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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