| Title: | Selection of Samples and Parameter Estimation in Finite Population |
|---|---|
| Description: | Allows the user to draw probabilistic samples and make inferences from a finite population based on several sampling designs. |
| Authors: | Hugo Andres Gutierrez Rojas <[email protected]> |
| Maintainer: | Hugo Andres Gutierrez Rojas <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 4.1.1 |
| Built: | 2025-01-25 03:02:59 UTC |
| Source: | https://github.com/psirusteam/teachingsampling |
This data set corresponds to some socioeconomic variables from 150266 people of a city in a particular year.
data(BigCity)data(BigCity)
The identifier of the household. It corresponds to an alphanumeric sequence (four letters and five digits).
The identifier of the person within the household. NOTE it is not a unique identifier of a person for the whole population. It corresponds to an alphanumeric sequence (five letters and two digits).
Households are located in geographic strata. There are 119 strata across the city.
Households are clustered in cartographic segments defined as primary sampling units (PSU). There are 1664 PSU and they are nested within strata.
Segments clustered within strata can be located within urban or rural areas along the city.
Sex of the person.
Per capita monthly income.
Per capita monthly expenditure.
A person's employment status.
This variable indicates whether the person is poor or not. It depends on income.
Hugo Andres Gutierrez Rojas [email protected]
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.
data(BigCity) attach(BigCity) estima <- data.frame(Income, Expenditure) # The population totals colSums(estima) # Some parameters of interest table(Poverty, Zone) xtabs(Income ~ Poverty + Zone) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Expenditure) # Some useful plots boxplot(Income ~ Poverty) barplot(table(Employment)) pie(table(MaritalST))data(BigCity) attach(BigCity) estima <- data.frame(Income, Expenditure) # The population totals colSums(estima) # Some parameters of interest table(Poverty, Zone) xtabs(Income ~ Poverty + Zone) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Expenditure) # Some useful plots boxplot(Income ~ Poverty) barplot(table(Employment)) pie(table(MaritalST))
This data set corresponds to some financial variables of 85396 industrial companies of a city in a particular fiscal year.
data(BigLucy)data(BigLucy)
The identifier of the company. It correspond to an alphanumeric sequence (two letters and three digits)
The address of the principal office of the company in the city
The industrial companies are discrimitnated according to the Taxes declared. There are small, medium and big companies
The country is divided by counties. A company belongs to a particular zone according to its cartographic location.
The total ammount of a company's earnings (or profit) in the previuos fiscal year. It is calculated by taking revenues and adjusting for the cost of doing business
The total number of persons working for the company in the previuos fiscal year
The total ammount of a company's income Tax
Indicates if the company uses the Internet and WEBmail options in order to make self-propaganda.
Indicates if the company is certified by the International Organization for Standardization.
The age of the company.
Cartographic segments by county. A segment comprises in average 10 companies located close to each other.
Hugo Andres Gutierrez Rojas [email protected]
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.
data(BigLucy) attach(BigLucy) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # The population totals colSums(estima) # Some parameters of interest table(SPAM,Level) xtabs(Income ~ Level+SPAM) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Taxes) hist(Employees) # Some useful plots boxplot(Income ~ Level) barplot(table(Level)) pie(table(SPAM))data(BigLucy) attach(BigLucy) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # The population totals colSums(estima) # Some parameters of interest table(SPAM,Level) xtabs(Income ~ Level+SPAM) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Taxes) hist(Employees) # Some useful plots boxplot(Income ~ Level) barplot(table(Level)) pie(table(SPAM))
Computes the Variance-Covariance matrix of the sample membership indicators in the population given a fixed sample size design
Deltakl(N, n, p)Deltakl(N, n, p)
N |
Population size |
n |
Sample size |
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one |
The th unit of the Variance-Covariance matrix of the sample membership indicators is defined as
The function returns a symmetric matrix of size containing the variances-covariances among the sample membership indicators for each pair of units in the finite population.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the Variance-Covariance matrix of the sample membership indicators Deltakl(N, n, p)# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the Variance-Covariance matrix of the sample membership indicators Deltakl(N, n, p)
Creates a matrix of domain indicator variables for every single unit in the selected sample or in the entire population
Domains(y)Domains(y)
y |
Vector of the domain of interest containing the membership of each unit to a specified category of the domain |
Each value of y represents the domain which a specified unit belongs
The function returns a matrix, where is the number of units in the selected
sample and is the number of categories of the domain of interest. The values of this matrix are zero, if the unit does not
belongs to a specified category and one, otherwise.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # This domain contains only two categories: "yes" and "no" x <- as.factor(c("yes","yes","yes","no","no","no","no","yes","yes")) Domains(x) ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units according # to a SI design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- sample(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variable SPAM is a domain of interest Doma <- Domains(SPAM) Doma # HT estimation of the absolute domain size for every category in the domain # of interest E.SI(N,n,Doma) ############ ## Example 3 ############ # Following with Example 2... # The variables of interest are: Income, Employees and Taxes # This function allows to estimate the population total of this variables for every # category in the domain of interest SPAM estima <- data.frame(Income, Employees, Taxes) SPAM.no <- estima*Doma[,1] SPAM.yes <- estima*Doma[,2] E.SI(N,n,SPAM.no) E.SI(N,n,SPAM.yes)############ ## Example 1 ############ # This domain contains only two categories: "yes" and "no" x <- as.factor(c("yes","yes","yes","no","no","no","no","yes","yes")) Domains(x) ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units according # to a SI design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- sample(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variable SPAM is a domain of interest Doma <- Domains(SPAM) Doma # HT estimation of the absolute domain size for every category in the domain # of interest E.SI(N,n,Doma) ############ ## Example 3 ############ # Following with Example 2... # The variables of interest are: Income, Employees and Taxes # This function allows to estimate the population total of this variables for every # category in the domain of interest SPAM estima <- data.frame(Income, Employees, Taxes) SPAM.no <- estima*Doma[,1] SPAM.yes <- estima*Doma[,2] E.SI(N,n,SPAM.no) E.SI(N,n,SPAM.yes)
This function computes the Horvitz-Thompson estimator of the population total according to a single stage sampling design.
E.1SI(NI, nI, y, PSU)E.1SI(NI, nI, y, PSU)
NI |
Population size of Primary Sampling Units. |
nI |
Sample size of Primary Sampling Units. |
y |
Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample. |
PSU |
Vector identifying the membership to the strata of each unit in the population. |
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest.
This function returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation.
Hugo Andres Gutierrez Rojas <hugogutierrez at gmail.com>
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas
data('BigCity') Households <- BigCity %>% group_by(HHID) %>% summarise(Stratum = unique(Stratum), PSU = unique(PSU), Persons = n(), Income = sum(Income), Expenditure = sum(Expenditure)) attach(Households) UI <- levels(as.factor(Households$PSU)) NI <- length(UI) nI <- 100 samI <- S.SI(NI, nI) sampleI <- UI[samI] CityI <- Households[which(Households$PSU %in% sampleI), ] attach(CityI) area <- as.factor(CityI$PSU) estima <- data.frame(CityI$Persons, CityI$Income, CityI$Expenditure) E.1SI(NI, nI, estima, area)data('BigCity') Households <- BigCity %>% group_by(HHID) %>% summarise(Stratum = unique(Stratum), PSU = unique(PSU), Persons = n(), Income = sum(Income), Expenditure = sum(Expenditure)) attach(Households) UI <- levels(as.factor(Households$PSU)) NI <- length(UI) nI <- 100 samI <- S.SI(NI, nI) sampleI <- UI[samI] CityI <- Households[which(Households$PSU %in% sampleI), ] attach(CityI) area <- as.factor(CityI$PSU) estima <- data.frame(CityI$Persons, CityI$Income, CityI$Expenditure) E.1SI(NI, nI, estima, area)
Computes the Horvitz-Thompson estimator of the population total according to a 2SI sampling design
E.2SI(NI, nI, Ni, ni, y, PSU)E.2SI(NI, nI, Ni, ni, y, PSU)
NI |
Population size of Primary Sampling Units |
nI |
Sample size of Primary Sampling Units |
Ni |
Vector of population sizes of Secundary Sampling Units selected in the first draw |
ni |
Vector of sample sizes of Secundary Sampling Units |
y |
Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample |
PSU |
Vector identifying the membership to the strata of each unit in the population |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Dise?o de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Uses Lucy data to draw a twostage simple random sample # accordind to a 2SI design. Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters or Primary Sampling Units UI<-c("A","B","C","D","E") NI <- length(UI) # The sample size is nI=3 nI <- 3 # Selects the sample of PSUs samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy3 Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] Lucy3<-Lucy[which(Zone==dataI[3]),] # The size of every single PSU N1<-dim(Lucy1)[1] N2<-dim(Lucy2)[1] N3<-dim(Lucy3)[1] Ni<-c(N1,N2,N3) # The sample size in every PSI is 135 Secondary Sampling Units n1<-135 n2<-135 n3<-135 ni<-c(n1,n2,n3) # Selects a sample of Secondary Sampling Units inside the PSUs sam1<-S.SI(N1,n1) sam2<-S.SI(N2,n2) sam3<-S.SI(N3,n3) # The information about each Secondary Sampling Unit in the PSUs # is saved in data1 ... data3 data1<-Lucy1[sam1,] data2<-Lucy2[sam2,] data3<-Lucy3[sam3,] # The information about each unit in the final selected sample is saved in data data<-rbind(data1, data2, data3) attach(data) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of the Population total E.2SI(NI,nI,Ni,ni,estima,Cluster) ######################################################## ## Example 2 Total Census to the entire population ######################################################## # Uses Lucy data to draw a cluster random sample # accordind to a SI design ... # Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters UI<-c("A","B","C","D","E") NI <- length(UI) # The sample size equals to the population size of PSU nI <- NI # Selects every single PSU samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy5 Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] Lucy3<-Lucy[which(Zone==dataI[3]),] Lucy4<-Lucy[which(Zone==dataI[4]),] Lucy5<-Lucy[which(Zone==dataI[5]),] # The size of every single PSU N1<-dim(Lucy1)[1] N2<-dim(Lucy2)[1] N3<-dim(Lucy3)[1] N4<-dim(Lucy4)[1] N5<-dim(Lucy5)[1] Ni<-c(N1,N2,N3,N4,N5) # The sample size of Secondary Sampling Units equals to the size of each PSU n1<-N1 n2<-N2 n3<-N3 n4<-N4 n5<-N5 ni<-c(n1,n2,n3,n4,n5) # Selects every single Secondary Sampling Unit inside the PSU sam1<-S.SI(N1,n1) sam2<-S.SI(N2,n2) sam3<-S.SI(N3,n3) sam4<-S.SI(N4,n4) sam5<-S.SI(N5,n5) # The information about each unit in the cluster is saved in Lucy1 ... Lucy5 data1<-Lucy1[sam1,] data2<-Lucy2[sam2,] data3<-Lucy3[sam3,] data4<-Lucy4[sam4,] data5<-Lucy5[sam5,] # The information about each Secondary Sampling Unit # in the sample (census) is saved in data data<-rbind(data1, data2, data3, data4, data5) attach(data) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of the Population total E.2SI(NI,nI,Ni,ni,estima,Cluster) # Sampling error is null############ ## Example 1 ############ # Uses Lucy data to draw a twostage simple random sample # accordind to a 2SI design. Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters or Primary Sampling Units UI<-c("A","B","C","D","E") NI <- length(UI) # The sample size is nI=3 nI <- 3 # Selects the sample of PSUs samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy3 Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] Lucy3<-Lucy[which(Zone==dataI[3]),] # The size of every single PSU N1<-dim(Lucy1)[1] N2<-dim(Lucy2)[1] N3<-dim(Lucy3)[1] Ni<-c(N1,N2,N3) # The sample size in every PSI is 135 Secondary Sampling Units n1<-135 n2<-135 n3<-135 ni<-c(n1,n2,n3) # Selects a sample of Secondary Sampling Units inside the PSUs sam1<-S.SI(N1,n1) sam2<-S.SI(N2,n2) sam3<-S.SI(N3,n3) # The information about each Secondary Sampling Unit in the PSUs # is saved in data1 ... data3 data1<-Lucy1[sam1,] data2<-Lucy2[sam2,] data3<-Lucy3[sam3,] # The information about each unit in the final selected sample is saved in data data<-rbind(data1, data2, data3) attach(data) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of the Population total E.2SI(NI,nI,Ni,ni,estima,Cluster) ######################################################## ## Example 2 Total Census to the entire population ######################################################## # Uses Lucy data to draw a cluster random sample # accordind to a SI design ... # Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters UI<-c("A","B","C","D","E") NI <- length(UI) # The sample size equals to the population size of PSU nI <- NI # Selects every single PSU samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The sampling frame of Secondary Sampling Unit is saved in Lucy1 ... Lucy5 Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] Lucy3<-Lucy[which(Zone==dataI[3]),] Lucy4<-Lucy[which(Zone==dataI[4]),] Lucy5<-Lucy[which(Zone==dataI[5]),] # The size of every single PSU N1<-dim(Lucy1)[1] N2<-dim(Lucy2)[1] N3<-dim(Lucy3)[1] N4<-dim(Lucy4)[1] N5<-dim(Lucy5)[1] Ni<-c(N1,N2,N3,N4,N5) # The sample size of Secondary Sampling Units equals to the size of each PSU n1<-N1 n2<-N2 n3<-N3 n4<-N4 n5<-N5 ni<-c(n1,n2,n3,n4,n5) # Selects every single Secondary Sampling Unit inside the PSU sam1<-S.SI(N1,n1) sam2<-S.SI(N2,n2) sam3<-S.SI(N3,n3) sam4<-S.SI(N4,n4) sam5<-S.SI(N5,n5) # The information about each unit in the cluster is saved in Lucy1 ... Lucy5 data1<-Lucy1[sam1,] data2<-Lucy2[sam2,] data3<-Lucy3[sam3,] data4<-Lucy4[sam4,] data5<-Lucy5[sam5,] # The information about each Secondary Sampling Unit # in the sample (census) is saved in data data<-rbind(data1, data2, data3, data4, data5) attach(data) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of the Population total E.2SI(NI,nI,Ni,ni,estima,Cluster) # Sampling error is null
Computes the Horvitz-Thompson estimator of the population total according to a BE sampling design
E.BE(y, prob)E.BE(y, prob)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
prob |
Inclusion probability for each unit in the population |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under an BE sampling design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a Bernoulli sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n=400 prob=n/N sam <- S.BE(N,prob) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.BE(estima,prob)# Uses the Lucy data to draw a Bernoulli sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n=400 prob=n/N sam <- S.BE(N,prob) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.BE(estima,prob)
Computes the estimation of regression coefficients using the principles of the Horvitz-Thompson estimator
E.Beta(N, n, y, x, ck=1, b0=FALSE)E.Beta(N, n, y, x, ck=1, b0=FALSE)
N |
The population size |
n |
The sample size |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
x |
Vector, matrix or data frame containing the recollected auxiliary information for every unit in the selected sample |
ck |
By default equals to one. It is a vector of weights induced by the structure of variance of the supposed model |
b0 |
By default FALSE. The intercept of the regression model |
Returns the estimation of the population regression coefficients in a supposed linear model, its estimated variance and its estimated coefficient of variation under an SI sampling design
The function returns a vector whose entries correspond to the estimated parameters of the regression coefficients
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
###################################################################### ## Example 1: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N, n) # The information about the units in the sample # is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common mean model estima<-data.frame(Income, Employees, Taxes) x <- rep(1,n) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### common ratio model estima<-data.frame(Income) x <- data.frame(Employees) E.Beta(N, n, estima,x,ck=x,b0=FALSE) ########### Simple regression model without intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### Multiple regression model without intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### Simple regression model with intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) E.Beta(N, n, estima,x,ck=1,b0=TRUE) ########### Multiple regression model with intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) E.Beta(N, n, estima,x,ck=1,b0=TRUE) ############################################################### ## Example 2: Linear models with discrete auxiliary information ############################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the sample units is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information Doma<-Domains(Level) ########### Poststratified common mean model estima<-data.frame(Income, Employees, Taxes) E.Beta(N, n, estima,Doma,ck=1,b0=FALSE) ########### Poststratified common ratio model estima<-data.frame(Income, Employees) x<-Doma*Taxes E.Beta(N, n, estima,x,ck=1,b0=FALSE)###################################################################### ## Example 1: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N, n) # The information about the units in the sample # is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common mean model estima<-data.frame(Income, Employees, Taxes) x <- rep(1,n) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### common ratio model estima<-data.frame(Income) x <- data.frame(Employees) E.Beta(N, n, estima,x,ck=x,b0=FALSE) ########### Simple regression model without intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### Multiple regression model without intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) E.Beta(N, n, estima,x,ck=1,b0=FALSE) ########### Simple regression model with intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) E.Beta(N, n, estima,x,ck=1,b0=TRUE) ########### Multiple regression model with intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) E.Beta(N, n, estima,x,ck=1,b0=TRUE) ############################################################### ## Example 2: Linear models with discrete auxiliary information ############################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the sample units is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information Doma<-Domains(Level) ########### Poststratified common mean model estima<-data.frame(Income, Employees, Taxes) E.Beta(N, n, estima,Doma,ck=1,b0=FALSE) ########### Poststratified common ratio model estima<-data.frame(Income, Employees) x<-Doma*Taxes E.Beta(N, n, estima,x,ck=1,b0=FALSE)
Computes the Horvitz-Thompson estimator of the population total according to a PS sampling design
E.piPS(y, Pik)E.piPS(y, Pik)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Pik |
Vector of inclusion probabilities for each unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated variance and its estimated coefficient of variation under a PPS sampling design. This function uses the results of approximate expressions for
the estimated variance of the Horvitz-Thompson estimator
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Matei, A. and Tille, Y. (2005), Evaluation of Variance Approximations and Estimators in Maximun
Entropy Sampling with Unequal Probability and Fixed Sample Design. Journal of Official Statistics. Vol 21, 4, 543-570.
