pbmseSFH: Parametric bootstrap mean squared error estimators of the...
In sae: Small Area Estimation

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2	pbmseSFH(formula, vardir, proxmat, B = 100, method = "REML", MAXITER = 100, PRECISION = 0.0001, data)

`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, 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 `pbmseSFH` is called.

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.

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 parametric bootstrap mean squared error estimates (`mse`) and the bias-corrected parametric 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.

Isabel Molina, Monica Pratesi and Nicola Salvati.

- 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.

eblupSFH, npbmseSFH, mseSFH

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

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