eblupFH {sae}

EBLUPs based on a Fay-Herriot model.

Description

This function gives the EBLUP (or EB predictor under normality) based on a Fay-Herriot model. Fitting method can be chosen between ML, REML and FH methods.

Usage

eblupFH(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

type of fitting method, to be chosen between "ML", "REML" or "FH" methods.

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 eblupFH 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", "ML"or "FH").

• 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.

• goodness: vector containing several goodness-of-fit measures: loglikehood, AIC, BIC, KIC and the measures proposed by Marhuenda et al. (2014): AICc, AICb1, AICb2, KICc, KICb1, KICb2. B must be must be greater than 0 to obtain these last measures.

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

References

- 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.

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

- Rao, J.N.K. (2003). Small Area Estimation. Wiley, London.

See Also

mseFH

Examples

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

# Fit FH model using REML method with indicators of 4 Major Areas as 
# explanatory variables.
resultREML <- eblupFH(yi ~ as.factor(MajorArea), SD^2)
resultREML

#Fit FH model using FH method
resultFH <- eblupFH(yi ~ as.factor(MajorArea), SD^2, method="FH")
resultFH

detach(milk)