# resimaxilikelihood: Estimate of the variance component in Fay Herriot Model using... In smallarea: Fits a Fay Herriot Model

## Description

This function returns a list with one element in it which is the estimate of the variance component in the Fay Herriot Model using residual maximum likelihood method. The estimates are obtained as a solution of equations known as REML equations. The solution is obtained numerically using Fisher-scoring algorithm. For more details please see the package vignette and the references. Note that our function does not accept any missing values.

## Usage

 `1` ```resimaxilikelihood(response, designmatrix, sampling.var,maxiter) ```

## Arguments

 `response` a numeric vector. It represents the response or the observed value 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. `maxiter` maximum number of iterations of fisher scoring

## Details

For more details see the package vignette

## Value

 `estimate` estimate of the variance component

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. Small Area Estimation, JNK Rao,Wiley 2003 Variance Components, Wiley Series in Probability and Statistics,2006 Searle, Casella, Mc-Culloh

## See Also

`prasadraoest` `maximlikelihood` `fayherriot`

## Examples

 ```1 2 3 4``` ```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) resimaxilikelihood(response,designmatrix,randomeffect.var,100) ```

smallarea documentation built on May 29, 2017, 6:09 p.m.