eblupSFH {sae}

EBLUPs based on a spatial Fay-Herriot model.

Description

This function gives small area estimators based on a spatial Fay-Herriot model, where area effects follow a SAR(1) process. Fitting method can be chosen between REML and ML.

Usage

eblupSFH(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 elements 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 eblupSHF is called.

Details

A typical model has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with duplicates removed.

A formula has an implied intercept term. To remove this use either y ~ x - 1 or y ~ 0 + x. See formula for more details of allowed formulae.

Value

The function returns a list with the following objects:

eblup

vector with the values of the estimators for the domains.

fit

a list containing the following objects:

• method: type of fitting method applied ("REML" or "ML").

• convergence: a logical value equal to TRUE if Fisher-scoring algorithm converges in less than MAXITER iterations.

• iterations: number of iterations performed by the Fisher-scoring algorithm.

• estcoef: a data frame with the estimated model coefficients in the first column (beta), their asymptotic standard errors in the second column (std.error), the t statistics in the third column (tvalue) and the p-values of the significance of each coefficient in last column (pvalue).

• refvar: estimated random effects variance.

• spatialcorr: estimated spatial correlation parameter.

• goodness: vector containing three goodness-of-fit measures: loglikehood, AIC and BIC.

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.

- Petrucci, A. and Salvati, N. (2006). Small area estimation for spatial correlation in watershed erosion assessment. Journal of Agricultural, Biological and Environmental Statistics 11, 169-182.

- Pratesi, M. and Salvati, N. (2008). Small area estimation: the EBLUP estimator based on spatially correlated random area effects. Statistical Methods & Applications 17, 113-141.

See Also

mseSFH, npbmseSFH, pbmseSFH

Examples

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

# Fit Spatial Fay-Herriot model using ML method
resultML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
                     method="ML", data=grapes)
resultML

# Fit Spatial Fay-Herriot model using REML method
resultREML <- eblupSFH(grapehect ~ area + workdays - 1, var, grapesprox,
                       data=grapes)
resultREML