maximlikelihood {smallarea}

Maximum likelihood estimates of the variance components and the unknown regression coefficients in Fay Herriot Model.

Description

This function returns a list of three elements the first one is the maximum likelihood estimate of the variance component,the second one is a vector of the maximum likelihood estimate of the unknown regression coefficients the first one being the coefficient of the intecept and the remaining ones are in the same order as the columns of the design matrix and the last one being the value of the maximized loglikelihood function in Fay Herriot model. it uses the optim in the stats package and the BFGS algorithm to minimize the negative loglikelihood. The initial value for this iterative proceedure of maximization are chosen as follows. The initial value for the variance component is the fay Prasad-rao estimate of the variance component, the initial value for the regression coefficients are the estimates of the regression coefficients using the multiple linear regression and ignoring the random effects.(For more details see vignette). Note that our function does not accept any missing values.

Usage

maximlikelihood(response, designmatrix, sampling.var)

Arguments

response

A numeric vector. It represents the response or the direct survey based estimators in the Fay Herriot Model

designmatrix

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.

sampling.var

A numeric vector consisting of the known sampling variances of each of the small area levels.

Details

For more details please see the package vignette

Value

estimate

Maximum likelihood estimate of the variance component

reg.coefficients

Maximum likelihood estimate of the unknown regression coefficients

loglikeli.optimum

The maximized value of the log likelihood function

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

prasadraoest fayherriot resimaxilikelihood

Examples

response=c(1,2,3,4,5)
designmatrix=cbind(c(1,1,1,1,1),c(1,2,4,4,1),c(2,1,3,1,5))
randomeffect.var=c(0.5,0.7,0.8,0.4,0.5)
maximlikelihood(response,designmatrix,randomeffect.var)