Fits a Fay Herriot model

Description

It has some useful functions which the users might find convenient for fitting Fay Herriot Model. Details are included in package vignette.

Details

Author(s)

Abhishek Nandy

Maintainer: Abhishek nandy<nandy006@umn.edu>

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

Examples

data=data.frame(response=c(1,2,3,4,8),D=c(0.2,0.5,0.1,0.9,1))
data
ans=smallareafit(response~D,data,method="FH")
ans1=smallareafit(response~D,data,method="REML")
ans2=smallareafit(response~D,data,method="PR")
ans3=smallareafit(response~D,data,method="ML")

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

Details

For more details please see the package vignette.

Value

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

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 )      

Estimate of the variance component in Fay Herriot Model using Fay Herriot Method

Description

This function returns a list with one element in it which is the estimate of the variance component in the Fay Herriot Model. The estimate is found by solving an equation (for details see vignette) and is due to Fay Herriot. The uniroot in the stats package is used to find the root. uniroot searches for a root of that equation in a particular interval the lower bound is 0 and the upper bound is set to estimate of the variance component using Prasad Rao method + three times the square root of the number of observation. It depends on the function prasadraoest in the same package. Note that our function does not accept missing values.

Usage

fayherriot(response, designmatrix, sampling.var)

Arguments

Details

For more details please see the attached vignette

Value

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 maximlikelihood 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)
fayherriot(response,designmatrix,randomeffect.var)

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

Details

For more details please see the package vignette

Value

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)

Estimate of the variance component in Fay Herriot Model using Prasad Rao Method

Description

This function returns a list with one element in it which is the estimate of the variance component in the Fay Herriot Model. The method used to get the estimate is the prasad rao method also known as BLUP.(for details see vignette). Note that our function does not accept any missing values.

Usage

prasadraoest(response, designmatrix, sampling.var)

Arguments

Details

For more details see the package vignette

Value

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

fayherriot maximlikelihood 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)
prasadraoest(response,designmatrix,randomeffect.var)

Estimate of the variance component in Fay Herriot Model using Residual Maximum Likelihood, REML.

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

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

Arguments

Details

For more details see the package vignette

Value

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. 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

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)

Fits a Fay Herriot Model to data

Description

Fits a Fay Herriot model to the data and returns a list of items which area estimates of different paramaters and mse of the estimates of the small area means the details of which are provided in the value section.

Usage

smallareafit(formula, data, method)

Arguments

Details

for more details see the vignette

Value

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

See Also

prasadraoest fayherriot resimaxilikelihood maximlikelihood

Examples

data=data.frame(response=c(1,2,3,4,8),D=c(0.2,0.5,0.1,0.9,1))
data
ans=smallareafit(response~D,data,method="FH")
ans1=smallareafit(response~D,data,method="REML")
ans2=smallareafit(response~D,data,method="PR")
ans3=smallareafit(response~D,data,method="ML")