TeachingSampling (version 4.1.1)

E.Beta: 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

Value

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

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

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

# NOT RUN {
######################################################################
## 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)
# }