npbmseSFH {sae}

Nonparametric bootstrap mean squared error estimator of the spatial EBLUPs under a spatial Fay-Herriot model.

Description

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

Usage

npbmseSFH(formula, vardir, proxmat, B = 100, 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.

B

number of bootstrap replicates. Default value is 100.

method

type of fitting method. Currently only "REML" method is available.

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 npbmseSFH is called.

Details

This function uses random number generation. To fix the seed, use set.seed.

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 terms specification of the form first + second indicates all the terms in first together with all the terms in second with any 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:

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

data frame containing the naive nonparametric bootstrap mean squared error estimates of the spatial EBLUPs (mse) and the bias-corrected nonparametric bootstrap mean squared error estimates of the spatial EBLUPs (msebc).

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.

See Also

eblupSFH, pbmseSFH, mseSFH

Examples

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

# Obtain the naive and bias-corrected non parametric bootstrap MSE 
# estimates using REML 
set.seed(123)
result <- npbmseSFH(grapehect ~ area + workdays - 1, var, grapesprox, B=2, data=grapes)
result