{z}_k)),$ but we calibrate on $\sum_{k\in U} \mathbf{x}_k-\sum_{k\in r} \mathbf{x}_k d_k$ instead of $\sum_{k\in U} \mathbf{x}_k.$\item Generalized exponential weight adjustment (Folsom and Singh, 2000; it can be implemented by using the argument \texttt{method="logit"} in gencalib()): $$p_k=1/F(\boldsymbol{\gamma}^T\mathbf{z}_k), w_k=d_kF(\mathbf{h}^T\mathbf{z}_k),$$ $$F(\mathbf{h}^T\mathbf{z}_k)=\frac{L(U-C)+U(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}{(U-C)+(C-L)\exp(A\mathbf{h}^T\mathbf{z}_k)}\in (L, U),$$ where $A=(U-L)/((C-L)(U-C))$ and $L\geq 0,1C>L,$ ($C=1$ in the paper of Deville and Sarndal, 1992). The g-weights are centered around of $C.$ For $L=1, C=2$ and $U=\infty, F(\mathbf{h}^T\mathbf{z}_k)$ approaches $1+\exp(\mathbf{h}^T\mathbf{z}_k)$ and for $C=1, L=0, U=\infty,$ $\exp(\mathbf{h}^T\mathbf{z}_k).$ \end{itemize} We exemplify the last form of response probabilities (generalized exponential weight adjustment) using artificial data. We generate a population of size $N=400$ and consider the auxiliary information $X$ following a Gamma distribution with parameters 3 and 4. The instrumental variable $Z$ is generated using the model $Z=2X+\varepsilon,$ where $\varepsilon\sim U(0,1).$ The variable of interest is $Y$ generated using the model $Y=3X+\varepsilon_1,$ where $\varepsilon_1\sim N(0,1).$ We consider here that the nonresponse is not missing at random and the response probabilities $p$ depend on the variable of interest $y$ which may be missing. We draw a simple random sampling without replecement of size $n=100$ and generate the set of respondents $r$ using Poisson sampling with the probabilties $p.$ The bounds are fixed to 1 and 5, and the constant $C=1.5.$ Three estimators are computed: \begin{itemize} \item the generalized calibration estimator using $Z$ as instrumental variable, \item the generalized calibration estimator using $Y$ as instrumental variable, \item the generalized calibration estimator using $X$ as instrumental variable, which is the same with the calibration estimator, but the g-weights are centered around $C$. \end{itemize} The convergence of the method is not guaranteed due to the bounds. Thus $g1, g2, g3$ can be null. If it the case, repeat the code (considering another $s$ and $r$). <>= N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= <> sampling.newpage() @ \end{document} sampling/inst/doc/calibration.R0000644000176200001440000003420714517464542016242 0ustar liggesusers### R code from vignette source 'calibration.Snw' ################################################### ### code chunk number 1: calibration.Snw:21-24 ################################################### library(sampling) ps.options(pointsize=12) options(width=60) ################################################### ### code chunk number 2: calib1 ################################################### data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), matrix(rep("B", 100), 100, 1, byrow = TRUE)) data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), 1000 * runif(250)) sex = runif(nrow(data)) for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 data = cbind.data.frame(data, sex) names(data) = c("state", "region", "income", "sex") summary(data) ################################################### ### code chunk number 3: calib2 ################################################### table(data$state) ################################################### ### code chunk number 4: calib3 ################################################### s=strata(data,c("state"),size=c(25,20), method="srswor") ################################################### ### code chunk number 5: calib31 ################################################### s=getdata(data,s) ################################################### ### code chunk number 6: calib32 ################################################### status=runif(nrow(s)) for(i in 1:length(status)) if(status[i]<0.3) status[i]=0 else status[i]=1 s=cbind.data.frame(s,status) ################################################### ### code chunk number 7: calib4 ################################################### s=rhg_strata(s,selection="region") ################################################### ### code chunk number 8: calib5 ################################################### sr=s[s$status==1,] ################################################### ### code chunk number 9: calib6 ################################################### X=cbind(disjunctive(data$sex),disjunctive(data$region)) ################################################### ### code chunk number 10: calib7 ################################################### total=c(t(rep(1,nrow(data)))%*%X) ################################################### ### code chunk number 11: calib8 ################################################### Xs = X[sr$ID_unit,] d = 1/(sr$Prob * sr$prob_resp) summary(d) ################################################### ### code chunk number 12: calib9 ################################################### g = calib(Xs, d, total, method = "linear") summary(g) ################################################### ### code chunk number 13: calib10 ################################################### w=d*g summary(w) ################################################### ### code chunk number 14: calib11 ################################################### checkcalibration(Xs, d, total, g) ################################################### ### code chunk number 15: calib12 ################################################### cat("stratum 1\n") data1=data[data$state=='A',] X1=X[data$state=='A',] total1=c(t(rep(1, nrow(data1))) %*% X1) sr1=sr[sr$Stratum==1,] Xs1=X[sr1$ID_unit,] d1 = 1/(sr1$Prob * sr1$prob_resp) g1=calib(Xs1, d1, total1, method = "linear") checkcalibration(Xs1, d1, total1, g1) cat("stratum 2\n") data2=data[data$state=='B',] X2=X[data$state=='B',] total2=c(t(rep(1, nrow(data2))) %*% X2) sr2=sr[sr$Stratum==2,] Xs2=X[sr2$ID_unit,] d2 = 1/(sr2$Prob * sr2$prob_resp) g2=calib(Xs2, d2, total2, method = "linear") checkcalibration(Xs2, d2, total2, g2) ################################################### ### code chunk number 16: calibration.Snw:157-176 (eval = FALSE) ################################################### ## data = rbind(matrix(rep("A", 150), 150, 1, byrow = TRUE), ## matrix(rep("B", 100), 100, 1, byrow = TRUE)) ## data = cbind.data.frame(data, c(rep(1, 60), rep(2,50), rep(3, 60), rep(1, 40), rep(2, 40)), ## 1000 * runif(250)) ## sex = runif(nrow(data)) ## for (i in 1:length(sex)) if (sex[i] < 0.3) sex[i] = 1 else sex[i] = 2 ## data = cbind.data.frame(data, sex) ## names(data) = c("state", "region", "income", "sex") ## summary(data) ## table(data$state) ## s=strata(data,c("state"),size=c(25,20), method="srswor") ## s=getdata(data,s) ## status=runif(nrow(s)) ## for(i in 1:length(status)) ## if(status[i]<0.3) status[i]=0 else status[i]=1 ## s=cbind.data.frame(s,status) ## s=rhg_strata(s,selection="region") ## sr=s[s$status==1,] ## X=cbind(disjunctive(data$sex),disjunctive(data$region)) ## total=c(t(rep(1,nrow(data)))%*%X) ## Xs = X[sr$ID_unit,] ## d = 1/(sr$Prob * sr$prob_resp) ## summary(d) ## g = calib(Xs, d, total, method = "linear") ## summary(g) ## w=d*g ## summary(w) ## checkcalibration(Xs, d, total, g) ## cat("stratum 1\n") ## data1=data[data$state=='A',] ## X1=X[data$state=='A',] ## total1=c(t(rep(1, nrow(data1))) %*% X1) ## sr1=sr[sr$Stratum==1,] ## Xs1=X[sr1$ID_unit,] ## d1 = 1/(sr1$Prob * sr1$prob_resp) ## g1=calib(Xs1, d1, total1, method = "linear") ## checkcalibration(Xs1, d1, total1, g1) ## cat("stratum 2\n") ## data2=data[data$state=='B',] ## X2=X[data$state=='B',] ## total2=c(t(rep(1, nrow(data2))) %*% X2) ## sr2=sr[sr$Stratum==2,] ## Xs2=X[sr2$ID_unit,] ## d2 = 1/(sr2$Prob * sr2$prob_resp) ## g2=calib(Xs2, d2, total2, method = "linear") ## checkcalibration(Xs2, d2, total2, g2) ## ## ## ## sampling.newpage() ## ################################################### ### code chunk number 17: ex1 ################################################### X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) # vector of population totals total=apply(X,2,"sum") Z=150:249 # the variable of interest Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) # inclusion probabilities pik=inclusionprobabilities(Z,20) # joint inclusion probabilities pikl=UPtillepi2(pik) # number of runs; let nsim=10000 for an accurate result nsim=10 c1=c2=c3=c4=c5=c6=numeric(nsim) for(i in 1:nsim) { # draws a sample s=UPtille(pik) # computes the inclusion prob. for the sample piks=pik[s==1] # the sample matrix of auxiliary information Xs=X[s==1,] # computes the g-weights g=calib(Xs,d=1/piks,total,method="linear") # computes the variable of interest in the sample Ys=Y[s==1] # computes the joint inclusion prob. for the sample pikls=pikl[s==1,s==1] # computes the calibration estimator and its variance estimation cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) c1[i]=cc$calest c2[i]=cc$evar # computes the variance estimator of the calibration estimator (second method) c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) # computes the variance estimator of the HT estimator using varest() c4[i]=varest(Ys,pik=piks) # computes the variance estimator of the HT estimator using varHT() c5[i]=varHT(Ys,pikls,2) # computes the Horvitz-Thompson estimator c6[i]=HTestimator(Ys,piks) } cat("the population total:",sum(Y),"\n") cat("the calibration estimator under simulations:", mean(c1),"\n") N=length(Y) delta=matrix(0,N,N) for(k in 1:(N-1)) for(l in (k+1):N) delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] diag(delta)=pik*(1-pik) var_HT=0 var_asym=0 e=lm(Y~X)$resid for(k in 1:N) for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} cat("the approximate variance of the calibration estimator:",var_asym,"\n") cat("first variance estimator of the calibration est. using calibev function:\n") cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") cat("second variance estimator of the calibration est. using varest