{"paper":{"title":"Embracing Spillover: Spatial Effects in Experiments","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Jack Fraser-Govil, Kieran DeWalt, Penny Hancock, Samuel I. Watson, Thomas A. Smith","submitted_at":"2026-07-07T17:08:54Z","abstract_excerpt":"Interventions delivered in space generate effects that spill over between experimental units. We develop a framework for spatial experiments in which causal estimands, inclduing direct, indirect, total, and dose--response effects, are linear functionals of a spillover kernel. Under cluster randomisation with a fixed exposure set size, the data identify the shape of the kernel but not its level: the level is aliased with the intercept and direct effect, at any sample size and under any outcome model. Every estimator therefore rests on an anchoring assumption that fixes the level. We derive an e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06506","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06506/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}