A unified framework for estimating direct causal effect under spatial confounding and interference, with the R package spaci
Abstract
Estimating causal effects is challenging with observational data due to the lack of exchangeability, and is further complicated with spatial data. In real-life applications such as agricultural and environmental studies, unobserved spatial factors (spatial confounding, SC) and interactions of units in nearby locations (spatial interference, SI) commonly occur jointly, yet existing parametric methods address them separately. We develop a unified framework that treats both simultaneously. We first define the estimand precisely and give an identification result. We then study two estimators. The matching estimator iDAPS integrates neighbourhood exposure and spatial proximity into propensity score matching with balance-optimised weights. We prove a variogram bias bound showing its confounding bias is controlled by the spatial variability of the confounder at the matched distance; this justifies the composite metric, yields a consistency result, and provides a computable diagnostic. The doubly robust estimator recoverU+ augments the propensity and outcome models with the recovered confounder and the exposure; we prove it is doubly robust up to an explicit residual bias from the unrecoverable confounder component. We show that independence-based standard errors are anticonservative under spatial dependence; we provide spatial heteroskedasticity and autocorrelation consistent (HAC), block-bootstrap, and randomisation-based alternatives whose calibration we verify. Every theoretical result is validated numerically. Estimating the effect of selective catalytic and non-catalytic reduction (SCR/SNCR) technologies on ambient ozone reveals no evidence of ozone reduction, while a naive analysis would have delivered a confidently wrong sign. All methods are implemented in the developed open-source R package spaci.
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BibTeX
@misc{ogunsola2026unified,
title = {{A unified framework for estimating direct causal effect under spatial confounding and interference, with the R package spaci}},
author = {Isqeel Ogunsola and Olatunji Johnson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28799},
eprint = {2609.28799},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28799},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A unified framework for estimating direct causal effect under spatial confounding and interference, with the R package spaci
AU - Isqeel Ogunsola
AU - Olatunji Johnson
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28799
UR - https://arxiv.org/abs/2609.28799
AB - Estimating causal effects is challenging with observational data due to the lack of exchangeability, and is further complicated with spatial data. In real-life applications such as agricultural and environmental studies, unobserved spatial factors (spatial confounding, SC) and interactions of units in nearby locations (spatial interference, SI) commonly occur jointly, yet existing parametric methods address them separately. We develop a unified framework that treats both simultaneously. We first define the estimand precisely and give an identification result. We then study two estimators. The matching estimator iDAPS integrates neighbourhood exposure and spatial proximity into propensity score matching with balance-optimised weights. We prove a variogram bias bound showing its confounding bias is controlled by the spatial variability of the confounder at the matched distance; this justifies the composite metric, yields a consistency result, and provides a computable diagnostic. The doubly robust estimator recoverU+ augments the propensity and outcome models with the recovered confounder and the exposure; we prove it is doubly robust up to an explicit residual bias from the unrecoverable confounder component. We show that independence-based standard errors are anticonservative under spatial dependence; we provide spatial heteroskedasticity and autocorrelation consistent (HAC), block-bootstrap, and randomisation-based alternatives whose calibration we verify. Every theoretical result is validated numerically. Estimating the effect of selective catalytic and non-catalytic reduction (SCR/SNCR) technologies on ambient ozone reveals no evidence of ozone reduction, while a naive analysis would have delivered a confidently wrong sign. All methods are implemented in the developed open-source R package spaci.
ER -