E.Beta {TeachingSampling}R Documentation

Estimation of the population regression coefficients

Description

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

Usage

E.Beta(y, x, Pik, ck=1, b0=FALSE)

Arguments

y Vector, matrix or data frame containig the recollected information of the variables of interest for every unit in the selected sample
x Vector, matrix or data frame containig the recollected auxiliary information for every unit in the selected sample
Pik A vector containing the inclusion probabilities for each 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

Value

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

Author(s)

Hugo Andrés Gutiérrez Rojas hugogutierrez@usantotomas.edu.co

References

Sarndal, C-E. and Swensson, B. and Wretman, J. (1992), Model Assisted Survey Sampling. Springer.
Guti'errez, H. A. (2009), Estrategias de muestreo: Dise~no de encuestas y estimaci'on de par'ametros. Editorial Universidad Santo Tom'as.

See Also

GREG.SI

Examples

######################################################################
## Example 1: Linear models involving continuous auxiliary information
######################################################################

# Draws a simple random sample without replacement
data(Lucy)
data(Marco)
N <- dim(Marco)[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 the units in the sample
Pik<-rep(n/N,n)

########### common mean model ###################

estima<-data.frame(Income, Employees, Taxes)
x <- rep(1,n)
E.Beta(estima,x,Pik,ck=1,b0=FALSE)

########### common ratio model ###################

estima<-data.frame(Income)
x <- data.frame(Employees)
E.Beta(estima,x,Pik,ck=x,b0=FALSE)

########### Simple regression model without intercept ###################

estima<-data.frame(Income, Employees)                                                                                                          
x <- data.frame(Taxes)                                                                                                                        
E.Beta(estima,x,Pik,ck=1,b0=FALSE)                                                                                    
                                         
########### Multiple regression model without intercept ###################

estima<-data.frame(Income)
x <- data.frame(Employees, Taxes)
E.Beta(estima,x,Pik,ck=1,b0=FALSE)

########### Simple regression model with intercept ###################
 
estima<-data.frame(Income, Employees)
x <- data.frame(Taxes)
E.Beta(estima,x,Pik,ck=1,b0=TRUE) 
                    
########### Multiple regression model with intercept ###################

estima<-data.frame(Income)                            
x <- data.frame(Employees, Taxes)          
E.Beta(estima,x,Pik,ck=1,b0=TRUE)

####################################################################
## Example 2: Linear models involving discrete auxiliary information
####################################################################

# Draws a simple random sample without replacement
data(Lucy)
data(Marco)
N <- dim(Marco)[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)
# Vector of inclusion probabilities for the units in the sample
Pik<-rep(n/N,n)

########### Poststratified common mean model ###################

estima<-data.frame(Income, Employees, Taxes)
E.Beta(estima,Doma,Pik,ck=1,b0=FALSE)

########### Poststratified common ratio model ###################

estima<-data.frame(Income, Employees)
x<-Doma*Taxes
E.Beta(estima,x,Pik,ck=1,b0=FALSE)

[Package TeachingSampling version 0.7.6 Index]