GREG.SI {TeachingSampling}

The Generalized Regression Estimator under SI sampling design

Description

Computes the generalized regression estimator of the population total for several variables of interest under simple random sampling without replacement

Usage

GREG.SI(N, n, y, x, tx, b, b0=FALSE)

Arguments

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

Value

The function returns a vector of total population estimates for each variable of interest, its estimated standard error and its estimated coefficient of variation.

Author(s)

Hugo Andres Gutierrez Rojas [e-mail]

References

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.

See Also

E.Beta

Examples

######################################################################
## 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)