| estimate.unknownsampvar {smallarea} | R Documentation |
Estimates of variance component, unknown sampling variance, regression coefficients and small area means in Fay Herriot model with unknown sampling variance.
Description
The function returns a list of 5 elements. The first element is an estimate of the variance component , the second element is an estimate of the parameter related to sampling variance, the third element is a vector of estimates of the regression coefficients in the Fay-Herriot model, the fourth element is a vector of the predictors pf the small area means and last element is the design matrix, the first column being a column of ones and the remaining columns represent the values of the covariates for different small areas. See details below.
Usage
estimate.unknownsampvar(response, mat.design, sample.size)
Arguments
response |
A numeric vector. It represents the response or the direct survey based estimators in the Fay Herriot Model |
mat.design |
A numeric matrix. The first column is a column of ones(also called the intercept). The other columns consist of observations of each of the covariates or the explanatory variable in Fay Herriot Model. |
sample.size |
A numeric vector. The known sample sizes used to calculate the direct survey based estimators. |
Details
For more details please see the package vignette.
Value
psi.hat |
Estimate of the variance component |
del.hat |
Estimate of the parameter for sampling variance |
beta.hat |
Estimate of the unknown regression coefficients |
theta.hat |
Predictors of the small area means |
mat.design |
design matrix |
Author(s)
Abhishek Nandy
References
On measuring the variability of small area estimators under a basic area level model. Datta, Rao, Smith. Biometrika(2005),92, 1,pp. 183-196 Large Sample Techniques for Statistics, Springer Texts in Statistics. Jiming Jiang. Chapters - 4,12 and 13.
See Also
Examples
set.seed( 55 ) # setting a random seed
require(MASS) # the function mvrnorm requires MASS
x1 <- rep( 1, 10 ) # vector of ones representing intercept
x2 <- rnorm( 10 ) # vector of covariates randomly generated
x <- cbind( x1, x2 ) # design matrix
x <- as.matrix( x ) # coercing into class matrix
n <- rbinom (10, 20, 0.4) # generating sample sizes for each small area
psi <- 1 # true value of the psi parameter
delta <- 1 # true value of the delta parameter
beta <- c( 1, 0.5 ) # true values of the regression parameters
theta <- mvrnorm( 1, as.vector( x %*% beta ), diag(10) ) # true small area means
y <- mvrnorm( 1, as.vector( theta ), diag( delta/n ) ) # design based estimators
estimate.unknownsampvar( y, x, n )