function:\n") cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") cat("the variance of the HT estimator:", var_HT, "\n") cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") ################################################### ### code chunk number 18: calibration.Snw:263-267 (eval = FALSE) ################################################### ## X=cbind(c(rep(1,50),rep(0,50)),c(rep(0,50),rep(1,50)),1:100) ## # vector of population totals ## total=apply(X,2,"sum") ## Z=150:249 ## # the variable of interest ## Y=5*Z*(rnorm(100,0,sqrt(1/3))+apply(X,1,"sum")) ## # inclusion probabilities ## pik=inclusionprobabilities(Z,20) ## # joint inclusion probabilities ## pikl=UPtillepi2(pik) ## # number of runs; let nsim=10000 for an accurate result ## nsim=10 ## c1=c2=c3=c4=c5=c6=numeric(nsim) ## for(i in 1:nsim) ## { ## # draws a sample ## s=UPtille(pik) ## # computes the inclusion prob. for the sample ## piks=pik[s==1] ## # the sample matrix of auxiliary information ## Xs=X[s==1,] ## # computes the g-weights ## g=calib(Xs,d=1/piks,total,method="linear") ## # computes the variable of interest in the sample ## Ys=Y[s==1] ## # computes the joint inclusion prob. for the sample ## pikls=pikl[s==1,s==1] ## # computes the calibration estimator and its variance estimation ## cc=calibev(Ys,Xs,total,pikls,d=1/piks,g,with=FALSE,EPS=1e-6) ## c1[i]=cc$calest ## c2[i]=cc$evar ## # computes the variance estimator of the calibration estimator (second method) ## c3[i]=varest(Ys,Xs,pik=piks,w=g/piks) ## # computes the variance estimator of the HT estimator using varest() ## c4[i]=varest(Ys,pik=piks) ## # computes the variance estimator of the HT estimator using varHT() ## c5[i]=varHT(Ys,pikls,2) ## # computes the Horvitz-Thompson estimator ## c6[i]=HTestimator(Ys,piks) ## } ## cat("the population total:",sum(Y),"\n") ## cat("the calibration estimator under simulations:", mean(c1),"\n") ## N=length(Y) ## delta=matrix(0,N,N) ## for(k in 1:(N-1)) ## for(l in (k+1):N) ## delta[k,l]=delta[l,k]=pikl[k,l]-pik[k]*pik[l] ## diag(delta)=pik*(1-pik) ## var_HT=0 ## var_asym=0 ## e=lm(Y~X)$resid ## for(k in 1:N) ## for(l in 1:N) {var_HT=var_HT+Y[k]*Y[l]*delta[k,l]/(pik[k]*pik[l]) ## var_asym=var_asym+e[k]*e[l]*delta[k,l]/(pik[k]*pik[l])} ## cat("the approximate variance of the calibration estimator:",var_asym,"\n") ## cat("first variance estimator of the calibration est. using calibev function:\n") ## cat("MSE of the first variance estimator:", var(c2)+(mean(c2)-var_asym)^2,"\n") ## cat("second variance estimator of the calibration est. using varest function:\n") ## cat("MSE of the second variance estimator:", var(c3)+(mean(c3)-var_asym)^2,"\n") ## cat("the Horvitz-Thompson estimator under simulations:", mean(c6),"\n") ## cat("the variance of the HT estimator:", var_HT, "\n") ## cat("the variance estimator of the HT estimator under simulations:", mean(c4),"\n") ## cat("MSE of the variance estimator 1 of HT estimator:", var(c4)+(mean(c4)-var_HT)^2,"\n") ## cat("MSE of the variance estimator 2 of HT estimator:", var(c5)+(mean(c5)-var_HT)^2,"\n") ## ## sampling.newpage() ## ################################################### ### code chunk number 19: gen1 ################################################### N=400 n=100 X=rgamma(N,3,4) total=sum(X) Z=2*X+runif(N) Y=3*X+rnorm(N) print(cor(X,Y)) print(cor(X,Z)) L=1 U=5 C=1.5 