fSAE.Area: Compute small area estimates based on the basic area-level model.

Description

This function returns small area estimates based on the basic area-level model, also known as the Fay-Herriot model. It calls fSAE.Unit to carry out the computations.

Usage

fSAE.Area(est.init, var.init, X, x, ...)

Arguments

est.init

m-vector of initial estimates, where m is the number of in-sample areas.

var.init

m-vector of corresponding variance estimates.

M x p matrix of area-level covariates (typically population means), where M is the number of areas for which estimates are computed. If missing, a column vector of ones of the same length as est.init is used, corresponding to a model with an intercept only. The M areas may or may not equal the m areas for which initial estimates are provided. For example, estimates for out-of-sample areas, for which no initial estimates are available, are computed as long as the corresponding rows of auxiliary means are in X. It is also possible to compute estimates only for a subset of sample areas, see the help for argument x.

an optional m x p matrix with auxiliary area-level covariates to be used for fitting the model, where the rows correspond to the components of est.init. If the M areas corresponding to the rows of X do not contain all m areas corresponding to est.init, x must be provided separately in order to be able to fit the model.

...

additional arguments passed to fSAE.Unit. For example, passing an M-vector Narea with area population sizes (along with the matrix X of population means) allows to compute aggregates of the small area estimates. See the documentation of function fSAE.Unit for a description of other possible arguments.

Value

An object of class sae containing the small area estimates and MSEs, the model fit, and model selection measures.

References

R.E. Fay and R.A. Herriot (1979). Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data. Journal of the American Statistical Association 74(366), 269-277.

J.N.K. Rao and I. Molina (2015). Small Area Estimation. Wiley.

Examples

Run this code

# NOT RUN {
d <- generateFakeData()

# first compute input estimates without "borrowing strength" over areas
sae0 <- fSAE(y0 ~ x + area2, data=d$sam, area="area", popdata=d$Xpop,
             type="direct", keep.data=TRUE)

# compute small area estimates based on the basic area-level model
#   using the above survey regression estimates as input
sae <- fSAE.Area(EST(sae0), MSE(sae0), X=sae0$Xp)
EST(sae)  # estimates
RMSE(sae)  # standard errors
# }