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SpaCE: The Spatial Confounding Environment
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Introduces SpaCE, a Python toolkit and data collection of semi-synthetic spatial confounding benchmarks, with AutoML-fitted outcomes and GMRF residuals, and benchmarks several spatial and ML causal methods on them.
Problem
Evaluating causal inference methods that alleviate spatial confounding lacks realistic benchmark datasets with ground-truth counterfactuals, since confounders and counterfactuals are unobservable in real spatial data.
Approach
Generate semi-synthetic outcomes from real treatment and covariates using an AutoGluon ensemble with spatially-aware validation splits, sample exogenous residuals from a Gaussian Markov Random Field matching observed spatial autocorrelation, then mask spatial confounders to create benchmark datasets with smoothness and confounding scores.
Key results
- Across benchmark datasets, spatial+ achieves the lowest binary ATE error in high-smoothness settings (0.03 ± 0.03) while GMERR/spatial perform best on continuous ERF in several settings.
- Linear spatial baselines (GMERR, S2SLS) offer only very small improvement over OLS across environments, and GCNN underperforms linear models overall.
- Mixed-effects analysis indicates errors decrease with higher spatial smoothness and increase with higher confounding score for most baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use spatial+ instead of other evaluated baselines | Spatial confounding estimation · Binary-treatment datasets | ATE error | Helped |
| Use spatial+ instead of other evaluated baselines | Spatial confounding estimation · Continuous-treatment datasets | ERF error | Hurt |
| Use gmerror instead of other evaluated baselines | Spatial confounding estimation · Continuous-treatment datasets | ERF error | No clear effect |
| Use linear spatial regression baselines instead of OLS | Spatial confounding estimation · All environments | Causal estimation error | Helped |
| Use GCNN instead of linear spatial regression baselines | Spatial confounding estimation · Heat Exposure and Wildfires environments | Causal estimation error | Helped |
| Increase spatial smoothness | Evaluated spatial confounding baselines · Across datasets | Causal estimation error | Helped |
| Increase confounding score | Evaluated spatial confounding baselines · Across datasets | Causal estimation error | Hurt |
| Mask spatial confounders rather than use all confounders | OLS, XGBoost, and MLP · cdcsvi_nohsdp_poverty_cont | Estimation performance | Hurt |
| Use a spatially-aware train-validation split instead of a random split | AutoML predictive model · SpaCE environment generation | Validation performance | Helped |
Surprising findings
- Linear spatial regression baselines show only very small improvements over OLS across all environments.
- GCNN, despite being a neural network, performs worse than linear models overall, though it does better in two Heat Exposure and Wildfires environments.
Limitations
- Semi-synthetic outcomes use an additive noise model, which may not capture non-additive confounding in count or binary outcomes.
- Benchmark data are not designed to infer causal effects in the original real-world data sources, limiting their use for real causal conclusions.
- Interference between units is not addressed.
Experimental setup
Datasets: Social Vulnerability Index (CDC/ATSDR) Synthetic Medicare Data for Environmental Health Studies PRISM climate data NOAA data PM2.5 total and component datasets US broadband usage data US county election and demographic data
Benchmarks: SpaCE benchmark datasets (124 SpaceDatasets)
Metrics: absolute bias (ATE) root mean integrated squared error (ERF) PEHE (ITE)
Baselines: OLS XGBoost MLP S2SLS GMERR spatial spatial+ GCNN DAPSM
Builds on: AutoGluon PySAL Ray Tune Hydra
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