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a sample according to a piPS # without replacement design data(Lucy) attach(Lucy) # The inclusion probability of each unit is proportional to the variable Income # The selected sample of size n=400 n <- 400 res <- S.piPS(n, Income) sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Pik.s is the inclusion probability of every single unit in the selected sample Pik.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s) # Same results than HT function HT(estima, Pik.s)# Uses the Lucy data to draw a sample according to a piPS # without replacement design data(Lucy) attach(Lucy) # The inclusion probability of each unit is proportional to the variable Income # The selected sample of size n=400 n <- 400 res <- S.piPS(n, Income) sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Pik.s is the inclusion probability of every single unit in the selected sample Pik.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s) # Same results than HT function HT(estima, Pik.s)
Computes the Horvitz-Thompson estimator of the population total according to a PO sampling design
E.PO(y, Pik)E.PO(y, Pik)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Pik |
Vector of inclusion probabilities for each unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under a PO sampling design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population size is 2396. The expected sample size is 400 # The inclusion probability is proportional to the variable Income n <- 400 Pik<-n*Income/sum(Income) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The inclusion probabilities of each unit in the selected smaple inclusion <- Pik[sam] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.PO(estima,inclusion)# Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population size is 2396. The expected sample size is 400 # The inclusion probability is proportional to the variable Income n <- 400 Pik<-n*Income/sum(Income) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The inclusion probabilities of each unit in the selected smaple inclusion <- Pik[sam] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.PO(estima,inclusion)
Computes the Hansen-Hurwitz estimator of the population total according to a probability proportional to size sampling with replacement design
E.PPS(y, pk)E.PPS(y, pk)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
pk |
A vector containing selection probabilities for each unit in the sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation estimated under a probability proportional to size sampling with replacement design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res <- S.PPS(m,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # pk.s is the selection probability of each unit in the selected sample pk.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.PPS(estima,pk.s)# Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res <- S.PPS(m,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # pk.s is the selection probability of each unit in the selected sample pk.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.PPS(estima,pk.s)
Computes the estimation of a population quantile using the principles of the Horvitz-Thompson estimator
E.Quantile(y, Qn, Pik)E.Quantile(y, Qn, Pik)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Qn |
Quantile of interest |
Pik |
A vector containing inclusion probabilities for each unit in the sample. If missing, the function will assign the same weights to each unit in the sample |
Returns the estimation of the population quantile of every single variable of interest
The function returns a vector whose entries correspond to the estimated quantiles of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vectors y and x give the values of the variables of interest y<-c(32, 34, 46, 89, 35) x<-c(52, 60, 75, 100, 50) z<-cbind(y,x) # Inclusion probabilities for a design of size n=2 Pik<-c(0.58, 0.34, 0.48, 0.33, 0.27) # Estimation of the sample median E.Quantile(y, 0.5) # Estimation of the sample Q1 E.Quantile(x, 0.25) # Estimation of the sample Q3 E.Quantile(z, 0.75) # Estimation of the sample median E.Quantile(z, 0.5, Pik) ############ ## Example 2 ############ # Uses the Lucy data to draw a PPS sample with replacement data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income # The sample size is m=400 m=400 res <- S.PPS(m,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) # The vector of selection probabilities of units in the sample pk.s <- res[,2] # The vector of inclusion probabilities of units in the sample Pik.s<-1-(1-pk.s)^m # The information about the sample units is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of sample median E.Quantile(estima,0.5,Pik.s)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vectors y and x give the values of the variables of interest y<-c(32, 34, 46, 89, 35) x<-c(52, 60, 75, 100, 50) z<-cbind(y,x) # Inclusion probabilities for a design of size n=2 Pik<-c(0.58, 0.34, 0.48, 0.33, 0.27) # Estimation of the sample median E.Quantile(y, 0.5) # Estimation of the sample Q1 E.Quantile(x, 0.25) # Estimation of the sample Q3 E.Quantile(z, 0.75) # Estimation of the sample median E.Quantile(z, 0.5, Pik) ############ ## Example 2 ############ # Uses the Lucy data to draw a PPS sample with replacement data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income # The sample size is m=400 m=400 res <- S.PPS(m,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) # The vector of selection probabilities of units in the sample pk.s <- res[,2] # The vector of inclusion probabilities of units in the sample Pik.s<-1-(1-pk.s)^m # The information about the sample units is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # Estimation of sample median E.Quantile(estima,0.5,Pik.s)
Computes the Horvitz-Thompson estimator of the population total according to an SI sampling design
E.SI(N, n, y)E.SI(N, n, y)
N |
Population size |
n |
Sample size |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under an SI sampling design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Uses the Lucy data to draw a random sample of units according to a SI design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.SI(N,n,estima) ############ ## Example 2 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the size of each domain in SPAM estima <- data.frame(Doma) E.SI(N,n,Doma) ############ ## Example 3 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the parameters of the variables of interest # for every category in the domain SPAM estima <- data.frame(Income, Employees, Taxes) SPAM.no <- cbind(Doma[,1], estima*Doma[,1]) SPAM.yes <- cbind(Doma[,1], estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the category in the domain SPAM # The remaining columns estimates the parameters of interest # within the corresponding category in the domain SPAM E.SI(N,n,SPAM.no) E.SI(N,n,SPAM.yes) ############ ## Example 4 ############ # Following with Example 1. The variable SPAM is a domain of interest # and the variable ISO is a populational subgroup of interest Doma <- Domains(SPAM) estima <- Domains(Zone) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the first category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.no <- data.frame(SpamNO=Doma[,1], Zones=estima*Doma[,1]) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the second category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.yes <- data.frame(SpamYES=Doma[,2], Zones=estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # first category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last # two columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.no) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # second category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last two # columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.yes)############ ## Example 1 ############ # Uses the Lucy data to draw a random sample of units according to a SI design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.SI(N,n,estima) ############ ## Example 2 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the size of each domain in SPAM estima <- data.frame(Doma) E.SI(N,n,Doma) ############ ## Example 3 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the parameters of the variables of interest # for every category in the domain SPAM estima <- data.frame(Income, Employees, Taxes) SPAM.no <- cbind(Doma[,1], estima*Doma[,1]) SPAM.yes <- cbind(Doma[,1], estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the category in the domain SPAM # The remaining columns estimates the parameters of interest # within the corresponding category in the domain SPAM E.SI(N,n,SPAM.no) E.SI(N,n,SPAM.yes) ############ ## Example 4 ############ # Following with Example 1. The variable SPAM is a domain of interest # and the variable ISO is a populational subgroup of interest Doma <- Domains(SPAM) estima <- Domains(Zone) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the first category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.no <- data.frame(SpamNO=Doma[,1], Zones=estima*Doma[,1]) # Before running the following lines, notice that: # The first column indicates wheter the unit # belongs to the second category of SPAM or not # The remaining columns indicates wheter the unit # belogns to the categories of Zone SPAM.yes <- data.frame(SpamYES=Doma[,2], Zones=estima*Doma[,2]) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # first category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last # two columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.no) # Before running the following lines, notice that: # The first column always indicates the population size # The second column is an estimate of the size of the # second category in the domain SPAM # The remaining columns estimates the size of the categories # of Zone within the corresponding category of SPAM # Finnaly, note that the sum of the point estimates of the last two # columns gives exactly the point estimate in the second column E.SI(N,n,SPAM.yes)
Computes the Horvitz-Thompson estimator of the population total according to a probability proportional to size sampling without replacement design in each stratum
E.STpiPS(y, pik, S)E.STpiPS(y, pik, S)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
pik |
A vector containing inclusion probabilities for each unit in the sample |
S |
Vector identifying the membership to the strata of each unit in selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error, its estimated coefficient of variation and its corresponding DEFF in all of the strata and finally in the entire population
The function returns an array composed by several matrices representing each variable of interest. The columns of each matrix correspond to the estimated parameters of the variables of interest in each stratum and in the entire population
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-N1 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Draws a stratified sample S <- Level x <- Employees res <- S.STpiPS(S, x, nh) sam <- res[,1] pik <- res[,2] data <- Lucy[sam,] attach(data) estima <- data.frame(Income, Employees, Taxes) E.STpiPS(estima,pik,Level)# Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-N1 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Draws a stratified sample S <- Level x <- Employees res <- S.STpiPS(S, x, nh) sam <- res[,1] pik <- res[,2] data <- Lucy[sam,] attach(data) estima <- data.frame(Income, Employees, Taxes) E.STpiPS(estima,pik,Level)
Computes the Hansen-Hurwitz estimator of the population total according to a probability proportional to size sampling with replacement design
E.STPPS(y, pk, mh, S)E.STPPS(y, pk, mh, S)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
pk |
A vector containing selection probabilities for each unit in the sample |
mh |
Vector of sample size in each stratum |
S |
Vector identifying the membership to the strata of each unit in selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation in all of the stratum and finally in the entire population
The function returns an array composed by several matrices representing each variable of interest. The columns of each matrix correspond to the estimated parameters of the variables of interest in each stratum and in the entire population
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the sample size at each stratum m1<-83 m2<-100 m3<-200 mh<-c(m1,m2,m3) # Draws a stratified sample res<-S.STPPS(Level, Income, mh) # The selected sample sam<-res[,1] # The selection probability of each unit in the selected sample pk <- res[,2] pk # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.STPPS(estima,pk,mh,Level)# Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the sample size at each stratum m1<-83 m2<-100 m3<-200 mh<-c(m1,m2,m3) # Draws a stratified sample res<-S.STPPS(Level, Income, mh) # The selected sample sam<-res[,1] # The selection probability of each unit in the selected sample pk <- res[,2] pk # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.STPPS(estima,pk,mh,Level)
Computes the Horvitz-Thompson estimator of the population total according to a STSI sampling design
E.STSI(S, Nh, nh, y)E.STSI(S, Nh, nh, y)
S |
Vector identifying the membership to the strata of each unit in the population |
Nh |
Vector of stratum sizes |
nh |
Vector of sample sizes in each stratum |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation in all of the strata and finally in the entire population
The function returns an array composed by several matrices representing each variable of interest. The columns of each matrix correspond to the estimated parameters of the variables of interest in each stratum and in the entire population
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Uses the Lucy data to draw a stratified random sample # according to a SI design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 Nh <- c(N1,N2,N3) # Defines the sample size at each stratum n1<-N1 n2<-100 n3<-200 nh<-c(n1,n2,n3) # Draws a stratified sample sam <- S.STSI(Level, Nh, nh) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.STSI(Level,Nh,nh,estima) ############ ## Example 2 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the parameters of the variables of interest # for every category in the domain SPAM SPAM.no <- estima*Doma[,1] SPAM.yes <- estima*Doma[,2] E.STSI(Level, Nh, nh, Doma) E.STSI(Level, Nh, nh, SPAM.no) E.STSI(Level, Nh, nh, SPAM.yes)############ ## Example 1 ############ # Uses the Lucy data to draw a stratified random sample # according to a SI design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 Nh <- c(N1,N2,N3) # Defines the sample size at each stratum n1<-N1 n2<-100 n3<-200 nh<-c(n1,n2,n3) # Draws a stratified sample sam <- S.STSI(Level, Nh, nh) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.STSI(Level,Nh,nh,estima) ############ ## Example 2 ############ # Following with Example 1. The variable SPAM is a domain of interest Doma <- Domains(SPAM) # This function allows to estimate the parameters of the variables of interest # for every category in the domain SPAM SPAM.no <- estima*Doma[,1] SPAM.yes <- estima*Doma[,2] E.STSI(Level, Nh, nh, Doma) E.STSI(Level, Nh, nh, SPAM.no) E.STSI(Level, Nh, nh, SPAM.yes)
Computes the Horvitz-Thompson estimator of the population total according to an SY sampling design
E.SY(N, a, y)E.SY(N, a, y)
N |
Population size |
a |
Number of groups dividing the population |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation under an SY sampling design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a Systematic sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population is divided in 6 groups # The selected sample sam <- S.SY(N,6) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.SY(N,6,estima)# Uses the Lucy data to draw a Systematic sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population is divided in 6 groups # The selected sample sam <- S.SY(N,6) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.SY(N,6,estima)
This function performs a method of trimming sampling weights based on the evenly redistribution of the net ammount of weight loss among units whose weights were not trimmed. This way, the sum of the timmed sampling weights remains the same as the original weights.
