mseFH {sae}

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

Description

Calculates the mean squared error estimator of the EBLUP under a Fay-Herriot model. The EBLUP might have been obtained by either ML, REML or by FH fitting methods.

Usage

mseFH(formula, vardir, method = "REML", MAXITER = 100, PRECISION = 0.0001, B = 0, 
      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.

method

method used to fit the Fay-Herriot model, which can be either "ML", "REML" or "FH" methods. Default is "REML" method.

MAXITER

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

PRECISION

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

B

number of bootstrap replicates to calculate the goodness-of-fit measures proposed by Marhuenda et al. (2014). Default value is 0 indicating that these measures are not calculated.

data

optional data frame containing the variables named in formula and vardir. By default the variables are taken from the environment from which mseFH 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:

est

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

mse

a vector with the estimated mean squared errors of the EBLUPs for the small domains.

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

References

- Datta, G.S. and Lahiri, P. (2000). A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica 10, 613-627.

- Datta, G.S., Rao, J.N.K. and Smith D.D. (2005). On measuring the variability of small area estimators under a basic area level model. Biometrika 92, 183-196.

- Fay, R.E. and Herriot, R.A. (1979). Estimation of income from small places: An application of James-Stein procedures to census data. Journal of the American Statistical Association 74, 269-277.

- Jiang, J. (1996). REML estimation: asymptotic behavior and related topics. Annals of Statistics 24, 255-286.

- Marhuenda, Y., Morales, D. and Pardo, M.C. (2014). Information criteria for Fay-Herriot model selection. Computational Statistics and Data Analysis 70, 268-280.

- Prasad, N. and Rao, J. (1990). The estimation of the mean squared error of small-area estimators. Journal of the American Statistical Association 85, 163-171.

See Also

eblupFH

Examples

# Load data set  
data(milk)   
attach(milk)

# Fit Fay-Herriot model using ML method with indicators 
# of 4 Major Areas as explanatory variables and compute
# estimated MSEs of EB estimators
resultML <- mseFH(yi ~ as.factor(MajorArea), SD^2, method="ML")
resultML

# Fit Fay-Herriot model using REML method and compute 
# estimated MSEs of EB estimators
resultREML <- mseFH(yi ~ as.factor(MajorArea), SD^2)
resultREML

# Fit Fay-Herriot model using FH method and compute 
# estimated MSEs of EB estimators
resultFH <- mseFH(yi ~ as.factor(MajorArea), SD^2, method="FH")
resultFH

detach(milk)