A=(U-L)/((C-L)*(U-C)) p=((U-C)+(C-L)*exp(A*Y*0.3))/(L*(U-C)+U*(C-L)*exp(A*Y*0.3)) summary(p) bounds=c(L,U) s=srswor(n,N) r=numeric(n) for(j in 1:n) if(runif(1)>= library(sampling) ps.options(pointsize=12) options(width=60) @ \section{Examples of maximum entropy sampling design and related functions} a) Example 1 @ Consider the Belgian municipalities data set as population, and a sample size n=50 <>= data(belgianmunicipalities) attach(belgianmunicipalities) n=50 @ Compute the inclusion probabilties proportional to the `averageincome' variable <>= pik=inclusionprobabilities(averageincome,n) @ Draw a random sample using the maximum entropy sampling design <>= s=UPmaxentropy(pik) @ The sample is <>= as.character(Commune[s==1]) @ Compute the joint inclusion probabilities <>= pi2=UPmaxentropypi2(pik) @ Check the result <>= rowSums(pi2)/pik/n detach(belgianmunicipalities) @ b) Example 2 @ Selection of samples from Belgian municipalities data set, sample size 50. Once the matrix q (see below) is computed, a sample is quickly selected. Monte Carlo simulation can be used to compare the true inclusion probabilities with the estimated ones. <>= data(belgianmunicipalities) attach(belgianmunicipalities) pik=inclusionprobabilities(averageincome,50) pik=pik[pik!=1] n=sum(pik) pikt=UPMEpiktildefrompik(pik) w=pikt/(1-pikt) q=UPMEqfromw(w,n) @ Draw a sample using the q matrix <>= UPMEsfromq(q) @ Monte Carlo simulation to check the sample selection; the difference between pik and the estimated inclusion prob. (object tt below) is almost 0. <>= sim=10000 N=length(pik) tt=rep(0,N) for(i in 1:sim) tt = tt+UPMEsfromq(q) tt=tt/sim max(abs(tt-pik)) detach(belgianmunicipalities) @ \section{Example of unequal probability (UP) sampling designs} Selection of samples from the Belgian municipalities data set, with equal or unequal probabilities, and study of the Horvitz-Thompson estimator accuracy using boxplots. The following sampling schemes are used: Poisson, random systematic, random pivotal, Till\'e, Midzuno, systematic, pivotal, and simple random sampling without replacement. Monte Carlo simulations are used to study the accuracy of the Horvitz-Thompson estimator of a population total. The aim of this example is to demonstrate the effect of using auxiliary information in sampling designs. We use: \begin{itemize} \item some $\pi$ps sampling designs with Horvitz-Thompson estimation, using auxiliary information in a sampling desing (size measurements of population units in 2004); \item simple random sampling without replacement with Horvitz-Thompson estimation, where no auxiliary information is used. \end{itemize} <>= b=data(belgianmunicipalities) pik=inclusionprobabilities(belgianmunicipalities$Tot04,200) N=length(pik) n=sum(pik) @ Number of simulations (for an accurate result, increase this value to 10000): <>= sim=10 ss=array(0,c(sim,8)) @ Defines the variable of interest: <>= y=belgianmunicipalities$TaxableIncome @ Simulation and computation of the Horvitz-Thompson estimators: <>= ht=numeric(8) for(i in 1:sim) { cat("Step ",i,"\n") s=UPpoisson(pik) ht[1]=HTestimator(y[s==1],pik[s==1]) s=UPrandomsystematic(pik) ht[2]=HTestimator(y[s==1],pik[s==1]) s=UPrandompivotal(pik) ht[3]=HTestimator(y[s==1],pik[s==1]) s=UPtille(pik) ht[4]=HTestimator(y[s==1],pik[s==1]) s=UPmidzuno(pik) ht[5]=HTestimator(y[s==1],pik[s==1]) s=UPsystematic(pik) ht[6]=HTestimator(y[s==1],pik[s==1]) s=UPpivotal(pik) ht[7]=HTestimator(y[s==1],pik[s==1]) s=srswor(n,N) ht[8]=HTestimator(y[s==1],rep(n/N,n)) ss[i,]=ht } @ Boxplots of the estimators: <>= colnames(ss) <- c("poisson","rsyst","rpivotal","tille","midzuno","syst","pivotal","srswor") boxplot(data.frame(ss), las=3) <>= <> <> <> <> <> sampling.newpage() @ \end{document} sampling/inst/doc/HT_Hajek_estimators.pdf0000644000176200001440000037315414517474042020215 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 4042 /Filter /FlateDecode /N 52 /First 415 >> stream x[kseRb7@*kxrvę+ZxsE R,ϨQ\x{qitvu6wA.t 5SCJ]ꔶ N(:P)*;N%>+}Ci9v&ԧNCKdRwf`gζ3a*8MCo윏;#d !LE1X9hs֩,!,$cg`,x S;02sx4Ƽ(xo}?Y]n;)P V),XX±hBca1bREp6.'?_W=tm#^ orl9d%7Ӂ:VЯ5_DجקM7 [}\9>bC=KǗG@fylَ+ {y8q݉ r9ϗ/RX OAXmh|QA"+8 ?mE el_gOSj_ᆨvGTݝA9!-r"'TvrtXN4a_NΒQ1냂FP}@PXP4޻|ȯۇ/^<6b-6vf46&%k}gwO`]nh܄[ǹyݣ?>7p7s3[ ǹ1yۗOeBL8 nqnan{3pݮnMXNrsOv$=^6 yӿkfQ{̰-̨@;˳ bF(=@gu^ܶ)Kr?й)-_ҽ)]ĥ9]'}# $%_ڌ&Aݾv_POrJLP7 ]Н >j+MǬt^9[eupBzwkuh9(]ߥ(-?|X`ɴ]gL&1$l m:!yt7wKjv `1[3tG!y 8z:晘.4IB3%74s: 協7.6&2 %KKi2h.Ry0\`Tqʃѱ<^y"*E@%r̈́*S@]r+.+h@r T˥2?\-qKer_*s SޘT&32pD~ 4 ejACP&wD}}€O Vy U8©5UIFIUws hX +@d[:҅"%y.$hQƇ$2Aׯl_<綛pFk2}d/K{_hc",#r"(QPk$1`oHd3yHXmfĚR2dbT c3˔o1:qw2Ι "v1?9_*!]x-Vf 7tƭbɈY]to7WU JoUqUUW1fW9(@1XôvcP\ Ff}mNcl5c|e3t%37qh3?0p_6e 2k/bf+@#2=Z0%n>7p9tF=c,7hk`9#`ޑPUMjB7sَ&4?_}4;-hR%G.kwV;Og;շ[r)Yvvl?;nn]w e}.sX@="䫙! 6XD88cHV۳_˒5|rpw^t~Ąa⨏sA+쪫\)W^b3U4SpB.#Z!6,#= ;$+x[Tf᠇b+;.ތLO/q!i|߶H؏KI0tЎC=5 siH0:'Z>D+kn]$1%$tPHyCbeS`(+9,I+"q1H@ރ46L5X,&빷lY}dx'*tZ%&*zW1aauA>qh92pԞTLք =R9]Hن]Ӆ}-a~lhvꑲD-Nyb(>a׽?ە7E_ )_5}Y]뫐ByP%-Wo}݄ǶUmhђӦЎcK a_f؆*:ưg?>F%=~ R3^ >-אwP:y}a-!r@@k4~)?Ľt { Cgh}xj}n[r9ase1]a ˤdMlYqcjjF#Y39MM}LZ0lua՚ݺe RE n@w)X ğqLSgJ9r_R[24I=뽯݅"t>A`ig Jzs, g%ʲ, "#bÀ֙`:׳*(4 g؎L hendstream endobj 55 0 obj << /Filter /FlateDecode /Length 696 >> stream xmTMo0Wx$ ! 8l[jWHL7IPV=M̼ su;Uٛ=w]yil;<[[j<=?׾+v`&ߴț<^*;~&Q>MS >_P{=s@dkx;`VY`s4JaQܡn.Uu9\Y6><ٴ.Z.4>Dӗ}~r:-d0VWk,8yLһʮӮђ[*mLr?q 5F8@=@)& 8Rx uD\j2HV0CzL] bctI g$`htы0\F0s jd< I6zg W qȐ+#k .bsrbmXK7ǵH7Gnb>&jؐu1VljOu$՟qWS/%1{\xB!K(hHTЖ枃Jρϯv=k2UKς_:~$/ ~E+7ˢ/ l(/} -+ZXukoԝE?ZKqendstream endobj 56 0 obj << /Filter /FlateDecode /Length 739 >> stream xmUMo0WxvHUdCmU^!1H#x?gx]OTm$|͜s_Iss :L;<Sz==׾f`*_`ɫڟk3'iѴ}=M;7rfnj-eSӵOLg~8 )ok A8 $`I\3`Af<Z]! xNky"7 _㓧q H`nḱRONH=CpB:# =%888QA~!*zƜАT?!~> tw8y*sύ }nFE>7*QύR>7G];~<6OIyktg>O:yұϓN|I/|yIg>O:y҅ϓ.}2 L> stream xmUMo:W5?$R. d9M eCkmCp;;w~>|3E_?O]5߶w]Occ]=~?}Oyh9%?۹׬B|Ɯ>);vw%g43>\ 6 EJ78 1{~`W(-;]%=xe_,b+-O;q\L}UI--=BKE1p[! 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sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) ################################################### ### code chunk number 3: up2 ################################################### sim=10 ss=ss1=array(0,c(sim,4)) ################################################### ### code chunk number 4: up3 ################################################### cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) ################################################### ### code chunk number 5: up4 ################################################### ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } ################################################### ### code chunk number 6: up5 ################################################### #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } ################################################### ### code