# E.Beta: Estimation of the population regression coefficients under SI... In TeachingSampling: Selection of Samples and Parameter Estimation in Finite Population

## Description

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

## Usage

 `1` ```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 hagutierrezro@gmail.com

## 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.

`GREG.SI`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82``` ```###################################################################### ## 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) ```

TeachingSampling documentation built on April 22, 2020, 1:05 a.m.