mseSFH {sae}

Mean squared error estimator of the spatial EBLUP under a spatial Fay-Herriot model.

Description

Calculates analytical mean squared error estimates of the spatial EBLUPs obtained from the fit of a spatial Fay-Herriot model, in which area effects follow a Simultaneously Autorregressive (SAR) process.

Usage

mseSFH(formula, vardir, proxmat, method = "REML", MAXITER = 100, 
       PRECISION = 0.0001, data)

Arguments

formula

an object of class formula (or one that can be coerced to that class): a symbolic description of the model to be fitted. The variables included in formula must have a length equal to the number of domains D. Details of model specification are given under Details.

vardir

vector containing the D sampling variances of direct estimators for each domain. The values must be sorted as the variables in formula.

proxmat

D*D proximity matrix or data frame with values in the interval [0,1] containing the proximities between the row and column domains. The rows add up to 1. The rows and columns of this matrix must be sorted as the variables in formula.

method

type of fitting method, to be chosen between "REML" or "ML". Default value is REML.

MAXITER

maximum number of iterations allowed for the Fisher-scoring algorithm. Default value is 100.

PRECISION

convergence tolerance limit for the Fisher-scoring algorithm. Default value is 0.0001.

data

optional data frame containing the variables named in formula and vardir. By default the variables are taken from the environment from which mseSFH is called.

Value

The function returns a list with the following objects:

est

a list with the results of the estimation process: eblup and fit. For the description of these objects, see Value of eblupSFH function.

mse

a vector with the analytical mean squared error estimates of the spatial EBLUPs.

In case that formula, vardir or proxmat contain NA values a message is printed and no action is done.

Author(s)

Isabel Molina, Monica Pratesi and Nicola Salvati.

References

- Small Area Methods for Poverty and Living Conditions Estimates (SAMPLE), funded by European Commission, Collaborative Project 217565, Call identifier FP7-SSH-2007-1.

- Molina, I., Salvati, N. and Pratesi, M. (2009). Bootstrap for estimating the MSE of the Spatial EBLUP. Computational Statistics 24, 441-458.

- Singh, B., Shukla, G. and Kundu, D. (2005). Spatio-temporal models in small area estimation. Survey Methodology 31, 183-195.

See Also

eblupSFH, npbmseSFH, pbmseSFH

Examples

data(grapes)       # Load data set
data(grapesprox)   # Load proximity matrix 

# Calculate analytical MSE estimates using REML method
result <- mseSFH(grapehect ~ area + workdays - 1, var, grapesprox, data=grapes)
result