chunk number 7: HT_Hajek_estimators.Snw:137-145 (eval = FALSE) ################################################### ## data(belgianmunicipalities) ## attach(belgianmunicipalities) ## # sample size ## n=20 ## pik=inclusionprobabilities(Tot04,n) ## N=length(pik) ## sim=10 ## ss=ss1=array(0,c(sim,4)) ## cat("Case 1\n") ## y1=rep(3,N) ## cat("Case 2\n") ## y2=TaxableIncome ## cat("Case 3\n") ## x=1:N ## pik3=inclusionprobabilities(x,n) ## y3=1/pik3 ## cat("Case 4\n") ## epsilon=rnorm(N,0,sqrt(1/3)) ## pik4=pik3 ## y4=5*(x+epsilon) ## ht=numeric(4) ## hajek=numeric(4) ## for(i in 1:sim) ## { ## cat("Simulation ",i,"\n") ## cat("Case 1\n") ## s=UPtille(pik) ## ht[1]=HTestimator(y1[s==1],pik[s==1]) ## hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") ## cat("Case 2\n") ## s1=UPpoisson(pik) ## ht[2]=HTestimator(y2[s1==1],pik[s1==1]) ## hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") ## cat("Case 3\n") ## ht[3]=HTestimator(y3[s==1],pik3[s==1]) ## hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") ## cat("Case 4\n") ## ht[4]=HTestimator(y4[s==1],pik4[s==1]) ## hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ## ss[i,]=ht ## ss1[i,]=hajek ## } ## #true values ## tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) ## for(i in 1:4) ## { ## cat("Case ",i,"\n") ## cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") ## MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 ## cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") ## cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") ## MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 ## cat("MSE Hajek estimator:",MSE2,"\n") ## cat("Ratio of the two MSE:", MSE1/MSE2,"\n") ## } ## ## ## ## sampling.newpage() sampling/inst/doc/HT_Hajek_estimators.Snw0000644000176200001440000001202514515747167020207 0ustar liggesusers\documentclass[a4paper]{article} %\VignetteIndexEntry{Horvitz-Thompson estimator and Hajek estimator} %\VignettePackage{sampling} \newcommand{\sampling}{{\tt sampling}} \newcommand{\R}{{\tt R}} \setlength{\parindent}{0in} \setlength{\parskip}{.1in} \setlength{\textwidth}{140mm} \setlength{\oddsidemargin}{10mm} \title{Comparing the Horvitz-Thompson estimator and Hajek estimator} \author{} \usepackage{Sweave} \usepackage[latin1]{inputenc} \usepackage{amsmath} \begin{document} \maketitle <>= library(sampling) ps.options(pointsize=12) options(width=60) @ Consider a finite population with labels $U=\{1, 2, \dots, N\}.$ Suppose $y_k, k\in U$ are values of the variable of interest in the population. We wish to estimate the total $\sum_{k=1}^N y_k$ using a sample $s$ selected from the population $U.$ Assume that the sample is taken according to a sampling scheme having inclusion probabilities $\pi_k= Pr(k\in s).$ When $\pi_k$ is proportional to a positive quantity $x_k$ available over $U,$ and $s$ has a predetermined sample size $n,$ then $$\pi_k=\frac{nx_k}{\sum_{i=1}^N x_i},$$ and the sampling scheme is said to be probability proportional to size ($\pi$ps). The H\'ajek estimator of the population total is defined as $$\hat{y}_{Hajek}=N\frac{\sum_{k\in s} y_k/\pi_k}{\sum_{k\in s} 1/\pi_k},$$ while the Horvitz-Thompson estimator is $$\hat{y}_{HT}=\sum_{k\in s} y_k/\pi_k.