Estimation of the population regression coefficients under SI designs
Computes the estimation of regression coefficients using the principles of the Horvitz-Thompson estimator
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 hagutierrezro@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: 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)
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