E.Trim(dk, L, U)E.Trim(dk, L, U)
dk |
Vector of original sampling weights. |
L |
Lower bound for weights. |
U |
Upper bound for weights. |
The function returns a vector of trimmed sampling weigths.
This function returns a vector of trimmed weights.
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com> with contributions from Javier Nunez <javier_nunez at inec.gob.ec>
Valliant, R. et. al. (2013), Practical Tools for Designing and
Weigthing Survey Samples. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas
y estimacion de parametros. Editorial Universidad Santo Tomas.
# Example 1 dk <- c(1, 1, 1, 10) summary(dk) L <- 1 U <- 3.5 * median(dk) dkTrim <- E.Trim(dk, L, U) sum(dk) sum(dkTrim) # Example 2 dk <- rnorm(1000, 10, 10) L <- 1 U <- 3.5 * median(dk) dkTrim <- E.Trim(dk, L, U) sum(dk) sum(dkTrim) summary(dk) summary(dkTrim) hist(dk) hist(dkTrim)# Example 1 dk <- c(1, 1, 1, 10) summary(dk) L <- 1 U <- 3.5 * median(dk) dkTrim <- E.Trim(dk, L, U) sum(dk) sum(dkTrim) # Example 2 dk <- rnorm(1000, 10, 10) L <- 1 U <- 3.5 * median(dk) dkTrim <- E.Trim(dk, L, U) sum(dk) sum(dkTrim) summary(dk) summary(dkTrim) hist(dk) hist(dkTrim)
This function computes a weighted estimator of the population total and estimates its variance by using the Ultimate Cluster technique. This approximation performs well in many sampling designs. The user specifically needs to declare the variables of interest, the primary sampling units, the strata, and the sampling weights for every singlt unit in the sample.
E.UC(S, PSU, dk, y)E.UC(S, PSU, dk, y)
S |
Vector identifying the membership to the strata of each unit in selected sample. |
PSU |
Vector identifying the membership to the strata of each unit in the population. |
dk |
Sampling weights of the units in the sample. |
y |
Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample. |
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest.
This function returns the estimation of the population total of every single variable of interest, its estimated standard error and its estimated coefficient of variation.
Hsugo Andres Gutierrez Rojas <hugogutierrez at gmail.com>
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas
############################# ## Example 1: ## ## Stratified Two-stage SI ## ############################# data('BigCity') FrameI <- BigCity %>% group_by(PSU) %>% summarise(Stratum = unique(Stratum), Persons = n(), Income = sum(Income), Expenditure = sum(Expenditure)) attach(FrameI) sizes = FrameI %>% group_by(Stratum) %>% summarise(NIh = n(), nIh = 2, dI = NIh/nIh) NIh <- sizes$NIh nIh <- sizes$nIh samI <- S.STSI(Stratum, NIh, nIh) UI <- levels(as.factor(FrameI$PSU)) sampleI <- UI[samI] FrameII <- left_join(sizes, BigCity[which(BigCity$PSU %in% sampleI), ]) attach(FrameII) HHdb <- FrameII %>% group_by(PSU) %>% summarise(Ni = length(unique(HHID))) Ni <- as.numeric(HHdb$Ni) ni <- ceiling(Ni * 0.1) ni sum(ni) sam = S.SI(Ni[1], ni[1]) clusterII = FrameII[which(FrameII$PSU == sampleI[1]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[1]/ni[1] clusterHH$dk <- clusterHH$dI * clusterHH$dki data = clusterHH for (i in 2:length(Ni)) { sam = S.SI(Ni[i], ni[i]) clusterII = FrameII[which(FrameII$PSU == sampleI[i]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[i]/ni[i] clusterHH$dk <- clusterHH$dI * clusterHH$dki data1 = clusterHH data = rbind(data, data1) } sum(data$dk) attach(data) estima <- data.frame(Income, Expenditure) area <- as.factor(PSU) stratum <- as.factor(Stratum) E.UC(stratum, area, dk, estima) ################################ ## Example 2: ## ## Self weighted Two-stage SI ## ################################ data('BigCity') FrameI <- BigCity %>% group_by(PSU) %>% summarise(Stratum = unique(Stratum), Households = length(unique(HHID)), Income = sum(Income), Expenditure = sum(Expenditure)) attach(FrameI) sizes = FrameI %>% group_by(Stratum) %>% summarise(NIh = n(), nIh = 2) NIh <- sizes$NIh nIh <- sizes$nIh resI <- S.STpiPS(Stratum, Households, nIh) head(resI) samI <- resI[, 1] piI <- resI[, 2] UI <- levels(as.factor(FrameI$PSU)) sampleI <- data.frame(PSU = UI[samI], dI = 1/piI) FrameII <- left_join(sampleI, BigCity[which(BigCity$PSU %in% sampleI[,1]), ]) attach(FrameII) HHdb <- FrameII %>% group_by(PSU) %>% summarise(Ni = length(unique(HHID))) Ni <- as.numeric(HHdb$Ni) ni <- 5 sam = S.SI(Ni[1], ni) clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[1]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[1]/ni clusterHH$dk <- clusterHH$dI * clusterHH$dki data = clusterHH for (i in 2:length(Ni)) { sam = S.SI(Ni[i], ni) clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[i]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[i]/ni clusterHH$dk <- clusterHH$dI * clusterHH$dki data1 = clusterHH data = rbind(data, data1) } sum(data$dk) attach(data) estima <- data.frame(Income, Expenditure) area <- as.factor(PSU) stratum <- as.factor(Stratum) E.UC(stratum, area, dk, estima)############################# ## Example 1: ## ## Stratified Two-stage SI ## ############################# data('BigCity') FrameI <- BigCity %>% group_by(PSU) %>% summarise(Stratum = unique(Stratum), Persons = n(), Income = sum(Income), Expenditure = sum(Expenditure)) attach(FrameI) sizes = FrameI %>% group_by(Stratum) %>% summarise(NIh = n(), nIh = 2, dI = NIh/nIh) NIh <- sizes$NIh nIh <- sizes$nIh samI <- S.STSI(Stratum, NIh, nIh) UI <- levels(as.factor(FrameI$PSU)) sampleI <- UI[samI] FrameII <- left_join(sizes, BigCity[which(BigCity$PSU %in% sampleI), ]) attach(FrameII) HHdb <- FrameII %>% group_by(PSU) %>% summarise(Ni = length(unique(HHID))) Ni <- as.numeric(HHdb$Ni) ni <- ceiling(Ni * 0.1) ni sum(ni) sam = S.SI(Ni[1], ni[1]) clusterII = FrameII[which(FrameII$PSU == sampleI[1]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[1]/ni[1] clusterHH$dk <- clusterHH$dI * clusterHH$dki data = clusterHH for (i in 2:length(Ni)) { sam = S.SI(Ni[i], ni[i]) clusterII = FrameII[which(FrameII$PSU == sampleI[i]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[i]/ni[i] clusterHH$dk <- clusterHH$dI * clusterHH$dki data1 = clusterHH data = rbind(data, data1) } sum(data$dk) attach(data) estima <- data.frame(Income, Expenditure) area <- as.factor(PSU) stratum <- as.factor(Stratum) E.UC(stratum, area, dk, estima) ################################ ## Example 2: ## ## Self weighted Two-stage SI ## ################################ data('BigCity') FrameI <- BigCity %>% group_by(PSU) %>% summarise(Stratum = unique(Stratum), Households = length(unique(HHID)), Income = sum(Income), Expenditure = sum(Expenditure)) attach(FrameI) sizes = FrameI %>% group_by(Stratum) %>% summarise(NIh = n(), nIh = 2) NIh <- sizes$NIh nIh <- sizes$nIh resI <- S.STpiPS(Stratum, Households, nIh) head(resI) samI <- resI[, 1] piI <- resI[, 2] UI <- levels(as.factor(FrameI$PSU)) sampleI <- data.frame(PSU = UI[samI], dI = 1/piI) FrameII <- left_join(sampleI, BigCity[which(BigCity$PSU %in% sampleI[,1]), ]) attach(FrameII) HHdb <- FrameII %>% group_by(PSU) %>% summarise(Ni = length(unique(HHID))) Ni <- as.numeric(HHdb$Ni) ni <- 5 sam = S.SI(Ni[1], ni) clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[1]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[1]/ni clusterHH$dk <- clusterHH$dI * clusterHH$dki data = clusterHH for (i in 2:length(Ni)) { sam = S.SI(Ni[i], ni) clusterII = FrameII[which(FrameII$PSU == sampleI$PSU[i]), ] sam.HH <- data.frame(HHID = unique(clusterII$HHID)[sam]) clusterHH <- left_join(sam.HH, clusterII, by = "HHID") clusterHH$dki <- Ni[i]/ni clusterHH$dk <- clusterHH$dI * clusterHH$dki data1 = clusterHH data = rbind(data, data1) } sum(data$dk) attach(data) estima <- data.frame(Income, Expenditure) area <- as.factor(PSU) stratum <- as.factor(Stratum) E.UC(stratum, area, dk, estima)
Computes the Hansen-Hurwitz estimator of the population total according to a simple random sampling with replacement design
E.WR(N, m, y)E.WR(N, m, y)
N |
Population size |
m |
Sample size |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Returns the estimation of the population total of every single variable of interest, its estimated variance and its estimated coefficient of variation estimated under an simple random with replacement design
The function returns a data matrix whose columns correspond to the estimated parameters of the variables of interest
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Uses the Lucy data to draw a random sample according to a WR design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- S.WR(N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.WR(N,m,estima)# Uses the Lucy data to draw a random sample according to a WR design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- S.WR(N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.WR(N,m,estima)
Computes the generalized regression estimator of the population total for several variables of interest under simple random sampling without replacement
GREG.SI(N, n, y, x, tx, b, b0=FALSE)GREG.SI(N, n, y, x, tx, b, b0=FALSE)
N |
The population size |
n |
The sample size |
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
x |
Vector, matrix or data frame containing the recollected auxiliary information for every unit in the selected sample |
tx |
Vector containing the populations totals of the auxiliary information |
b |
Vector of estimated regression coefficients |
b0 |
By default FALSE. The intercept of the regression model |
The function returns a vector of total population estimates for each variable of interest, its estimated standard error and its estimated coefficient of variation.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
###################################################################### ## Example 1: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common mean model estima<-data.frame(Income, Employees, Taxes) x <- rep(1,n) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- c(N) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### common ratio model estima<-data.frame(Income) x <- data.frame(Employees) model <- E.Beta(N, n, estima, x, ck=x,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Employees) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model without intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Multiple regression model without intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1, b0=FALSE) b <- as.matrix(model[1,,]) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model with intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) ########### Multiple regression model with intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) #################################################################### ## Example 2: Linear models with discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model estima<-data.frame(Income, Employees, Taxes) model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common ratio model estima<-data.frame(Income, Employees) x <- Doma*Taxes model <- E.Beta(N, n, estima, x ,ck=1,b0=FALSE) b <- as.matrix(model[1,,]) tx <- colSums(Domains(Lucy$Level)*Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ###################################################################### ## Example 3: Domains estimation trough the postestratified estimator ###################################################################### # Draws a simple random sample without replacement data(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model for the # Income total in each poststratum ################### estima<-Doma*Income model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Employees total in each poststratum ################### estima<-Doma*Employees model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Taxes total in each poststratum ################### estima<-Doma*Taxes model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE)###################################################################### ## Example 1: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common mean model estima<-data.frame(Income, Employees, Taxes) x <- rep(1,n) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- c(N) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### common ratio model estima<-data.frame(Income) x <- data.frame(Employees) model <- E.Beta(N, n, estima, x, ck=x,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Employees) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model without intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Multiple regression model without intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1, b0=FALSE) b <- as.matrix(model[1,,]) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model with intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) ########### Multiple regression model with intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) #################################################################### ## Example 2: Linear models with discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model estima<-data.frame(Income, Employees, Taxes) model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common ratio model estima<-data.frame(Income, Employees) x <- Doma*Taxes model <- E.Beta(N, n, estima, x ,ck=1,b0=FALSE) b <- as.matrix(model[1,,]) tx <- colSums(Domains(Lucy$Level)*Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ###################################################################### ## Example 3: Domains estimation trough the postestratified estimator ###################################################################### # Draws a simple random sample without replacement data(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model for the # Income total in each poststratum ################### estima<-Doma*Income model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Employees total in each poststratum ################### estima<-Doma*Employees model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Taxes total in each poststratum ################### estima<-Doma*Taxes model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE)
Computes the Hansen-Hurwitz Estimator estimator of the population total for several variables of interest
HH(y, pk)HH(y, pk)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
pk |
A vector containing selection probabilities for each unit in the selected sample |
The Hansen-Hurwitz estimator is given by
where is the value of the variables of interest for the th unit, and is its corresponding
selection probability. This estimator is restricted to with replacement sampling designs.
