{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:3ZMXAFOVNGYVZ3HG4U4ZOHJB67","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6aff46ea58b30627cbec56fb82f6ef5fb91c28761204afdc853cb2470ce51b43","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-12T05:14:38Z","title_canon_sha256":"3d9387962d14298c2f098a9b10e885f2492e2dc967adf0311515095df1613b5b"},"schema_version":"1.0","source":{"id":"2505.07232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07232","created_at":"2026-08-18T01:11:47Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07232v2","created_at":"2026-08-18T01:11:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07232","created_at":"2026-08-18T01:11:47Z"},{"alias_kind":"pith_short_12","alias_value":"3ZMXAFOVNGYV","created_at":"2026-08-18T01:11:47Z"},{"alias_kind":"pith_short_16","alias_value":"3ZMXAFOVNGYVZ3HG","created_at":"2026-08-18T01:11:47Z"},{"alias_kind":"pith_short_8","alias_value":"3ZMXAFOV","created_at":"2026-08-18T01:11:47Z"}],"graph_snapshots":[{"event_id":"sha256:c0938612d8905c6574d60873baaa77f77a1fdefdaf4d1faca74c7f81ebe8eb4f","target":"graph","created_at":"2026-08-18T01:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.07232/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate spatial confounding in the presence of multivariate disease dependence. In the \"analysis model perspective\" of spatial confounding, adding a spatially dependent random effect can lead to significant variance inflation of the posterior distribution of the fixed effects. The \"data generation perspective\" views covariates as stochastic and correlated with an unobserved spatial confounder, leading to inferior statistical inference over multiple realizations. Although multiple methods have been proposed for adjusting statistical models to mitigate spatial confounding in estimating re","authors_text":"Kyle Lin Wu, Sudipto Banerjee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-12T05:14:38Z","title":"Spatial Confounding in Multivariate Areal Data Analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07232","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cc15a4a62e7d647bdc8f1ed95ce56844250302791ab75f9bbaafbdd484ee6b21","target":"record","created_at":"2026-08-18T01:11:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6aff46ea58b30627cbec56fb82f6ef5fb91c28761204afdc853cb2470ce51b43","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ME","submitted_at":"2025-05-12T05:14:38Z","title_canon_sha256":"3d9387962d14298c2f098a9b10e885f2492e2dc967adf0311515095df1613b5b"},"schema_version":"1.0","source":{"id":"2505.07232","kind":"arxiv","version":2}},"canonical_sha256":"de597015d569b15cece6e539971d21f7c1d9f84c9f6699de2549ceb16bbe85ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de597015d569b15cece6e539971d21f7c1d9f84c9f6699de2549ceb16bbe85ca","first_computed_at":"2026-08-18T01:11:47.401260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-18T01:11:47.401260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k0amzdkcvyOOgWEnY5G8Y4ceCP3RdO1GaVqaBfGgEYmCVnlGytyEgA7jL9KrL83M8RCn9R1ghW98EE+qk2v8BA==","signature_status":"signed_v1","signed_at":"2026-08-18T01:11:47.403320Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.07232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc15a4a62e7d647bdc8f1ed95ce56844250302791ab75f9bbaafbdd484ee6b21","sha256:c0938612d8905c6574d60873baaa77f77a1fdefdaf4d1faca74c7f81ebe8eb4f"],"state_sha256":"951d1cd5f1dde72a881c4b6ff1c29a9dfd5738fb4d34e820ba40f98d952622a2"}