$$ S$\ddot{a}$rndal, Swenson, and Wretman (1992, p. 182) give several cases for considering the H\'ajek estimator as `usually the better estimator' compared to the Horvitz-Thompson estimator when a $\pi$ps sampling design is used: \begin{itemize} \item[a)] the $y_k-\bar{y}_U$ tend to be small, \item[b)] the sample size is not fixed, \item[c)] $\pi_k$ are weakly or negatively correlated with $y_k$. \end{itemize} Monte Carlo simulation is used here to compare the accuracy of both estimators using a sample size (or the expected value of the sample size) equal to 20. Four cases are considered: \begin{itemize} \item[Case 1.] $y_k$ is constant for $k=1, \dots, N$; this case corresponds to the case a) above; \item[Case 2.] Poisson sampling is used to draw a sample $s$; this case corresponds to the case b) above; \item[Case 3.] $y_k$ are generated using the following model: $x_k=k, \pi_k=nx_k/\sum_{i=1}^N x_i, y_k=1/\pi_k;$ this case corresponds to the case c) above; \item[Case 4.] $y_k$ are generated using the following model: $x_k=k, y_k=5(x_k+\epsilon_k),\epsilon_k\sim N(0, 1/3);$ in this case the Horvitz-Thompson estimator should perform better than the H\'ajek estimator. \end{itemize} Till\'e sampling is used in Cases 1, 3 and 4. Poisson sampling is used in Case 2. The \verb@belgianmunicipalities@ dataset is used in Cases 1 and 2 as population, with $x_k=Tot04_k.$ In Case 2, the variable of interest is TaxableIncome. The mean square error (MSE) is computed using simulations for each case and estimator. The H\'ajek estimator should perform better than the Horvitz-Thompson estimator in Cases 1, 2 and 3. <>= data(belgianmunicipalities) attach(belgianmunicipalities) # sample size n=20 pik=inclusionprobabilities(Tot04,n) N=length(pik) @ Number of runs (for an accurate result, increase this value to 10000): <>= sim=10 ss=ss1=array(0,c(sim,4)) @ Defines the variables of interest: <>= cat("Case 1\n") y1=rep(3,N) cat("Case 2\n") y2=TaxableIncome cat("Case 3\n") x=1:N pik3=inclusionprobabilities(x,n) y3=1/pik3 cat("Case 4\n") epsilon=rnorm(N,0,sqrt(1/3)) pik4=pik3 y4=5*(x+epsilon) @ Monte-Carlo simulation and computation of the Horvitz-Thompson and H\'ajek estimators: <>= ht=numeric(4) hajek=numeric(4) for(i in 1:sim) { cat("Simulation ",i,"\n") cat("Case 1\n") s=UPtille(pik) ht[1]=HTestimator(y1[s==1],pik[s==1]) hajek[1]=Hajekestimator(y1[s==1],pik[s==1],N,type="total") cat("Case 2\n") s1=UPpoisson(pik) ht[2]=HTestimator(y2[s1==1],pik[s1==1]) hajek[2]=Hajekestimator(y2[s1==1],pik[s1==1],N,type="total") cat("Case 3\n") ht[3]=HTestimator(y3[s==1],pik3[s==1]) hajek[3]=Hajekestimator(y3[s==1],pik3[s==1],N,type="total") cat("Case 4\n") ht[4]=HTestimator(y4[s==1],pik4[s==1]) hajek[4]=Hajekestimator(y4[s==1],pik4[s==1],N,type="total") ss[i,]=ht ss1[i,]=hajek } @ Estimation of the MSE and computation of the ratio $MSE_{HT}/MSE_{Hajek}:$ <>= #true values tv=c(sum(y1),sum(y2),sum(y3),sum(y4)) for(i in 1:4) { cat("Case ",i,"\n") cat("The mean of the Horvitz-Thompson estimators:",mean(ss[,i])," and the true value:",tv[i],"\n") MSE1=var(ss[,i])+(mean(ss[,i])-tv[i])^2 cat("MSE Horvitz-Thompson estimator:",MSE1,"\n") cat("The mean of the Hajek estimators:",mean(ss1[,i])," and the true value:",tv[i],"\n") MSE2=var(ss1[,i])+(mean(ss1[,i])-tv[i])^2 cat("MSE Hajek estimator:",MSE2,"\n") cat("Ratio of the two MSE:", MSE1/MSE2,"\n") } <>= <> <> <> <> <> sampling.newpage() @ \end{document}