The function returns a vector of total population estimates for each variable of interest, its estimated standard error and its estimated coefficient of variation.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vectors y1 and y2 give the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # Selection of a random sample with replacement sam <- sample(5,2, replace=TRUE, prob=pk) # The selected sample is U[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Hansen-Hurwitz estimator HH(y1[sam],pk[sam]) HH(y2[sam],pk[sam]) HH(y3[sam,],pk[sam]) ############ ## Example 2 ############ # Uses the Lucy data to draw a simple random sample with replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- sample(N,m,replace=TRUE) # The vector of selection probabilities of units in the sample pk <- rep(1/N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HH(estima, pk) ################################################################ ## Example 3 HH is unbiased for with replacement sampling designs ################################################################ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # p is the probability of selection of every possible sample p <- p.WR(N,m,pk) p sum(p) # The sample membership matrix for random size without replacement sampling designs Ind <- nk(N,m) Ind # The support with the values of the elements Qy <- SupportWR(N,m, ID=y) Qy # The support with the values of the elements Qp <- SupportWR(N,m, ID=pk) Qp # The HT estimates for every single sample in the support HH1 <- HH(Qy[1,], Qp[1,])[1,] HH2 <- HH(Qy[2,], Qp[2,])[1,] HH3 <- HH(Qy[3,], Qp[3,])[1,] HH4 <- HH(Qy[4,], Qp[4,])[1,] HH5 <- HH(Qy[5,], Qp[5,])[1,] HH6 <- HH(Qy[6,], Qp[6,])[1,] HH7 <- HH(Qy[7,], Qp[7,])[1,] HH8 <- HH(Qy[8,], Qp[8,])[1,] HH9 <- HH(Qy[9,], Qp[9,])[1,] HH10 <- HH(Qy[10,], Qp[10,])[1,] HH11 <- HH(Qy[11,], Qp[11,])[1,] HH12 <- HH(Qy[12,], Qp[12,])[1,] HH13 <- HH(Qy[13,], Qp[13,])[1,] HH14 <- HH(Qy[14,], Qp[14,])[1,] HH15 <- HH(Qy[15,], Qp[15,])[1,] # The HT estimates arranged in a vector Est <- c(HH1, HH2, HH3, HH4, HH5, HH6, HH7, HH8, HH9, HH10, HH11, HH12, HH13, HH14, HH15) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vectors y1 and y2 give the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # Selection of a random sample with replacement sam <- sample(5,2, replace=TRUE, prob=pk) # The selected sample is U[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Hansen-Hurwitz estimator HH(y1[sam],pk[sam]) HH(y2[sam],pk[sam]) HH(y3[sam,],pk[sam]) ############ ## Example 2 ############ # Uses the Lucy data to draw a simple random sample with replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- sample(N,m,replace=TRUE) # The vector of selection probabilities of units in the sample pk <- rep(1/N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HH(estima, pk) ################################################################ ## Example 3 HH is unbiased for with replacement sampling designs ################################################################ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # p is the probability of selection of every possible sample p <- p.WR(N,m,pk) p sum(p) # The sample membership matrix for random size without replacement sampling designs Ind <- nk(N,m) Ind # The support with the values of the elements Qy <- SupportWR(N,m, ID=y) Qy # The support with the values of the elements Qp <- SupportWR(N,m, ID=pk) Qp # The HT estimates for every single sample in the support HH1 <- HH(Qy[1,], Qp[1,])[1,] HH2 <- HH(Qy[2,], Qp[2,])[1,] HH3 <- HH(Qy[3,], Qp[3,])[1,] HH4 <- HH(Qy[4,], Qp[4,])[1,] HH5 <- HH(Qy[5,], Qp[5,])[1,] HH6 <- HH(Qy[6,], Qp[6,])[1,] HH7 <- HH(Qy[7,], Qp[7,])[1,] HH8 <- HH(Qy[8,], Qp[8,])[1,] HH9 <- HH(Qy[9,], Qp[9,])[1,] HH10 <- HH(Qy[10,], Qp[10,])[1,] HH11 <- HH(Qy[11,], Qp[11,])[1,] HH12 <- HH(Qy[12,], Qp[12,])[1,] HH13 <- HH(Qy[13,], Qp[13,])[1,] HH14 <- HH(Qy[14,], Qp[14,])[1,] HH15 <- HH(Qy[15,], Qp[15,])[1,] # The HT estimates arranged in a vector Est <- c(HH1, HH2, HH3, HH4, HH5, HH6, HH7, HH8, HH9, HH10, HH11, HH12, HH13, HH14, HH15) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y)
Computes the Horvitz-Thompson estimator of the population total for several variables of interest
HT(y, Pik)HT(y, Pik)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Pik |
A vector containing the inclusion probabilities for each unit in the selected sample |
The Horvitz-Thompson estimator is given by
where is the value of the variables of interest for the th unit, and
its corresponding inclusion probability. This estimator could be used for without replacement designs
as well as for with replacement designs.
The function returns a vector of total population estimates for each variable of interest.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Uses the Lucy data to draw a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- sample(N,n) # The vector of inclusion probabilities for each unit in the sample pik <- rep(n/N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HT(estima, pik) ############ ## Example 2 ############ # Uses the Lucy data to draw a simple random sample with replacement data(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- sample(N,m,replace=TRUE) # The vector of selection probabilities of units in the sample pk <- rep(1/N,m) # Computation of the inclusion probabilities pik <- 1-(1-pk)^m # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HT(estima, pik) ############ ## Example 3 ############ # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) # Selection of a random sample sam <- sample(5,2) # The selected sample U[sam] # The inclusion probabilities for these two units inclusion[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Horvitz-Thompson estimator HT(y1[sam],inclusion[sam]) HT(y2[sam],inclusion[sam]) HT(y3[sam,],inclusion[sam]) ############ ## Example 4 ############ # Following Example 3... With replacement sampling # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.9, 0.025, 0.025, 0.025, 0.025) # Computation of the inclusion probabilities pik <- 1-(1-pk)^m # Selection of a random sample with replacement sam <- sample(5,2, replace=TRUE, prob=pk) # The selected sample U[sam] # The inclusion probabilities for these two units inclusion[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Horvitz-Thompson estimator HT(y1[sam],inclusion[sam]) HT(y2[sam],inclusion[sam]) HT(y3[sam,],inclusion[sam]) #################################################################### ## Example 5 HT is unbiased for without replacement sampling designs ## Fixed sample size #################################################################### # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) Ind # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion sum(inclusion) # The support with the values of the elements Qy <-Support(N,n,ID=y) Qy # The HT estimates for every single sample in the support HT1<- HT(y[Ind[1,]==1], inclusion[Ind[1,]==1]) HT2<- HT(y[Ind[2,]==1], inclusion[Ind[2,]==1]) HT3<- HT(y[Ind[3,]==1], inclusion[Ind[3,]==1]) HT4<- HT(y[Ind[4,]==1], inclusion[Ind[4,]==1]) HT5<- HT(y[Ind[5,]==1], inclusion[Ind[5,]==1]) HT6<- HT(y[Ind[6,]==1], inclusion[Ind[6,]==1]) HT7<- HT(y[Ind[7,]==1], inclusion[Ind[7,]==1]) HT8<- HT(y[Ind[8,]==1], inclusion[Ind[8,]==1]) HT9<- HT(y[Ind[9,]==1], inclusion[Ind[9,]==1]) HT10<- HT(y[Ind[10,]==1], inclusion[Ind[10,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y) #################################################################### ## Example 6 HT is unbiased for without replacement sampling designs ## Random sample size #################################################################### # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample membership matrix for random size without replacement sampling designs Ind <- IkRS(N) Ind # p is the probability of selection of every possible sample p <- c(0.59049, 0.06561, 0.06561, 0.06561, 0.06561, 0.06561, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00009, 0.00009, 0.00009, 0.00009, 0.00009, 0.00001) sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion sum(inclusion) # The support with the values of the elements Qy <-SupportRS(N, ID=y) Qy # The HT estimates for every single sample in the support HT1<- HT(y[Ind[1,]==1], inclusion[Ind[1,]==1]) HT2<- HT(y[Ind[2,]==1], inclusion[Ind[2,]==1]) HT3<- HT(y[Ind[3,]==1], inclusion[Ind[3,]==1]) HT4<- HT(y[Ind[4,]==1], inclusion[Ind[4,]==1]) HT5<- HT(y[Ind[5,]==1], inclusion[Ind[5,]==1]) HT6<- HT(y[Ind[6,]==1], inclusion[Ind[6,]==1]) HT7<- HT(y[Ind[7,]==1], inclusion[Ind[7,]==1]) HT8<- HT(y[Ind[8,]==1], inclusion[Ind[8,]==1]) HT9<- HT(y[Ind[9,]==1], inclusion[Ind[9,]==1]) HT10<- HT(y[Ind[10,]==1], inclusion[Ind[10,]==1]) HT11<- HT(y[Ind[11,]==1], inclusion[Ind[11,]==1]) HT12<- HT(y[Ind[12,]==1], inclusion[Ind[12,]==1]) HT13<- HT(y[Ind[13,]==1], inclusion[Ind[13,]==1]) HT14<- HT(y[Ind[14,]==1], inclusion[Ind[14,]==1]) HT15<- HT(y[Ind[15,]==1], inclusion[Ind[15,]==1]) HT16<- HT(y[Ind[16,]==1], inclusion[Ind[16,]==1]) HT17<- HT(y[Ind[17,]==1], inclusion[Ind[17,]==1]) HT18<- HT(y[Ind[18,]==1], inclusion[Ind[18,]==1]) HT19<- HT(y[Ind[19,]==1], inclusion[Ind[19,]==1]) HT20<- HT(y[Ind[20,]==1], inclusion[Ind[20,]==1]) HT21<- HT(y[Ind[21,]==1], inclusion[Ind[21,]==1]) HT22<- HT(y[Ind[22,]==1], inclusion[Ind[22,]==1]) HT23<- HT(y[Ind[23,]==1], inclusion[Ind[23,]==1]) HT24<- HT(y[Ind[24,]==1], inclusion[Ind[24,]==1]) HT25<- HT(y[Ind[25,]==1], inclusion[Ind[25,]==1]) HT26<- HT(y[Ind[26,]==1], inclusion[Ind[26,]==1]) HT27<- HT(y[Ind[27,]==1], inclusion[Ind[27,]==1]) HT28<- HT(y[Ind[28,]==1], inclusion[Ind[28,]==1]) HT29<- HT(y[Ind[29,]==1], inclusion[Ind[29,]==1]) HT30<- HT(y[Ind[30,]==1], inclusion[Ind[30,]==1]) HT31<- HT(y[Ind[31,]==1], inclusion[Ind[31,]==1]) HT32<- HT(y[Ind[32,]==1], inclusion[Ind[32,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10, HT11, HT12, HT13, HT14, HT15, HT16, HT17, HT18, HT19, HT20, HT21, HT22, HT23, HT24, HT25, HT26, HT27, HT28, HT29, HT30, HT31, HT32) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y) ################################################################ ## Example 7 HT is unbiased for with replacement sampling designs ################################################################ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # p is the probability of selection of every possible sample p <- p.WR(N,m,pk) p sum(p) # The sample membership matrix for random size without replacement sampling designs Ind <- IkWR(N,m) Ind # The support with the values of the elements Qy <- SupportWR(N,m, ID=y) Qy # Computation of the inclusion probabilities pik <- 1-(1-pk)^m pik # The HT estimates for every single sample in the support HT1 <- HT(y[Ind[1,]==1], pik[Ind[1,]==1]) HT2 <- HT(y[Ind[2,]==1], pik[Ind[2,]==1]) HT3 <- HT(y[Ind[3,]==1], pik[Ind[3,]==1]) HT4 <- HT(y[Ind[4,]==1], pik[Ind[4,]==1]) HT5 <- HT(y[Ind[5,]==1], pik[Ind[5,]==1]) HT6 <- HT(y[Ind[6,]==1], pik[Ind[6,]==1]) HT7 <- HT(y[Ind[7,]==1], pik[Ind[7,]==1]) HT8 <- HT(y[Ind[8,]==1], pik[Ind[8,]==1]) HT9 <- HT(y[Ind[9,]==1], pik[Ind[9,]==1]) HT10 <- HT(y[Ind[10,]==1], pik[Ind[10,]==1]) HT11 <- HT(y[Ind[11,]==1], pik[Ind[11,]==1]) HT12 <- HT(y[Ind[12,]==1], pik[Ind[12,]==1]) HT13 <- HT(y[Ind[13,]==1], pik[Ind[13,]==1]) HT14 <- HT(y[Ind[14,]==1], pik[Ind[14,]==1]) HT15 <- HT(y[Ind[15,]==1], pik[Ind[15,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10, HT11, HT12, HT13, HT14, HT15) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y)############ ## Example 1 ############ # Uses the Lucy data to draw a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- sample(N,n) # The vector of inclusion probabilities for each unit in the sample pik <- rep(n/N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HT(estima, pik) ############ ## Example 2 ############ # Uses the Lucy data to draw a simple random sample with replacement data(Lucy) N <- dim(Lucy)[1] m <- 400 sam <- sample(N,m,replace=TRUE) # The vector of selection probabilities of units in the sample pk <- rep(1/N,m) # Computation of the inclusion probabilities pik <- 1-(1-pk)^m # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) HT(estima, pik) ############ ## Example 3 ############ # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) # Selection of a random sample sam <- sample(5,2) # The selected sample U[sam] # The