Package 'geoaddSAE2'

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

data	A data frame containing the direct estimates, known sampling variances, covariates, and spatial coordinates.
formula	A model formula giving the response variable on the left-hand side and covariates to be modelled linearly on the right-hand side. Use y ~ 1 if no linear covariates are used.
vardir	Unquoted name of the column containing the known sampling variances of the direct estimates.
nonlinear	Character vector containing the names of covariates to be modelled nonlinearly using P-splines.
spatial	Character vector of length two containing the names of the spatial coordinate variables, for example c("lat", "lon").
knots	Optional basis dimension for the nonlinear P-spline terms. If NULL, the basis dimension is selected automatically.
spatial_k	Optional basis dimension for the spatial thin plate regression spline. If NULL, the default from mgcv is used.
method	Smoothing-parameter estimation method passed to mgcv::gam. Currently, "REML" is used by default.
compare	Logical. If TRUE, Fay-Herriot and Spatial Fay-Herriot comparison models are also fitted. These comparison models require the optional sae package.
proxmat	Optional spatial proximity matrix used by the Spatial Fay-Herriot comparison model.
proxmat_k	Number of nearest neighbours used when constructing the spatial proximity matrix automatically. Default is 4.
B	Number of parametric bootstrap replications used to estimate the MSE. Default is 100.
seed	Optional integer seed for reproducibility.

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

x	An object of class geosae
digits	Number of decimal digits to print. Default 4.
...	Additional arguments passed to other methods.

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

object	An object of class geosae
...	Additional arguments passed to other methods.

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.

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