fastsae: High-Performance Frequentist and Bayesian Small Area Estimation in R

fastsae provides a high-performance, unified framework for Small Area Estimation (SAE) in R. It combines compiled C++ (RcppArmadillo, OpenMP, sparse Cholesky factorisations for the spatial models) for frequentist EBLUP models with INLA (Integrated Nested Laplace Approximations) for Bayesian hierarchical models. It is orders of magnitude faster than classical packages (sae, emdi) and MCMC (tipsae) at realistic numbers of domains (see the benchmarks below), and reproduces the sae estimates where both use the same method.

Highlights

⚡ Blazing Fast: Optimized C++ Fisher-scoring and deterministic INLA Laplace approximations turn minutes of runtime into milliseconds.
🎯 Validated Against Reference Packages: REML estimates and analytical MSEs agree with sae for interior estimates; deliberate, documented differences where sae is not valid (e.g. $\hat\rho$ on the boundary, ML information for ML). Bayesian posteriors agree closely with Stan HMC ($r = 0.989$).
🔀 Unified Interface: Common S3 workflow (summary, coef, fitted, residuals, autoplot, compare_sae) for both paradigms.
🧵 Multi-Threaded Bootstrap: OpenMP-accelerated parametric and non-parametric bootstrap MSE.
🗺️ Comprehensive Spatial & Temporal: SAR, Besag ICAR, BYM2, Spatial Lag, AR(1), and RW(1/2).
💾 Low Memory: Structured and sparse linear algebra instead of dense $D \times D$ inverses (spatial FH with a few thousand domains runs in seconds).

Supported Models

Frequentist EBLUP (C++ / OpenMP)

Function	Model Level	Structure	MSE Estimation
`eblup_fh()`	Area-level	Standard Fay-Herriot with IID domain effects	Analytical (Prasad-Rao)
`eblup_sfh()`	Area-level	Spatial SAR(1) autoregressive effects	Analytical, Bootstrap
`eblup_stfh()`	Area-level	Spatio-temporal SAR(1) + AR(1) dynamics	Analytical, Bootstrap
`eblup_bhf()`	Unit-level	Battese-Harter-Fuller nested error regression	Bootstrap

Bayesian Hierarchical Models (INLA)

Function	Model Level	Distributions	Random Effects
`hb_area()`	Area-level	Gaussian, Beta, Binomial, Poisson, NegBin, Gamma	IID, BYM2, Besag ICAR, RW(1/2), AR(1)
`hb_unit()`	Unit-level	Gaussian	Unit-level nested error

Performance at a Glance

1. Frequentist EBLUP with analytical MSE

Model ($n = 1,000$ domains, 5 covariates)	`fastsae`	`sae`	`emdi`
Fay-Herriot	0.00119 s (0.503 MB)	1.50 s (72.0 MB; 1,263x slower)	51.0 s (3.69 GB; 42,874x slower)
Spatial Fay-Herriot	1.00 s (0.203 MB)	67.2 s (1.88 GB; 67x slower)	51.1 s (3.68 GB; 51x slower)
Spatio-Temporal FH ($T = 5$)	75.3 s (3.29 MB)	1790 s (31.7 GB; 24x slower)	-

2. Bayesian Beta models: INLA vs Stan MCMC (largest $n$ benchmarked)

Model	$n$	`fastsae::hb_area` (INLA)	`tipsae::fit_sae` (Stan)	Speedup
Beta	1,000	1.61 s (25.9 MB)	187 s (17.9 GB)	117x
Spatial Beta (Besag ICAR)	1,000	1.87 s (161 MB)	404 s (22.5 GB)	217x
Spatio-Temporal Beta (Besag + RW1, $T = 5$)	50	1.71 s (17.1 MB)	908 s (4.77 GB)	530x

Times are medians of bench::mark(); memory is the total memory allocated by R during one call (bench::mark()$mem_alloc), not the peak resident memory. The fastsae rows were re-measured with fastsae 1.0.0 (frequentist on 2026-10-13, benchmarks/bench_frequentist_fastsae.R; Bayesian on 2026-10-14, benchmarks/bench_bayes_fastsae.R); the sae/emdi rows come from an earlier run of the same design (simulated data, 5 covariates) on different random draws, the tipsae rows from an earlier run on the same data. See the benchmark article for all sizes.

Installation

Install from CRAN:

install.packages("fastsae")

Or install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("ridsonap/fastsae")

To enable Bayesian models, install INLA:

install.packages(
  "INLA",
  repos = c(getOption("repos"), INLA = "https://inla.r-inla-download.org/R/stable"),
  dep = TRUE
)

Quick Start

library(fastsae)

# 1. Frequentist Fay-Herriot (C++)
fit_fh <- eblup_fh(y ~ x1 + x2 + x3, vardir = ~vardir, data = na.omit(mys))
summary(fit_fh)

# 2. Diagnostic & Visualization
autoplot(fit_fh, type = "estimates")

📖 Documentation & Tutorials

Explore comprehensive guides, mathematical formulations, and worked examples:

👉 https://ridsonap.github.io/fastsae/

Citation

citation("fastsae")

Bug reports and feature requests are welcome on the issue tracker.