The Generalized Regression Estimator under SI sampling design
Computes the generalized regression estimator of the population total for several variables of interest under simple random sampling without replacement
GREG.SI(N, n, y, x, tx, b, 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 |
tx |
Vector containing the populations totals of the auxiliary information |
b |
Vector of estimated regression coefficients |
b0 |
By default FALSE. The intercept of the regression model |
The function returns a vector of total population estimates for each variable of interest, its estimated standard error and its estimated coefficient of variation.
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) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- c(N) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### common ratio model estima<-data.frame(Income) x <- data.frame(Employees) model <- E.Beta(N, n, estima, x, ck=x,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Employees) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model without intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- sum(Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Multiple regression model without intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1, b0=FALSE) b <- as.matrix(model[1,,]) tx <- c(sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ########### Simple regression model with intercept estima<-data.frame(Income, Employees) x <- data.frame(Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) ########### Multiple regression model with intercept estima<-data.frame(Income) x <- data.frame(Employees, Taxes) model <- E.Beta(N, n, estima, x, ck=1,b0=TRUE) b <- as.matrix(model[1,,]) tx <- c(N, sum(Lucy$Employees), sum(Lucy$Taxes)) GREG.SI(N,n,estima,x,tx, b, b0=TRUE) #################################################################### ## Example 2: Linear models with discrete auxiliary information #################################################################### # Draws a simple random sample without replacement data(Lucy) N <- dim(Lucy)[1] n <- 400 sam <- S.SI(N,n) # The information about the units in the sample is stored in an object called data data <- Lucy[sam,] attach(data) names(data) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model estima<-data.frame(Income, Employees, Taxes) model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common ratio model estima<-data.frame(Income, Employees) x <- Doma*Taxes model <- E.Beta(N, n, estima, x ,ck=1,b0=FALSE) b <- as.matrix(model[1,,]) tx <- colSums(Domains(Lucy$Level)*Lucy$Taxes) GREG.SI(N,n,estima,x,tx, b, b0=FALSE) ###################################################################### ## Example 3: Domains estimation trough the postestratified estimator ###################################################################### # Draws a simple random sample without replacement data(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) # The auxiliary information is discrete type Doma<-Domains(Level) ########### Poststratified common mean model for the # Income total in each poststratum ################### estima<-Doma*Income model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Employees total in each poststratum ################### estima<-Doma*Employees model <- E.Beta(N, n, estima, Doma, ck=1,b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE) ########### Poststratified common mean model for the # Taxes total in each poststratum ################### estima<-Doma*Taxes model <- E.Beta(N, n, estima, Doma, ck=1, b0=FALSE) b <- t(as.matrix(model[1,,])) tx <- colSums(Domains(Lucy$Level)) GREG.SI(N,n,estima,Doma,tx, b, b0=FALSE)
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