inclusion probabilities for these two units inclusion[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Horvitz-Thompson estimator HT(y1[sam],inclusion[sam]) HT(y2[sam],inclusion[sam]) HT(y3[sam,],inclusion[sam]) ############ ## Example 4 ############ # Following Example 3... With replacement sampling # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.9, 0.025, 0.025, 0.025, 0.025) # Computation of the inclusion probabilities pik <- 1-(1-pk)^m # Selection of a random sample with replacement sam <- sample(5,2, replace=TRUE, prob=pk) # The selected sample U[sam] # The inclusion probabilities for these two units inclusion[sam] # The values of the variables of interest for the units in the sample y1[sam] y2[sam] y3[sam,] # The Horvitz-Thompson estimator HT(y1[sam],inclusion[sam]) HT(y2[sam],inclusion[sam]) HT(y3[sam,],inclusion[sam]) #################################################################### ## Example 5 HT is unbiased for without replacement sampling designs ## Fixed sample size #################################################################### # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) Ind # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion sum(inclusion) # The support with the values of the elements Qy <-Support(N,n,ID=y) Qy # The HT estimates for every single sample in the support HT1<- HT(y[Ind[1,]==1], inclusion[Ind[1,]==1]) HT2<- HT(y[Ind[2,]==1], inclusion[Ind[2,]==1]) HT3<- HT(y[Ind[3,]==1], inclusion[Ind[3,]==1]) HT4<- HT(y[Ind[4,]==1], inclusion[Ind[4,]==1]) HT5<- HT(y[Ind[5,]==1], inclusion[Ind[5,]==1]) HT6<- HT(y[Ind[6,]==1], inclusion[Ind[6,]==1]) HT7<- HT(y[Ind[7,]==1], inclusion[Ind[7,]==1]) HT8<- HT(y[Ind[8,]==1], inclusion[Ind[8,]==1]) HT9<- HT(y[Ind[9,]==1], inclusion[Ind[9,]==1]) HT10<- HT(y[Ind[10,]==1], inclusion[Ind[10,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y) #################################################################### ## Example 6 HT is unbiased for without replacement sampling designs ## Random sample size #################################################################### # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample membership matrix for random size without replacement sampling designs Ind <- IkRS(N) Ind # p is the probability of selection of every possible sample p <- c(0.59049, 0.06561, 0.06561, 0.06561, 0.06561, 0.06561, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00729, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00081, 0.00009, 0.00009, 0.00009, 0.00009, 0.00009, 0.00001) sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion sum(inclusion) # The support with the values of the elements Qy <-SupportRS(N, ID=y) Qy # The HT estimates for every single sample in the support HT1<- HT(y[Ind[1,]==1], inclusion[Ind[1,]==1]) HT2<- HT(y[Ind[2,]==1], inclusion[Ind[2,]==1]) HT3<- HT(y[Ind[3,]==1], inclusion[Ind[3,]==1]) HT4<- HT(y[Ind[4,]==1], inclusion[Ind[4,]==1]) HT5<- HT(y[Ind[5,]==1], inclusion[Ind[5,]==1]) HT6<- HT(y[Ind[6,]==1], inclusion[Ind[6,]==1]) HT7<- HT(y[Ind[7,]==1], inclusion[Ind[7,]==1]) HT8<- HT(y[Ind[8,]==1], inclusion[Ind[8,]==1]) HT9<- HT(y[Ind[9,]==1], inclusion[Ind[9,]==1]) HT10<- HT(y[Ind[10,]==1], inclusion[Ind[10,]==1]) HT11<- HT(y[Ind[11,]==1], inclusion[Ind[11,]==1]) HT12<- HT(y[Ind[12,]==1], inclusion[Ind[12,]==1]) HT13<- HT(y[Ind[13,]==1], inclusion[Ind[13,]==1]) HT14<- HT(y[Ind[14,]==1], inclusion[Ind[14,]==1]) HT15<- HT(y[Ind[15,]==1], inclusion[Ind[15,]==1]) HT16<- HT(y[Ind[16,]==1], inclusion[Ind[16,]==1]) HT17<- HT(y[Ind[17,]==1], inclusion[Ind[17,]==1]) HT18<- HT(y[Ind[18,]==1], inclusion[Ind[18,]==1]) HT19<- HT(y[Ind[19,]==1], inclusion[Ind[19,]==1]) HT20<- HT(y[Ind[20,]==1], inclusion[Ind[20,]==1]) HT21<- HT(y[Ind[21,]==1], inclusion[Ind[21,]==1]) HT22<- HT(y[Ind[22,]==1], inclusion[Ind[22,]==1]) HT23<- HT(y[Ind[23,]==1], inclusion[Ind[23,]==1]) HT24<- HT(y[Ind[24,]==1], inclusion[Ind[24,]==1]) HT25<- HT(y[Ind[25,]==1], inclusion[Ind[25,]==1]) HT26<- HT(y[Ind[26,]==1], inclusion[Ind[26,]==1]) HT27<- HT(y[Ind[27,]==1], inclusion[Ind[27,]==1]) HT28<- HT(y[Ind[28,]==1], inclusion[Ind[28,]==1]) HT29<- HT(y[Ind[29,]==1], inclusion[Ind[29,]==1]) HT30<- HT(y[Ind[30,]==1], inclusion[Ind[30,]==1]) HT31<- HT(y[Ind[31,]==1], inclusion[Ind[31,]==1]) HT32<- HT(y[Ind[32,]==1], inclusion[Ind[32,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10, HT11, HT12, HT13, HT14, HT15, HT16, HT17, HT18, HT19, HT20, HT21, HT22, HT23, HT24, HT25, HT26, HT27, HT28, HT29, HT30, HT31, HT32) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y) ################################################################ ## Example 7 HT is unbiased for with replacement sampling designs ################################################################ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y<-c(32, 34, 46, 89, 35) # The population size is N=5 N <- length(U) # The sample size is m=2 m <- 2 # pk is the probability of selection of every single unit pk <- c(0.35, 0.225, 0.175, 0.125, 0.125) # p is the probability of selection of every possible sample p <- p.WR(N,m,pk) p sum(p) # The sample membership matrix for random size without replacement sampling designs Ind <- IkWR(N,m) Ind # The support with the values of the elements Qy <- SupportWR(N,m, ID=y) Qy # Computation of the inclusion probabilities pik <- 1-(1-pk)^m pik # The HT estimates for every single sample in the support HT1 <- HT(y[Ind[1,]==1], pik[Ind[1,]==1]) HT2 <- HT(y[Ind[2,]==1], pik[Ind[2,]==1]) HT3 <- HT(y[Ind[3,]==1], pik[Ind[3,]==1]) HT4 <- HT(y[Ind[4,]==1], pik[Ind[4,]==1]) HT5 <- HT(y[Ind[5,]==1], pik[Ind[5,]==1]) HT6 <- HT(y[Ind[6,]==1], pik[Ind[6,]==1]) HT7 <- HT(y[Ind[7,]==1], pik[Ind[7,]==1]) HT8 <- HT(y[Ind[8,]==1], pik[Ind[8,]==1]) HT9 <- HT(y[Ind[9,]==1], pik[Ind[9,]==1]) HT10 <- HT(y[Ind[10,]==1], pik[Ind[10,]==1]) HT11 <- HT(y[Ind[11,]==1], pik[Ind[11,]==1]) HT12 <- HT(y[Ind[12,]==1], pik[Ind[12,]==1]) HT13 <- HT(y[Ind[13,]==1], pik[Ind[13,]==1]) HT14 <- HT(y[Ind[14,]==1], pik[Ind[14,]==1]) HT15 <- HT(y[Ind[15,]==1], pik[Ind[15,]==1]) # The HT estimates arranged in a vector Est <- c(HT1, HT2, HT3, HT4, HT5, HT6, HT7, HT8, HT9, HT10, HT11, HT12, HT13, HT14, HT15) Est # The HT is actually desgn-unbiased data.frame(Ind, Est, p) sum(Est*p) sum(y)
Creates a matrix of values (0, if the unit belongs to a specified sample and 1, otherwise) for every possible sample under fixed sample size designs without replacement
Ik(N, n)Ik(N, n)
N |
Population size |
n |
Sample size |
The function returns a matrix of rows and columns. The th column corresponds to the sample
membership indicator, of the th unit, to a possible sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ik(N,n) # The first unit, Yves, belongs to the first four possible samples# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ik(N,n) # The first unit, Yves, belongs to the first four possible samples
Creates a matrix of values (0, if the unit belongs to a specified sample and 1, otherwise) for every possible sample under random sample size designs without replacement
IkRS(N)IkRS(N)
N |
Population size |
The function returns a matrix of rows and columns. The th column corresponds to the sample
membership indicator, of the th unit, to a possible sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 3 # The sample membership matrix for fixed size without replacement sampling designs IkRS(N) # The first sample is a null one and the last sample is a census# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 3 # The sample membership matrix for fixed size without replacement sampling designs IkRS(N) # The first sample is a null one and the last sample is a census
Creates a matrix of values (1, if the unit belongs to a specified sample and 0, otherwise) for every possible sample under fixed sample size designs without replacement
IkWR(N, m)IkWR(N, m)
N |
Population size |
m |
Sample size |
The function returns a matrix of rows and columns. The th column corresponds to the sample
membership indicator, of the th unit, to a possible sample. It returns a value of 1, even if the element is selected more than once in a with replacement sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The sample membership matrix for fixed size without replacement sampling designs IkWR(N,m)# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The sample membership matrix for fixed size without replacement sampling designs IkWR(N,m)
Adjustment of a table on the margins
IPFP(Table, Col.knw, Row.knw, tol=0.0001)IPFP(Table, Col.knw, Row.knw, tol=0.0001)
Table |
A contingency table |
Col.knw |
A vector containing the true totals of the columns |
Row.knw |
A vector containing the true totals of the Rows |
tol |
The control value, by default equal to 0.0001 |
Adjust a contingency table on the know margins of the population with the Raking Ratio method
Hugo Andres Gutierrez Rojas [email protected]
Deming, W. & Stephan, F. (1940), On a least squares adjustment of a sampled frequency
table when the expected marginal totals are known. Annals of Mathematical Statistics, 11, 427-444.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Some example of Ardilly and Tille Table <- matrix(c(80,90,10,170,80,80,150,210,130),3,3) rownames(Table) <- c("a1", "a2","a3") colnames(Table) <- c("b1", "b2","b3") # The table with labels Table # The known and true margins Col.knw <- c(150,300,550) Row.knw <- c(430,360,210) # The adjusted table IPFP(Table,Col.knw,Row.knw,tol=0.0001) ############ ## Example 2 ############ # Draws a simple random sample data(Lucy) attach(Lucy) N<-dim(Lucy)[1] n<-400 sam<-sample(N,n) data<-Lucy[sam,] attach(data) dim(data) # Two domains of interest Doma1<-Domains(Level) Doma2<-Domains(SPAM) # Cross tabulate of domains SPAM.no<-Doma2[,1]*Doma1 SPAM.yes<-Doma2[,2]*Doma1 # Estimation E.SI(N,n,Doma1) E.SI(N,n,Doma2) est1 <-E.SI(N,n,SPAM.no)[,2:4] est2 <-E.SI(N,n,SPAM.yes)[,2:4] est1;est2 # The contingency table estimated from above Table <- cbind(est1[1,],est2[1,]) rownames(Table) <- c("Big", "Medium","Small") colnames(Table) <- c("SPAM.no", "SPAM.yes") # The known and true margins Col.knw <- colSums(Domains(Lucy$SPAM)) Row.knw<- colSums(Domains(Lucy$Level)) # The adjusted table IPFP(Table,Col.knw,Row.knw,tol=0.0001)############ ## Example 1 ############ # Some example of Ardilly and Tille Table <- matrix(c(80,90,10,170,80,80,150,210,130),3,3) rownames(Table) <- c("a1", "a2","a3") colnames(Table) <- c("b1", "b2","b3") # The table with labels Table # The known and true margins Col.knw <- c(150,300,550) Row.knw <- c(430,360,210) # The adjusted table IPFP(Table,Col.knw,Row.knw,tol=0.0001) ############ ## Example 2 ############ # Draws a simple random sample data(Lucy) attach(Lucy) N<-dim(Lucy)[1] n<-400 sam<-sample(N,n) data<-Lucy[sam,] attach(data) dim(data) # Two domains of interest Doma1<-Domains(Level) Doma2<-Domains(SPAM) # Cross tabulate of domains SPAM.no<-Doma2[,1]*Doma1 SPAM.yes<-Doma2[,2]*Doma1 # Estimation E.SI(N,n,Doma1) E.SI(N,n,Doma2) est1 <-E.SI(N,n,SPAM.no)[,2:4] est2 <-E.SI(N,n,SPAM.yes)[,2:4] est1;est2 # The contingency table estimated from above Table <- cbind(est1[1,],est2[1,]) rownames(Table) <- c("Big", "Medium","Small") colnames(Table) <- c("SPAM.no", "SPAM.yes") # The known and true margins Col.knw <- colSums(Domains(Lucy$SPAM)) Row.knw<- colSums(Domains(Lucy$Level)) # The adjusted table IPFP(Table,Col.knw,Row.knw,tol=0.0001)
This data set corresponds to a random sample of BigLucy. It contains some financial variables of 2396 industrial companies of a city in a particular fiscal year.
data(Lucy)data(Lucy)
The identifier of the company. It correspond to an alphanumeric sequence (two letters and three digits)
The address of the principal office of the company in the city
The industrial companies are discrimitnated according to the Taxes declared. There are small, medium and big companies
The city is divided by geoghrafical zones. A company is classified in a particular zone according to its address
The total ammount of a company's earnings (or profit) in the previuos fiscal year. It is calculated by taking revenues and adjusting for the cost of doing business
The total number of persons working for the company in the previuos fiscal year
The total ammount of a company's income Tax
Indicates if the company uses the Internet and WEBmail options in order to make self-propaganda.
