eblupFH function

EBLUPs based on a Fay-Herriot model.

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.

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.

Returns

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)