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Table 1 Summaries of spatial measurement errors

From: Spatial measurement errors in the field of spatial epidemiology

Classes Subclass Observed data Nonzero γs
Pure spatial location measurement errors Instrumental errors (e.g., global positioning systems errors) (L, Y0, X) γ 0, γ 6, γ 8
Non-instrumental errors: multiple address (L, Y0, X) γ 0, γ 6, γ 8
Non-instrumental errors: geocoding errors (L, Y, X) γ 0, γ 2, γ 3, γ6
Non-instrumental errors: outcome aggregations (L, Y, X) γ 0, γ 3, γ 4, γ8
Non-instrumental errors: covariate aggregations (L, Y0, X) γ 0, γ 6, γ8
Location-based outcome measurement errors Purely outcome measurement errors (L0, Y, X0) γ4
  Missing outcome measurement (L0, Y, X0) γ4
Location-based covariate measurement errors Location-based covariate measurement errors (L0, Y0, X) γ 6, γ 7, γ8
Covariate-Outcome spatial misaligned measurement errors Covariate-Outcome spatial misaligned measurement errors (L, Y, X) γ 0 , γ 4 , γ 6, γ 7, γ8
  1. L = L 0 + ΔL, where ΔL = γ 0L0 + γ 1Y + γ 2X + εL; Y = Y 0 + Δ Y, where ΔY = γ 3 L + γ 4 Y 0 + γ 5 X + εy; X = X 0 + ΔX, where ΔX = γ 6L + γ 7Y + γ 8X0 + εX. (L 0, Y 0, X 0), (L, Y, X) and (ΔL, ΔY, ΔX) are the true measures, observed values and measurement error of the outcome location, outcome, and covariate measures, respectively