Spatial Propensity Score Weighting

Standard IPTW estimates the propensity score from individual covariates alone and ignores geography. Spatial PSW adds spatially referenced variables — location coordinates, area-level characteristics, spatial lag terms — to the propensity score model, and adjusts inference for spatial autocorrelation. This reduces bias from geographic confounding that standard IPTW would leave unaddressed.

Include covariates that predict treatment assignment and are spatially structured: area-level demographics, distance to infrastructure, spatial lag of the outcome or treatment, or geographic coordinates (e.g., via spline terms). The goal is to absorb location-based differences in treatment probability that would otherwise confound the causal estimate.

After computing weights, examine standardized mean differences for all covariates (including spatial ones) in the weighted sample. Additionally, map the geographic distribution of weighted treated and control units, and optionally compute a weighted version of Moran's I to test whether spatial clustering of treatment assignment has been reduced.

Use spatially robust standard errors such as Conley (1999) spatial HAC standard errors, which allow for correlation among units within a geographic bandwidth, or cluster-robust standard errors at a meaningful geographic unit (county, grid cell). Ordinary or heteroskedasticity-only robust SEs will understate uncertainty when residual spatial autocorrelation remains.

Not directly. Standard spatial PSW inherits the stable unit treatment value assumption (SUTVA) from IPTW, meaning it assumes no interference between units. If spatial spillovers are substantial, the causal estimand must be redefined (e.g., direct and spillover effects), and more specialized methods for interference are needed.