Package {geoaddSAE2}

geoaddSAE2: Geoadditive Small Area Estimation for Area Level

Description

Fits area-level Geoadditive Small Area Estimation (SAE) models: a extension of the Fay-Herriot model that represents nonlinear covariate effects with and spatial variation, estimated by REML within a linear mixed model framework (via mgcv), with Mean Squared Error obtained by parametric bootstrap. The package also lets users compare the geoadditive model against the classical Fay-Herriot and Spatial Fay-Herriot models, both of which are provided by, and fitted with, the existing sae package.

Details

Main entry point: geosae.

Author(s)

Maintainer: Amalyah Rizky Khairunnisa Sutarto 222212489@stis.ac.id

Authors:

• Amalyah Rizky Khairunnisa Sutarto 222212489@stis.ac.id

• Novi Hidayat Pusponegoro novie@stis.ac.id [thesis advisor]

Fit an Area-Level Geoadditive Small Area Estimation Model

Description

Fits area-level Geoadditive Small Area Estimation (SAE) models, an extension of the Fay-Herriot model that incorporates linear covariate effects, nonlinear covariate effects represented by penalized splines, and spatial variation represented by a bivariate thin plate regression spline.

Usage

geosae(
  data,
  formula,
  vardir,
  nonlinear,
  spatial,
  knots = NULL,
  spatial_k = NULL,
  method = c("REML"),
  compare = FALSE,
  proxmat = NULL,
  proxmat_k = 4,
  B = 100,
  seed = NULL
)

Arguments

Details

Model parameters and smoothing parameters are estimated by Restricted Maximum Likelihood (REML) within a linear mixed model framework using mgcv. The Mean Squared Error (MSE) of the Geoadditive SAE estimates is estimated using parametric bootstrap.

When compare = TRUE, the function also fits the classical Fay-Herriot and Spatial Fay-Herriot models using implementations provided by the optional sae package. The sae package is not required when compare = FALSE.

Value

An object of class "geosae". The returned list contains area-level estimates, model diagnostics, fixed-effect parameter estimates, model comparisons when requested, and the underlying fitted model objects.

Examples

data(simulated_sae)

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

fit
summary(fit)
head(fit$estimation)


## Not run: 
fit_cmp <- geosae(
  data      = simulated_sae,
  formula   = y ~ x1 + x2,
  vardir    = vardir,
  nonlinear = "x3",
  spatial   = c("lat", "lon"),
  compare   = TRUE,
  B         = 100,
  seed      = 1
)

fit_cmp$comparison

## End(Not run)

Print method for geosae object

Description

Print method for geosae object

Usage

## S3 method for class 'geosae'
print(x, digits = 4, ...)

Arguments

Value

Invisibly returns the input object of class "geosae". The method prints the main model settings and area-level estimation results to the console.

Simulated area-level small area estimation data

Description

A synthetic area-level small area estimation dataset used in package examples, demonstrations, and tests.

The data are generated using the following steps:

1. The population consists of 100 small areas, and a seed is set to ensure reproducibility of the simulated data.

2. Two-dimensional spatial coordinates are generated for each area, where latitude is generated from U(-11, 6) and longitude is generated from U(95, 141).

3. Two linear auxiliary variables are generated for each area: x1 ~ Bernoulli(0.5) and x2 ~ U(1, 5). A nonlinear auxiliary variable x3 ~ U(1, 5) is also generated.

4. The model parameters are set deterministically as \alpha = 0.5, \beta_1 = 1, and \beta_2 = 1.

5. The nonlinear covariate effect is generated using g(x3) = x3^2.

6. A continuous spatial effect is generated from the spatial coordinates using the smooth function h(lat, lon) = sin(lat) + cos(lon).

7. The true small area parameter is calculated as theta = \alpha + \beta_1 x1 + \beta_2 x2 + g(x3) + h(lat, lon).

8. The number of sampled units in each area is generated from n_i ~ U{10, 50}. The sampling error variance is then defined as vardir = \sigma_e^2/n_i, where \sigma_e^2 = 1.

9. The direct estimator is generated according to the sampling model y = theta + e, where e ~ N(0, vardir).

10. The area identifier, direct estimator, auxiliary variables, spatial coordinates, sampling variance, and true small area parameter are combined into a data frame called simulated_sae.

Usage

simulated_sae

Format

A data frame with 100 rows and 9 columns:

area

Area identifier.

y

Direct estimator (response).

x1

Binary auxiliary variable with a linear effect on the response.

x2

Continuous auxiliary variable with a linear effect on the response.

x3

Continuous auxiliary variable with a nonlinear effect on the response.

lat

Latitude-like spatial coordinate.

lon

Longitude-like spatial coordinate.

vardir

Known sampling variance of the direct estimator.

theta

True small area parameter used to generate the direct estimator.

Examples

data(simulated_sae)
head(simulated_sae)

Summary method for geosae object

Description

Summary method for geosae object

Usage

## S3 method for class 'geosae'
summary(object, ...)

Arguments

Value

Invisibly returns the input object of class "geosae". The method prints model diagnostics, fixed-effect parameter estimates, smooth-term information, MSE and RMSE summaries, and model comparison results when available.