Geoadditive Small Area Estimation for Area-Level Model

Fits area-level geoadditive small area estimation (SAE) models by extending the Fay-Herriot area-level model with linear, nonlinear, and spatial effects. The Fay-Herriot model is described by Fay and Herriot (1979) . Geoadditive models combine nonlinear covariate effects and spatial variation as described by Kammann and Wand (2003) , while their application to small area estimation is discussed by Pusponegoro et al. (2019) . Nonlinear covariate effects are represented using penalized splines, while spatial effects are represented using a smooth function of geographic coordinates. Models are estimated using restricted maximum likelihood (REML), and mean squared error (MSE) is estimated using a parametric bootstrap. The package also provides comparisons with the Fay-Herriot and spatial Fay-Herriot (SFH) models.

geoaddSAE2

geoaddSAE2 provides functions for fitting area-level Geoadditive Small Area Estimation (SAE) models. The Geoadditive SAE model extends the classical Fay-Herriot model by incorporating nonlinear covariate effects and spatial variation.

Authors

Amalyah Rizky Khairunnisa Sutarto, Novi Hidayat Pusponegoro

Maintainer

Amalyah Rizky Khairunnisa Sutarto [email protected]

Installation

You can install the released version of geoaddSAE2 from CRAN or find my github repository Github

install.packages("remotes")
remotes::install_github("amalyahrizky04/geoaddSAE2")

Example

The following example illustrates the basic use of geosae().

#Load the library
library(geoaddSAE2)

#Load the dataset
data(simulated_sae)

#Estimate geoadditive SAE only
fit <- geosae(
        data = simulated_sae, 
        formula = y ~ x1 + x2, 
        vardir = vardir, 
        nonlinear = "x3", 
        knots = c("x3" = 10),
        spatial = c("lat", "lon"), 
        B = 10,
        seed = 1
      )

#Estimate geoadditive SAE and compare with Fay-Herriot and Spatial Fay-Herriot
fit <- geosae(
        data = simulated_sae, 
        formula = y ~ x1 + x2, 
        vardir = vardir, 
        nonlinear = "x3", 
        knots = c("x3" = 10),
        spatial = c("lat", "lon"), 
        compare = TRUE,
        B = 10,
        seed = 1
      ) 
      
print(fit) 
summary(fit)

References

• Fay, R. E. and Herriot, R. A. (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.
• Ruppert, D. (2002). Selecting the Number of Knots for Penalized Splines. Journal of Computational and Graphical Statistics, 11(4), 735–757.
• Kammann, E. E., & Wand, M. P. (2003). Geoadditive models. Journal of the Royal Statistical Society. Series C: Applied Statistics, 52(1), 1–18.
• Rao, J. N. K. ., & Molina, Isabel. (2015). Small area estimation. John Wiley & Sons, Inc.
• Wood, S. N. (2025). Generalized additive models. Annual Review of Statistics and Its Application, 12(1), 497-526.