Hugo Andres Gutierrez Rojas [email protected]
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas.
data(Lucy) attach(Lucy) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # The population totals colSums(estima) # Some parameters of interest table(SPAM,Level) xtabs(Income ~ Level+SPAM) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Taxes) hist(Employees) # Some useful plots boxplot(Income ~ Level) barplot(table(Level)) pie(table(SPAM))data(Lucy) attach(Lucy) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) # The population totals colSums(estima) # Some parameters of interest table(SPAM,Level) xtabs(Income ~ Level+SPAM) # Correlations among characteristics of interest cor(estima) # Some useful histograms hist(Income) hist(Taxes) hist(Employees) # Some useful plots boxplot(Income ~ Level) barplot(table(Level)) pie(table(SPAM))
The function returns a matrix of rows and columns. Creates a matrix of values (0, if the unit does not belongs to a specified sample, 1, if the unit is selected once in the sample; 2, if the unit is selected twice in the sample, etc.) for every possible sample under fixed sample size designs with replacement
nk(N, m)nk(N, m)
N |
Population size |
m |
Sample size |
The function returns a matrix of rows and columns. The th column corresponds to the sample
selection indicator, of the th unit, to a possible sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The sample membership matrix for fixed size without replacement sampling designs nk(N,m)# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The sample membership matrix for fixed size without replacement sampling designs nk(N,m)
Creates a matrix containing every possible ordered sample under fixed sample size with replacement designs
OrderWR(N,m,ID=FALSE)OrderWR(N,m,ID=FALSE)
N |
Population size |
m |
Sample size |
ID |
By default FALSE, a vector of values (numeric or string) identifying each unit in the population |
The number of samples in a with replacement support is not equal to the number of ordered samples induced by a with replacement sampling design.
The function returns a matrix of rows and columns. Each row of this matrix
corresponds to a possible ordered sample.
Hugo Andres Gutierrez Rojas [email protected]. The author acknowledges to Hanwen Zhang for valuable suggestions.
Tille, Y. (2006), Sampling Algorithms. Springer
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas
# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # Under this context, there are five (5) possible ordered samples OrderWR(N,1) # The same output, but labeled OrderWR(N,1,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,1,ID=y) # If the smaple size is m=2, there are (25) possible ordered samples OrderWR(N,2) # The same output, but labeled OrderWR(N,2,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,2,ID=y) # Note that the number of ordered samples is not equal to the number of # samples in a well defined with-replacement support OrderWR(N,2) SupportWR(N,2) OrderWR(N,4) SupportWR(N,4)# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # Under this context, there are five (5) possible ordered samples OrderWR(N,1) # The same output, but labeled OrderWR(N,1,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,1,ID=y) # If the smaple size is m=2, there are (25) possible ordered samples OrderWR(N,2) # The same output, but labeled OrderWR(N,2,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) OrderWR(N,2,ID=y) # Note that the number of ordered samples is not equal to the number of # samples in a well defined with-replacement support OrderWR(N,2) SupportWR(N,2) OrderWR(N,4) SupportWR(N,4)
Computes the selection probability (sampling design) of each with replacement sample
p.WR(N, m, pk)p.WR(N, m, pk)
N |
Population size |
m |
Sample size |
pk |
A vector containing selection probabilities for each unit in the population |
Every with replacement sampling design is a particular case of a multinomial distribution.
where is the number of times that the -th unit is selected in a sample.
The function returns a vector of selection probabilities for every with-replacement sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # With replacement simple random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector pk is the sel?ection probability of the units in the finite population pk <- c(0.2, 0.2, 0.2, 0.2, 0.2) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p) ############ ## Example 2 ############ # With replacement PPS random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # Vector pk is the sel?ection probability of the units in the finite population pk <- x/sum(x) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p)############ ## Example 1 ############ # With replacement simple random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector pk is the sel?ection probability of the units in the finite population pk <- c(0.2, 0.2, 0.2, 0.2, 0.2) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p) ############ ## Example 2 ############ # With replacement PPS random sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # Vector pk is the sel?ection probability of the units in the finite population pk <- x/sum(x) sum(pk) N <- length(pk) m <- 3 # The smapling design p <- p.WR(N, m, pk) p sum(p)
Computes the first-order inclusion probability of each unit in the population given a fixed sample size design
Pik(p, Ind)Pik(p, Ind)
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one |
Ind |
A sample membership indicator matrix |
The inclusion probability of the th unit is defined as the probability that this unit will be
included in a sample, it is denoted by and obtained from a given sampling design as follows:
The function returns a vector of inclusion probabilities for each unit in the finite population.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion # The sum of inclusion probabilities is equal to the sample size n=2 sum(inclusion)# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # The sample membership matrix for fixed size without replacement sampling designs Ind <- Ik(N,n) # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the inclusion probabilities inclusion <- Pik(p, Ind) inclusion # The sum of inclusion probabilities is equal to the sample size n=2 sum(inclusion)
Computes the population vector of optimal inclusion probabilities under the Holmbergs's Approach
PikHol(n, sigma, e, Pi)PikHol(n, sigma, e, Pi)
n |
Vector of optimal sample sizes for each of the characteristics of interest. |
sigma |
A matrix containing the size measures for each characteristics of interest. |
e |
Maximum allowed error under the ANOREL approach. |
Pi |
Matrix of first order inclusion probabilities. By default, this probabilites are proportional to each sigma. |
Assuming that all of the characteristic of interest are equally important, the Holmberg's sampling design yields the following inclusion probabilities
where
and
Note that is a size measure associated with the k-th element in the q-th characteristic of interest.
The function returns a vector of inclusion probabilities.
Hugo Andres Gutierrez Rojas [email protected]
Holmberg, A. (2002), On the Choice of Sampling Design under GREG Estimation in Multiparameter Surveys.
RD Department, Statistics Sweden.
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas
####################### #### First example #### ####################### # Uses the Lucy data to draw an otpimal sample # in a multipurpose survey context data(Lucy) attach(Lucy) # Different sample sizes for two characteristics of interest: Employees and Taxes N <- dim(Lucy)[1] n <- c(350,400) # The size measure is the same for both characteristics of interest, # but the relationship in between is different sigy1 <- sqrt(Income^(1)) sigy2 <- sqrt(Income^(2)) # The matrix containign the size measures for each characteristics of interest sigma<-cbind(sigy1,sigy2) # The vector of optimal inclusion probabilities under the Holmberg's approach Piks<-PikHol(n,sigma,0.03) # The optimal sample size is given by the sum of piks n=round(sum(Piks)) # Performing the S.piPS function in order to select the optimal sample of size n res<-S.piPS(n,Piks) sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Pik.s is the vector of inclusion probability of every single unit # in the selected sample Pik.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s) ######################## #### Second example #### ######################## # We can define our own first inclusion probabilities data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- c(350,400) sigy1 <- sqrt(Income^(1)) sigy2 <- sqrt(Income^(2)) sigma<-cbind(sigy1,sigy2) pikas <- cbind(rep(400/N, N), rep(400/N, N)) Piks<-PikHol(n,sigma,0.03, pikas) n=round(sum(Piks)) n res<-S.piPS(n,Piks) sam <- res[,1] data <- Lucy[sam,] attach(data) names(data) Pik.s <- res[,2] estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s)####################### #### First example #### ####################### # Uses the Lucy data to draw an otpimal sample # in a multipurpose survey context data(Lucy) attach(Lucy) # Different sample sizes for two characteristics of interest: Employees and Taxes N <- dim(Lucy)[1] n <- c(350,400) # The size measure is the same for both characteristics of interest, # but the relationship in between is different sigy1 <- sqrt(Income^(1)) sigy2 <- sqrt(Income^(2)) # The matrix containign the size measures for each characteristics of interest sigma<-cbind(sigy1,sigy2) # The vector of optimal inclusion probabilities under the Holmberg's approach Piks<-PikHol(n,sigma,0.03) # The optimal sample size is given by the sum of piks n=round(sum(Piks)) # Performing the S.piPS function in order to select the optimal sample of size n res<-S.piPS(n,Piks) sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Pik.s is the vector of inclusion probability of every single unit # in the selected sample Pik.s <- res[,2] # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s) ######################## #### Second example #### ######################## # We can define our own first inclusion probabilities data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- c(350,400) sigy1 <- sqrt(Income^(1)) sigy2 <- sqrt(Income^(2)) sigma<-cbind(sigy1,sigy2) pikas <- cbind(rep(400/N, N), rep(400/N, N)) Piks<-PikHol(n,sigma,0.03, pikas) n=round(sum(Piks)) n res<-S.piPS(n,Piks) sam <- res[,1] data <- Lucy[sam,] attach(data) names(data) Pik.s <- res[,2] estima <- data.frame(Income, Employees, Taxes) E.piPS(estima,Pik.s)
Computes the second-order inclusion probabilities of each par of units in the population given a fixed sample size design
Pikl(N, n, p)Pikl(N, n, p)
N |
Population size |
n |
Sample size |
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one |
The second-order inclusion probability of the th units is defined as the probability that unit and unit
will be both included in a sample; it is denoted by and obtained from a given sampling design as follows:
The function returns a symmetric matrix of size containing the second-order inclusion probabilities
for each pair of units in the finite population.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the second-order inclusion probabilities Pikl(N, n, p)# Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every sample. p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Note that the sum of the elements of this vector is one sum(p) # Computation of the second-order inclusion probabilities Pikl(N, n, p)
For a given sample size, this function returns a vector of first order inclusion probabilities for a sampling design proportional to an auxiliary variable
PikPPS(n,x)PikPPS(n,x)
n |
Integer indicating the sample size |
x |
Vector of auxiliary information for each unit in the population |
For a given vector of auxiliary information with value for the -th unit and
population total , the following expression
is not always less than unity. A sequential algorithm must be used in order to ensure that for every unit in the population the inclusion probability gives less or equal to unity.
The function returns a vector of inclusion probabilities of size .
Every element of this vector is a value between zero and one.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ x <- c(30,41,50,170,43,200) n <- 3 # Two elements yields values bigger than one n*x/sum(x) # With this functions, all of the values are between zero and one PikPPS(n,x) # The sum is equal to the sample size sum(PikPPS(n,x)) ############ ## Example 2 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Gives the inclusion probabilities for the population accordin to a # proportional to size design without replacement of size n=4 pik <- PikPPS(4,x) pik # The selected sample is sum(pik) ############ ## Example 3 ############ # Uses the Lucy data to compute teh vector of inclusion probabilities # accordind to a piPS without replacement design data(Lucy) attach(Lucy) # The sample size n=400 # The selection probability of each unit is proportional to the variable Income pik <- PikPPS(n,Income) # The inclusion probabilities of the units in the sample pik # The sum of the values in pik is equal to the sample size sum(pik) # According to the design some elements must be selected # They are called forced inclusion units which(pik==1)############ ## Example 1 ############ x <- c(30,41,50,170,43,200) n <- 3 # Two elements yields values bigger than one n*x/sum(x) # With this functions, all of the values are between zero and one PikPPS(n,x) # The sum is equal to the sample size sum(PikPPS(n,x)) ############ ## Example 2 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Gives the inclusion probabilities for the population accordin to a # proportional to size design without replacement of size n=4 pik <- PikPPS(4,x) pik # The selected sample is sum(pik) ############ ## Example 3 ############ # Uses the Lucy data to compute teh vector of inclusion probabilities # accordind to a piPS without replacement design data(Lucy) attach(Lucy) # The sample size n=400 # The selection probability of each unit is proportional to the variable Income pik <- PikPPS(n,Income) # The inclusion probabilities of the units in the sample pik # The sum of the values in pik is equal to the sample size sum(pik) # According to the design some elements must be selected # They are called forced inclusion units which(pik==1)
For a given sample size, in each stratum, this function returns a vector of first order inclusion probabilities for an stratified sampling design proportional to an auxiliary variable.
PikSTPPS(S, x, nh)PikSTPPS(S, x, nh)
S |
Vector identifying the membership to the strata of each unit in the population. |
x |
Vector of auxiliary information for each unit in the population. |
nh |
The vector defningn the sample size in each stratum. |
is not always less than unity. A sequential algorithm must be used in order to ensure that for every unit in the population the inclusion probability gives a proper value; i.e. less or equal to unity.
A vector of inclusion probablilities in a stratified finite population.
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros. Editorial Universidad Santo Tomas Sarndal, C-E. and Swensson, B. and Wretman, J. (2003), Model Assisted Survey Sampling. Springer.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # The sample size in each stratum nh <- c(2,2) # The vector of inclusion probablities for a stratified piPS sample # without replacement of size two within each stratum Pik <- PikSTPPS(Strata, x, nh) Pik # Some checks sum(Pik) sum(nh) ############ ## Example 2 ############ # Uses the Lucy data to compute the vector of inclusion probablities # for a stratified random sample according to a piPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Computes the inclusion probabilities for the stratified population S <- Level x <- Employees Pik <- PikSTPPS(S, x, nh) # Some checks sum(Pik) sum(nh)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # The sample size in each stratum nh <- c(2,2) # The vector of inclusion probablities for a stratified piPS sample # without replacement of size two within each stratum Pik <- PikSTPPS(Strata, x, nh) Pik # Some checks sum(Pik) sum(nh) ############ ## Example 2 ############ # Uses the Lucy data to compute the vector of inclusion probablities # for a stratified random sample according to a piPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Computes the inclusion probabilities for the stratified population S <- Level x <- Employees Pik <- PikSTPPS(S, x, nh) # Some checks sum(Pik) sum(nh)
Draws a Bernoulli sample without replacement of expected size $n$ from a population of size $N$
S.BE(N, prob)S.BE(N, prob)
N |
Population size |
prob |
Inclusion probability for each unit in the population |
The selected sample is drawn according to a sequential procedure algorithm based on an uniform distribution. The Bernoulli sampling design is not a fixed sample size one.
