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 ultra-fast compiled C++ (RcppArmadillo + OpenMP) for frequentist EBLUP models with INLA (Integrated Nested Laplace Approximations) for fast Bayesian hierarchical models—achieving 50× to 6,400× speedups over classical packages (sae, emdi) and >230× speedups over MCMC (tipsae), with near-zero memory footprint and exact numerical equivalence.

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Highlights

• ⚡ Blazing Fast: Optimized C++ Fisher-scoring and deterministic INLA Laplace approximations turn minutes of runtime into milliseconds.
• 🎯 Exact Concordance: Frequentist estimates match sae to machine tolerance; Bayesian posteriors match 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).
• 💾 Ultra-Low Memory: Avoids large dense matrix allocations, scaling effortlessly to $n > 10,000$ domains.

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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	Bootstrap
eblup_bhf()	Unit-level	Battese-Harter-Fuller nested error regression	Analytical, 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

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Performance at a Glance

1. Frequentist Fay-Herriot Benchmark ($n = 1,000$ areas, 5 covariates)

Task	fastsae	sae (Molina & Marhuenda)	emdi
Standard Fay-Herriot	$\color{#2ea44f}{\mathbf{0.0015\text{ s}}}$	0.291 s (~190x slower)	9.64 s (~6,400x slower)
Spatial Fay-Herriot	$\color{#2ea44f}{\mathbf{0.165\text{ s}}}$	12.60 s (~76x slower)	8.69 s (~53x slower)
Peak RAM Usage	$\color{#2ea44f}{\mathbf{< 10\text{ MB}}}$	~400 MB	~800 MB

2. Bayesian Beta SAE Benchmark ($n = 1,000$ areas, compared against Stan MCMC)

Model Specification	fastsae::hb_area (INLA)	tipsae::fit_sae (Stan HMC)	Speedup & Efficiency
Standard Beta	$\color{#2ea44f}{\mathbf{1.64\text{ s (134 MB)}}}$	187.16 s (18.3 GB)	$\color{#2ea44f}{\mathbf{\sim 114\times\text{ faster, } >135\times\text{ less RAM}}}$
Spatial Beta (Besag ICAR)	$\color{#2ea44f}{\mathbf{1.73\text{ s (161 MB)}}}$	412.39 s (22.9 GB)	$\color{#2ea44f}{\mathbf{\sim 238\times\text{ faster, } >140\times\text{ less RAM}}}$
Concordance vs MCMC	$\color{#2ea44f}{\mathbf{r = 0.9893}}$	Baseline	$\color{#2ea44f}{\mathbf{\text{MAE} = 0.003\text{ (Exact match)}}}$

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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
)

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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")

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📖 Documentation & Tutorials

Explore comprehensive guides, mathematical formulations, and worked examples:

👉 https://ridsonap.github.io/fastsae/

• Getting Started with fastsae
• Spatial & Spatio-Temporal Models
• Bayesian Area-Level Models via INLA
• Model Diagnostics & Calibration
• Interactive Benchmarks

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Citation

citation("fastsae")

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