Intersectional Small Area Estimation from Survey and Census Data

Implements design-aware, margin-constrained estimation of population indicators for geographic areas crossed with demographic subgroups. Complex-survey microdata supply outcomes and association information, while one or more aggregate census tables supply overlapping population margins. A generalized iterative proportional fitting engine reconstructs a coherent latent population table, and an augmented model-assisted estimator produces domain means, proportions, and totals for sampled and unsampled intersections. Tools diagnose non-identification, compute linear-programming sensitivity bounds, propagate sampling and model uncertainty with replicate-weight or multiplier bootstrap procedures, enforce structural zeros, and benchmark estimates to official totals. The framework extends calibration ideas from Deville and Sarndal (1992) and small area estimation ideas from Fay and Herriot (1979) .

interSAE

interSAE implements joint margin-constrained intersectional small area estimation from complex-survey microdata and aggregate census margins.

The motivating problem is common in official statistics: a survey observes an outcome and several demographic variables, while published census tables give precise but overlapping margins rather than a full confidential microdata file. Direct survey estimates become unstable or unavailable after crossing a small geographic area with age, sex, residence, or another subgroup.

What the package does

1. Validates survey weights, strata, primary sampling units, and optional replicate weights.
2. Validates overlapping census tables and structural-zero declarations.
3. Reconstructs a coherent latent joint population table with generalized iterative proportional fitting.
4. Fits a survey-weighted Gaussian or binomial outcome model.
5. Produces augmented, model-assisted means, proportions, and totals.
6. Diagnoses the rank and nullity of the margin system.
7. Optionally computes linear-programming identification bounds and gamma sensitivity envelopes.
8. Refits the entire procedure under multiplier or supplied replicate weights.
9. Benchmarks domain estimates to an official aggregate.

Installation

install.packages("interSAE_0.1.0.tar.gz", repos = NULL, type = "source")

The core package uses only R recommended packages. Install lpSolve to compute identification bounds.

Minimal example

library(interSAE)

x <- inter_example()

design <- inter_design(
  x$survey,
  weights = "weight",
  area = "area",
  strata = "strata",
  psu = "psu"
)

margins <- census_margins(x$margins)

fit <- fit_inter_sae(
  unemployed ~ sex + age + residence + area,
  design = design,
  margins = margins,
  family = "binomial",
  domain = c("area", "sex")
)

inter_estimates(fit)
margin_diagnostics(fit)
check_identifiability(fit)

Optional sensitivity analysis:

if (requireNamespace("lpSolve", quietly = TRUE)) {
  inter_sensitivity(
    fit,
    gamma = c(1, 1.25, 1.5, 2, Inf),
    domain = list(area = "A1", sex = "Female")
  )
}

Interpretation

The fitted point estimate depends on the outcome model and on a coherent population reconstruction seeded by the weighted survey association structure. When aggregate margins do not identify the full joint table, the package says so explicitly. Identification bounds vary the latent joint table while holding published census margins fixed. Bootstrap intervals and identification bounds answer different questions and should be reported separately.

Scope of version 0.1.0

This release is a research implementation for categorical census dimensions and Gaussian or binary survey outcomes. It does not claim that aggregate margins alone identify a confidential joint population distribution. Applied work should document the outcome formula, structural zeros, sensitivity values, survey design, and benchmarking decisions.