The function returns a vector of size . Each element of this vector indicates if the unit was selected. Then,
if the value of this vector for unit is zero, the unit was not selected in the sample; otherwise, the unit was
selected in the sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
Tille, Y. (2006), Sampling Algorithms. Springer.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a Bernoulli sample without replacement of expected size n=3 # The inlusion probability is 0.6 for each unit in the population sam <- S.BE(5,0.6) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Bernoulli sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population size is 2396. If the expected sample size is 400 # then, the inclusion probability must be 400/2396=0.1669 sam <- S.BE(N,0.01669) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a Bernoulli sample without replacement of expected size n=3 # The inlusion probability is 0.6 for each unit in the population sam <- S.BE(5,0.6) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Bernoulli sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population size is 2396. If the expected sample size is 400 # then, the inclusion probability must be 400/2396=0.1669 sam <- S.BE(N,0.01669) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a probability proportional to size sample without replacement of size from a population of size .
S.piPS(n, x, e)S.piPS(n, x, e)
x |
Vector of auxiliary information for each unit in the population |
n |
Sample size |
e |
By default, a vector of size |
The selected sample is drawn according to the Sunter method (sequential-list procedure)
The function returns a matrix of rows and two columns. Each element of the first column indicates the unit that
was selected. Each element of the second column indicates the selection probability of this unit
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Draws a piPS sample without replacement of size n=3 res <- S.piPS(3,x) res sam <- res[,1] sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units accordind to a # piPS without replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income res <- S.piPS(400,Income) # The selected sample sam <- res[,1] # The inclusion probabilities of the units in the sample Pik.s <- res[,2] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Draws a piPS sample without replacement of size n=3 res <- S.piPS(3,x) res sam <- res[,1] sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units accordind to a # piPS without replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income res <- S.piPS(400,Income) # The selected sample sam <- res[,1] # The inclusion probabilities of the units in the sample Pik.s <- res[,2] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a Poisson sample of expected size $n$ from a population of size $N$
S.PO(N, Pik)S.PO(N, Pik)
N |
Population size |
Pik |
Vector of inclusion probabilities for each unit in the population |
The selected sample is drawn according to a sequential procedure algorithm based on a uniform distribution. The Poisson sampling design is not a fixed sample size one.
The function returns a vector of size . Each element of this vector indicates if the unit was selected. Then,
if the value of this vector for unit is zero, the unit was not selected in the sample; otherwise, the unit was
selected in the sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
Tille, Y. (2006), Sampling Algorithms. Springer.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a Bernoulli sample without replacement of expected size n=3 # "Erik" is drawn in every possible sample becuse its inclusion probability is one Pik <- c(0.5, 0.2, 1, 0.9, 0.5) sam <- S.PO(5,Pik) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 Pik<-n*Income/sum(Income) # None element of Pik bigger than one which(Pik>1) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a Bernoulli sample without replacement of expected size n=3 # "Erik" is drawn in every possible sample becuse its inclusion probability is one Pik <- c(0.5, 0.2, 1, 0.9, 0.5) sam <- S.PO(5,Pik) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a Poisson sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 Pik<-n*Income/sum(Income) # None element of Pik bigger than one which(Pik>1) # The selected sample sam <- S.PO(N,Pik) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a probability proportional to size sample with replacement of size from a population of size
S.PPS(m,x)S.PPS(m,x)
m |
Sample size |
x |
Vector of auxiliary information for each unit in the population |
The selected sample is drawn according to the cumulative total method (sequential-list procedure)
The function returns a matrix of rows and two columns. Each element of the first column indicates the unit that
was selected. Each element of the second column indicates the selection probability of this unit
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Draws a PPS sample with replacement of size m=3 res <- S.PPS(3,x) sam <- res[,1] # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res<-S.PPS(400,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Draws a PPS sample with replacement of size m=3 res <- S.PPS(3,x) sam <- res[,1] # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample according to a # PPS with replacement design data(Lucy) attach(Lucy) # The selection probability of each unit is proportional to the variable Income m <- 400 res<-S.PPS(400,Income) # The selected sample sam <- res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a simple random sample without replacement of size from a population of size
S.SI(N, n, e=runif(N))S.SI(N, n, e=runif(N))
N |
Population size |
n |
Sample size |
e |
By default, a vector of size |
The selected sample is drawn according to a selection-rejection (list-sequential) algorithm
The function returns a vector of size . Each element of this vector indicates if the unit was selected. Then,
if the value of this vector for unit is zero, the unit was not selected in the sample; otherwise, the unit was
selected in the sample.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Fan, C.T., Muller, M.E., Rezucha, I. (1962), Development of sampling plans by using sequential
(item by item) selection techniques and digital computer, Journal of the American Statistical Association, 57, 387-402.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Fixes the random numbers in order to select a sample # Ideal for teaching purposes in the blackboard e <- c(0.4938, 0.7044, 0.4585, 0.6747, 0.0640) # Draws a simple random sample without replacement of size n=3 sam <- S.SI(5,3,e) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Marco and Lucy data to draw a random sample according to a SI design data(Marco) data(Lucy) N <- dim(Lucy)[1] n <- 400 sam<-S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Fixes the random numbers in order to select a sample # Ideal for teaching purposes in the blackboard e <- c(0.4938, 0.7044, 0.4585, 0.6747, 0.0640) # Draws a simple random sample without replacement of size n=3 sam <- S.SI(5,3,e) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Marco and Lucy data to draw a random sample according to a SI design data(Marco) data(Lucy) N <- dim(Lucy)[1] n <- 400 sam<-S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a probability proportional to size simple random sample without
replacement of size in stratum of size
S.STpiPS(S,x,nh)S.STpiPS(S,x,nh)
S |
Vector identifying the membership to the strata of each unit in the population |
x |
Vector of auxiliary information for each unit in the population |
nh |
Vector of sample size in each stratum |
The selected sample is drawn according to the Sunter method (sequential-list procedure) in each stratum
The function returns a matrix of rows and two columns. Each element of the first column indicates the unit that
was selected. Each element of the second column indicates the inclusion probability of this unit
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # Then sample size in each stratum mh <- c(2,2) # Draws a stratified PPS sample with replacement of size n=4 res <- S.STPPS(Strata, x, mh) # The selected sample sam <- res[,1] U[sam] # The selection probability of each unit selected to be in the sample pk <- res[,2] pk ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # according to a piPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Draws a stratified sample S <- Level x <- Employees res <- S.STpiPS(S, x, nh) sam<-res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) # The selection probability of each unit selected in the sample pik <- res[,2] pik############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # Then sample size in each stratum mh <- c(2,2) # Draws a stratified PPS sample with replacement of size n=4 res <- S.STPPS(Strata, x, mh) # The selected sample sam <- res[,1] U[sam] # The selection probability of each unit selected to be in the sample pk <- res[,2] pk ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # according to a piPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) nh # Draws a stratified sample S <- Level x <- Employees res <- S.STpiPS(S, x, nh) sam<-res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) # The selection probability of each unit selected in the sample pik <- res[,2] pik
Draws a probability proportional to size simple random sample with
replacement of size in stratum of size
S.STPPS(S,x,mh)S.STPPS(S,x,mh)
S |
Vector identifying the membership to the strata of each unit in the population |
x |
Vector of auxiliary information for each unit in the population |
mh |
Vector of sample size in each stratum |
The selected sample is drawn according to the cumulative total method (sequential-list procedure) in each stratum
The function returns a matrix of rows and two columns. Each element of the first column indicates the unit that
was selected. Each element of the second column indicates the selection probability of this unit
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # Then sample size in each stratum mh <- c(2,2) # Draws a stratified PPS sample with replacement of size n=4 res <- S.STPPS(Strata, x, mh) # The selected sample sam <- res[,1] U[sam] # The selection probability of each unit selected to be in the sample pk <- res[,2] pk ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the sample size at each stratum m1<-70 m2<-100 m3<-200 mh<-c(m1,m2,m3) # Draws a stratified sample res<-S.STPPS(Level, Income, mh) # The selected sample sam<-res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) # The selection probability of each unit selected in the sample pk <- res[,2] pk############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The auxiliary information x <- c(52, 60, 75, 100, 50) # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") # Then sample size in each stratum mh <- c(2,2) # Draws a stratified PPS sample with replacement of size n=4 res <- S.STPPS(Strata, x, mh) # The selected sample sam <- res[,1] U[sam] # The selection probability of each unit selected to be in the sample pk <- res[,2] pk ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # according to a PPS design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the sample size at each stratum m1<-70 m2<-100 m3<-200 mh<-c(m1,m2,m3) # Draws a stratified sample res<-S.STPPS(Level, Income, mh) # The selected sample sam<-res[,1] # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data) # The selection probability of each unit selected in the sample pk <- res[,2] pk
Draws a simple random sample without replacement of size in stratum of size
S.STSI(S, Nh, nh)S.STSI(S, Nh, nh)
S |
Vector identifying the membership to the strata of each unit in the population |
Nh |
Vector of stratum sizes |
nh |
Vector of sample size in each stratum |
The selected sample is drawn according to a selection-rejection (list-sequential) algorithm in each stratum
The function returns a vector of size . Each element of this vector indicates the unit that was selected.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") Strata # The stratum sizes Nh <- c(3,2) # Then sample size in each stratum nh <- c(2,1) # Draws a stratified simple random sample without replacement of size n=3 sam <- S.STSI(Strata, Nh, nh) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # accordind to a SI design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 Nh <- c(N1,N2,N3) # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) # Draws a stratified sample sam <- S.STSI(Level, Nh, nh) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector Strata contains an indicator variable of stratum membership Strata <- c("A", "A", "A", "B", "B") Strata # The stratum sizes Nh <- c(3,2) # Then sample size in each stratum nh <- c(2,1) # Draws a stratified simple random sample without replacement of size n=3 sam <- S.STSI(Strata, Nh, nh) sam # The selected sample is U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a stratified random sample # accordind to a SI design in each stratum data(Lucy) attach(Lucy) # Level is the stratifying variable summary(Level) # Defines the size of each stratum N1<-summary(Level)[[1]] N2<-summary(Level)[[2]] N3<-summary(Level)[[3]] N1;N2;N3 Nh <- c(N1,N2,N3) # Defines the sample size at each stratum n1<-70 n2<-100 n3<-200 nh<-c(n1,n2,n3) # Draws a stratified sample sam <- S.STSI(Level, Nh, nh) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a Systematic sample of size $n$ from a population of size $N$
S.SY(N, a)S.SY(N, a)
N |
Population size |
a |
Number of groups dividing the population |
The selected sample is drawn according to a random start.
The function returns a vector of size . Each element of this vector indicates the unit that was selected.
Hugo Andres Gutierrez Rojas [email protected]. The author acknowledges to Kristina Stodolova [email protected] for valuable suggestions.
Madow, L.H. and Madow, W.G. (1944), On the theory of systematic sampling. Annals of Mathematical Statistics. 15, 1-24.
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The population of size N=5 is divided in a=2 groups # Draws a Systematic sample. sam <- S.SY(5,2) sam # The selected sample is U[sam] # There are only two possible samples ############ ## Example 2 ############ # Uses the Lucy data to draw a Systematic sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population is divided in 6 groups # The selected sample sam <- S.SY(N,6) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # The population of size N=5 is divided in a=2 groups # Draws a Systematic sample. sam <- S.SY(5,2) sam # The selected sample is U[sam] # There are only two possible samples ############ ## Example 2 ############ # Uses the Lucy data to draw a Systematic sample data(Lucy) attach(Lucy) N <- dim(Lucy)[1] # The population is divided in 6 groups # The selected sample sam <- S.SY(N,6) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Draws a simple random sample witht replacement of size from a population of size
S.WR(N, m)S.WR(N, m)
N |
Population size |
m |
Sample size |
The selected sample is drawn according to a sequential procedure algorithm based on a binomial distribution
The function returns a vector of size . Each element of this vector indicates the unit that was selected.
Hugo Andres Gutierrez Rojas [email protected]
Tille, Y. (2006), Sampling Algorithms. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a simple random sample witho replacement of size m=3 sam <- S.WR(5,3) sam # The selected sample U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units accordind to a # simple random sampling with replacement design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam<-S.WR(N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Draws a simple random sample witho replacement of size m=3 sam <- S.WR(5,3) sam # The selected sample U[sam] ############ ## Example 2 ############ # Uses the Lucy data to draw a random sample of units accordind to a # simple random sampling with replacement design data(Lucy) attach(Lucy) N <- dim(Lucy)[1] m <- 400 sam<-S.WR(N,m) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] data dim(data)
Creates a matrix containing every possible sample under fixed sample size designs
Support(N, n, ID=FALSE)Support(N, n, ID=FALSE)
N |
Population size |
n |
Sample size |
ID |
By default FALSE, a vector of values (numeric or string) identifying each unit in the population |
A support is defined as the set of samples such that for any sample in the support, all the permutations of the coordinates of the sample are also in the support
The function returns a matrix of rows and columns. Each row of this matrix
corresponds to a possible sample
Hugo Andres Gutierrez Rojas [email protected]
Tille, Y. (2006), Sampling Algorithms. Springer
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas
# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 2 # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples Support(N,n) # The same support, but labeled Support(N,n,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator Support(N,n,ID=y)# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) n <- 2 # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples Support(N,n) # The same support, but labeled Support(N,n,ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator Support(N,n,ID=y)
Creates a matrix containing every possible sample under random sample size designs
SupportRS(N, ID=FALSE)SupportRS(N, ID=FALSE)
N |
Population size |
ID |
By default FALSE, a vector of values (numeric or string) identifying each unit in the population |
A support is defined as the set of samples such that for any sample in the support, all the permutations of the coordinates of the sample are also in the support
The function returns a matrix of rows and columns. Each row of this matrix corresponds to a possible sample
Hugo Andres Gutierrez Rojas [email protected]
Tille, Y. (2006), Sampling Algorithms. Springer
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas
# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples SupportRS(N) # The same support, but labeled SupportRS(N, ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator SupportRS(N, ID=y)# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples SupportRS(N) # The same support, but labeled SupportRS(N, ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator SupportRS(N, ID=y)
Creates a matrix containing every possible sample under fixed sample size with replacement designs
SupportWR(N, m, ID=FALSE)SupportWR(N, m, ID=FALSE)
N |
Population size |
m |
Sample size |
ID |
By default FALSE, a vector of values (numeric or string) identifying each unit in the population |
A support is defined as the set of samples such that, for any sample in the support, all the permutations of the coordinates of the sample are also in the support
The function returns a matrix of rows and columns. Each row of this matrix
corresponds to a possible sample
Hugo Andres Gutierrez Rojas [email protected]
Ortiz, J. E. (2009), Simulacion y metodos estadisticos. Editorial Universidad Santo Tomas.
