Table 1.
Summaries of spatial measurement errors
| 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 |
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