E.Beta {TeachingSampling}

Estimation of the population regression coefficients under SI designs

Description

Computes the estimation of regression coefficients using the principles of the Horvitz-Thompson estimator

Usage

E.Beta(N, n, y, x, ck=1, 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

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

Details

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

Value

The function returns a vector whose entries correspond to the estimated parameters of the regression coefficients

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

GREG.SI

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)
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)