Tille, Y. (2006), Sampling Algorithms. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples SupportWR(N, m) # The same support, but labeled SupportWR(N, m, ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator SupportWR(N, m, ID=y)# Vector U contains the label of a population U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") N <- length(U) m <- 2 # The support for fixed size without replacement sampling designs # Under this context, there are ten (10) possibles samples SupportWR(N, m) # The same support, but labeled SupportWR(N, m, ID=U) # y is the variable of interest y<-c(32,34,46,89,35) # The following output is very useful when checking # the design-unbiasedness of an estimator SupportWR(N, m, ID=y)
Computes the population total of the characteristics of interest in clusters. This function is used in order to estimate totals when doing a Pure Cluster Sample.
T.SIC(y,Cluster)T.SIC(y,Cluster)
y |
Vector, matrix or data frame containing the recollected information of the variables of interest for every unit in the selected sample |
Cluster |
Vector identifying the membership to the cluster of each unit in the selected sample of clusters |
The function returns a matrix of clusters totals. The columns of each matrix correspond to the totals of the variables of interest in each cluster
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # Vector Cluster contains a indicator variable of cluster membership Cluster <- c("C1", "C2", "C1", "C2", "C1") Cluster # Draws a stratified simple random sample without replacement of size n=3 T.SIC(y1,Cluster) T.SIC(y2,Cluster) T.SIC(y3,Cluster) ######################################################## ## Example 2 Sampling and estimation in Cluster smapling ######################################################## # Uses Lucy data to draw a clusters sample according to a SI design # Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters UI<-c("A","B","C","D","E") NI=length(UI) # The sample size nI=2 # Draws a simple random sample of two clusters samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The information about each unit in the cluster is saved in Lucy1 and Lucy2 data(Lucy) Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] LucyI<-rbind(Lucy1,Lucy2) attach(LucyI) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) Ty<-T.SIC(estima,Cluster) # Estimation of the Population total E.SI(NI,nI,Ty)############ ## Example 1 ############ # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) y3<-cbind(y1,y2) # Vector Cluster contains a indicator variable of cluster membership Cluster <- c("C1", "C2", "C1", "C2", "C1") Cluster # Draws a stratified simple random sample without replacement of size n=3 T.SIC(y1,Cluster) T.SIC(y2,Cluster) T.SIC(y3,Cluster) ######################################################## ## Example 2 Sampling and estimation in Cluster smapling ######################################################## # Uses Lucy data to draw a clusters sample according to a SI design # Zone is the clustering variable data(Lucy) attach(Lucy) summary(Zone) # The population of clusters UI<-c("A","B","C","D","E") NI=length(UI) # The sample size nI=2 # Draws a simple random sample of two clusters samI<-S.SI(NI,nI) dataI<-UI[samI] dataI # The information about each unit in the cluster is saved in Lucy1 and Lucy2 data(Lucy) Lucy1<-Lucy[which(Zone==dataI[1]),] Lucy2<-Lucy[which(Zone==dataI[2]),] LucyI<-rbind(Lucy1,Lucy2) attach(LucyI) # The clustering variable is Zone Cluster <- as.factor(as.integer(Zone)) # The variables of interest are: Income, Employees and Taxes # This information is stored in a data frame called estima estima <- data.frame(Income, Employees, Taxes) Ty<-T.SIC(estima,Cluster) # Estimation of the Population total E.SI(NI,nI,Ty)
Computes the theoretical variance of the Horvitz-Thompson estimator given a without replacement fixed sample size design
VarHT(y, N, n, p)VarHT(y, N, n, p)
y |
Vector containing the recollected information of the characteristic of interest for every unit in the population |
N |
Population size |
n |
Sample size |
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one |
The variance of the Horvitz-Thompson estimator, under a given sampling design , is given by
The function returns the value of the theoretical variances of the Horviz-Thompson estimator.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
# Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Calculates the theoretical variance of the HT estimator VarHT(y1, N, n, p) VarHT(y2, N, n, p)# Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Calculates the theoretical variance of the HT estimator VarHT(y1, N, n, p) VarHT(y2, N, n, p)
This function estimates the variance of the Horvitz-Thompson estimator. Two different variance estimators are computed: the original one, due to Horvitz-Thompson and the one due to Sen (1953) and Yates, Grundy (1953). The two approaches yield unbiased estimator under fixed-size sampling schemes.
VarSYGHT(y, N, n, p)VarSYGHT(y, N, n, p)
y |
Vector containing the information of the characteristic of interest for every unit in the population. |
N |
Population size. |
n |
Sample size. |
p |
A vector containing the selection probabilities of a fixed size without replacement sampling design. The sum of the values of this vector must be one. |
The function returns two variance estimator for every possible sample within a fixed-size sampling support. The first estimator is due to Horvitz-Thompson and is given by the following expression:
The second estimator is due to Sen (1953) and Yates-Grundy (1953). It is given by the following expression:
This function returns a data frame of every possible sample in within a sampling support, with its corresponding variance estimates.
Hugo Andres Gutierrez Rojas <hagutierrezro at gmail.com>
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas
y estimacion de parametros. Editorial Universidad Santo Tomas.
# Example 1 # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Calculates the estimated variance for the HT estimator VarSYGHT(y1, N, n, p) VarSYGHT(y2, N, n, p) # Unbiasedness holds in the estimator of the total sum(y1) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.HT) sum(y2) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.HT) # Unbiasedness also holds in the two variances VarHT(y1, N, n, p) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.Var1) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.Var2) VarHT(y2, N, n, p) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.Var1) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.Var2) # Example 2: negative variance estimates x = c(2.5, 2.0, 1.1, 0.5) N = 4 n = 2 p = c(0.31, 0.20, 0.14, 0.03, 0.01, 0.31) VarSYGHT(x, N, n, p) # Unbiasedness holds in the estimator of the total sum(x) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.HT) # Unbiasedness also holds in the two variances VarHT(x, N, n, p) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.Var1) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.Var2)# Example 1 # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector y1 and y2 are the values of the variables of interest y1<-c(32, 34, 46, 89, 35) y2<-c(1,1,1,0,0) # The population size is N=5 N <- length(U) # The sample size is n=2 n <- 2 # p is the probability of selection of every possible sample p <- c(0.13, 0.2, 0.15, 0.1, 0.15, 0.04, 0.02, 0.06, 0.07, 0.08) # Calculates the estimated variance for the HT estimator VarSYGHT(y1, N, n, p) VarSYGHT(y2, N, n, p) # Unbiasedness holds in the estimator of the total sum(y1) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.HT) sum(y2) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.HT) # Unbiasedness also holds in the two variances VarHT(y1, N, n, p) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.Var1) sum(VarSYGHT(y1, N, n, p)$p * VarSYGHT(y1, N, n, p)$Est.Var2) VarHT(y2, N, n, p) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.Var1) sum(VarSYGHT(y2, N, n, p)$p * VarSYGHT(y2, N, n, p)$Est.Var2) # Example 2: negative variance estimates x = c(2.5, 2.0, 1.1, 0.5) N = 4 n = 2 p = c(0.31, 0.20, 0.14, 0.03, 0.01, 0.31) VarSYGHT(x, N, n, p) # Unbiasedness holds in the estimator of the total sum(x) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.HT) # Unbiasedness also holds in the two variances VarHT(x, N, n, p) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.Var1) sum(VarSYGHT(x, N, n, p)$p * VarSYGHT(x, N, n, p)$Est.Var2)
Computes the calibration weights (Chi-squared distance) for the estimation of the population total of several variables of interest.
Wk(x,tx,Pik,ck,b0)Wk(x,tx,Pik,ck,b0)
x |
Vector, matrix or data frame containing the recollected auxiliary information for every unit in the selected sample |
tx |
Vector containing the populations totals of the auxiliary information |
Pik |
A vector containing inclusion probabilities for each unit in the sample |
ck |
A vector of weights induced by the structure of variance of the supposed model |
b0 |
By default FALSE. The intercept of the regression model |
The calibration weights satisfy the following expression
The function returns a vector of calibrated weights.
Hugo Andres Gutierrez Rojas [email protected]
Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Gutierrez, H. A. (2009), Estrategias de muestreo: Diseno de encuestas y estimacion de parametros.
Editorial Universidad Santo Tomas.
############ ## Example 1 ############ # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # pik is some vector of inclusion probabilities in the sample # In this case the sample size is equal to the population size pik<-rep(1,5) w1<-Wk(x,tx=236,pik,ck=1,b0=FALSE) sum(x*w1) # Draws a sample size without replacement sam <- sample(5,2) pik <- c (0.8,0.2,0.2,0.5,0.3) # The auxiliary information an variable of interest in the selected smaple x.s<-x[sam] y.s<-y[sam] # The vector of inclusion probabilities in the selected smaple pik.s<-pik[sam] # Calibration weights under some specifics model w2<-Wk(x.s,tx=236,pik.s,ck=1,b0=FALSE) sum(x.s*w2) w3<-Wk(x.s,tx=c(5,236),pik.s,ck=1,b0=TRUE) sum(w3) sum(x.s*w3) w4<-Wk(x.s,tx=c(5,236),pik.s,ck=x.s,b0=TRUE) sum(w4) sum(x.s*w4) w5<-Wk(x.s,tx=236,pik.s,ck=x.s,b0=FALSE) sum(x.s*w5) ###################################################################### ## Example 2: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 Pik <- rep(n/N, n) sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common ratio model ################### estima<-data.frame(Income) x <- Employees tx <- sum(Lucy$Employees) w <- Wk(x, tx, Pik, ck=1, b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model without intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- sum(Lucy$Taxes) w<-Wk(x,tx,Pik,ck=x,b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model without intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model with intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- c(N,sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model with intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) #################################################################### ## Example 3: Linear models involving discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Vector of inclusion probabilities for units in the selected sample Pik<-rep(n/N,n) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model ################### estima<-data.frame(Income, Employees, Taxes) tx <- colSums(Domains(Lucy$Level)) w <- Wk(Doma,tx,Pik,ck=1,b0=FALSE) sum(Doma[,1]*w) sum(Doma[,2]*w) sum(Doma[,3]*w) tx # The calibration estimation colSums(estima*w) ########### Poststratified common ratio model ################### estima<-data.frame(Income, Employees) x<-Doma*Taxes tx <- colSums(Domains(Lucy$Level)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) sum(x[,3]*w) tx # The calibration estimation colSums(estima*w)############ ## Example 1 ############ # Without replacement sampling # Vector U contains the label of a population of size N=5 U <- c("Yves", "Ken", "Erik", "Sharon", "Leslie") # Vector x is the auxiliary information and y is the variables of interest x<-c(32, 34, 46, 89, 35) y<-c(52, 60, 75, 100, 50) # pik is some vector of inclusion probabilities in the sample # In this case the sample size is equal to the population size pik<-rep(1,5) w1<-Wk(x,tx=236,pik,ck=1,b0=FALSE) sum(x*w1) # Draws a sample size without replacement sam <- sample(5,2) pik <- c (0.8,0.2,0.2,0.5,0.3) # The auxiliary information an variable of interest in the selected smaple x.s<-x[sam] y.s<-y[sam] # The vector of inclusion probabilities in the selected smaple pik.s<-pik[sam] # Calibration weights under some specifics model w2<-Wk(x.s,tx=236,pik.s,ck=1,b0=FALSE) sum(x.s*w2) w3<-Wk(x.s,tx=c(5,236),pik.s,ck=1,b0=TRUE) sum(w3) sum(x.s*w3) w4<-Wk(x.s,tx=c(5,236),pik.s,ck=x.s,b0=TRUE) sum(w4) sum(x.s*w4) w5<-Wk(x.s,tx=236,pik.s,ck=x.s,b0=FALSE) sum(x.s*w5) ###################################################################### ## Example 2: Linear models involving continuous auxiliary information ###################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 Pik <- rep(n/N, n) sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) ########### common ratio model ################### estima<-data.frame(Income) x <- Employees tx <- sum(Lucy$Employees) w <- Wk(x, tx, Pik, ck=1, b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model without intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- sum(Lucy$Taxes) w<-Wk(x,tx,Pik,ck=x,b0=FALSE) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model without intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) ########### Simple regression model with intercept ################### estima<-data.frame(Income, Employees) x <- Taxes tx <- c(N,sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x*w) tx # The calibration estimation colSums(estima*w) ########### Multiple regression model with intercept ################### estima<-data.frame(Income) x <- cbind(Employees, Taxes) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) w <- Wk(x,tx,Pik,ck=1,b0=TRUE) sum(1*w) sum(x[,1]*w) sum(x[,2]*w) tx # The calibration estimation colSums(estima*w) #################################################################### ## Example 3: Linear models involving discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) attach(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # Vector of inclusion probabilities for units in the selected sample Pik<-rep(n/N,n) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model ################### estima<-data.frame(Income, Employees, Taxes) tx <- colSums(Domains(Lucy$Level)) w <- Wk(Doma,tx,Pik,ck=1,b0=FALSE) sum(Doma[,1]*w) sum(Doma[,2]*w) sum(Doma[,3]*w) tx # The calibration estimation colSums(estima*w) ########### Poststratified common ratio model ################### estima<-data.frame(Income, Employees) x<-Doma*Taxes tx <- colSums(Domains(Lucy$Level)) w <- Wk(x,tx,Pik,ck=1,b0=FALSE) sum(x[,1]*w) sum(x[,2]*w) sum(x[,3]*w) tx # The calibration estimation colSums(estima*w)