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Table 2 Relative root mean squared error and relative bias (in parenthesis) of parameter and impact estimators for scenarios E, F, G, H of Monte Carlo simulations (see Sect. 4) for various estimation methods

From: Reduced-bias estimation of spatial autoregressive models with incompletely geocoded data

Method \(\rho \) \(\beta _0\) \(\beta _1\) \(\beta _2\) \(\sigma \) \(D(\beta _1)\) \(M(\beta _1)\) \(T(\beta _1)\)
Scenario E
NCM 3.42 7.01 1.47 2.36 3.44 1.52 6.68 3.52
(\(-\) 0.17) (\(-\) 0.20) (0.03) (\(-\) 0.07) (\(-\) 0.70) (0.02) (\(-\) 0.08) (\(-\) 0.02)
DME 26.50 24.73 3.36 5.17 25.81 3.46 40.36 19.73
(\(-\) 25.62) (\(-\) 20.79) (1.87) (2.65) (24.89) (\(-\) 2.09) (\(-\) 39.42) (\(-\) 19.14)
PDM 85.04 34.12 4.10 7.02 41.29 2.95 37.40 17.85
(\(-\) 85.02) (\(-\) 31.62) (3.18) (5.72) (40.67) (\(-\) 0.21) (\(-\) 26.80) (\(-\) 12.35)
SPDM 29.77 26.93 3.17 4.97 25.99 2.68 47.67 22.28
(\(-\) 29.01) (\(-\) 23.84) (1.94) (2.86) (25.02) (\(-\) 0.65) (\(-\) 47.01) (\(-\) 21.83)
CIP 33.62 24.32 2.96 5.52 40.96 2.91 48.02 23.23
(\(-\) 33.00) (\(-\) 21.96) (2.34) (4.48) (40.44) (\(-\) 2.26) (\(-\) 47.43) (\(-\) 22.90)
Scenario F
NCM 2.66 5.59 1.10 1.65 2.14 1.15 5.18 2.74
(\(-\) 0.17) (0.18) (\(-\) 0.03) (0.14) (0.12) (\(-\) 0.04) (\(-\) 0.23) (\(-\) 0.13)
DME 26.43 24.93 2.27 3.90 24.32 3.20 40.64 20.07
(\(-\) 25.93) (\(-\) 23.09) (1.17) (2.37) (23.91) (\(-\) 2.59) (\(-\) 40.15) (\(-\) 19.79)
PDM 88.26 43.37 3.51 5.57 39.51 2.49 55.11 26.31
(\(-\) 88.25) (\(-\) 42.31) (3.10) (4.85) (39.22) (\(-\) 1.85) (\(-\) 54.37) (\(-\) 25.90)
SPDM 31.69 30.18 2.24 3.73 23.90 2.07 50.01 23.64
(\(-\) 31.37) (\(-\) 28.95) (1.53) (2.75) (23.52) (\(-\) 1.28) (\(-\) 49.78) (\(-\) 23.49)
CIP 33.96 26.72 2.81 5.00 36.06 2.38 48.42 23.29
(\(-\) 33.67) (\(-\) 25.60) (2.49) (4.55) (35.86) (\(-\) 2.00) (\(-\) 48.15) (\(-\) 23.14)
Scenario G
NCM 4.67 10.23 2.14 3.72 4.36 2.18 9.09 4.82
(\(-\) 0.10) (0.27) (0.01) (\(-\) 0.02) (\(-\) 0.86) (0.03) (0.22) (0.12)
DME 21.86 24.29 3.66 5.96 24.63 4.08 35.26 17.55
(\(-\) 20.49) (\(-\) 17.05) (0.84) (0.33) (23.43) (\(-\) 2.12) (\(-\) 33.81) (\(-\) 16.64)
PDM 80.09 33.36 3.67 5.86 37.55 3.72 46.57 22.36
(\(-\) 80.05) (\(-\) 27.57) (1.55) (0.81) (36.58) (\(-\) 1.32) (\(-\) 44.73) (\(-\) 21.21)
SPDM 27.07 29.30 3.56 5.75 24.73 3.50 45.52 21.30
(\(-\) 26.00) (\(-\) 23.52) (1.15) (0.85) (23.40) (\(-\) 0.34) (\(-\) 44.62) (\(-\) 20.63)
CIP 31.00 25.80 2.95 4.30 41.10 3.57 45.71 22.40
(\(-\) 30.14) (\(-\) 21.94) (1.43) (1.28) (40.46) (\(-\) 2.40) (\(-\) 44.85) (\(-\) 21.86)
Scenario H
NCM 5.04 10.24 2.11 3.85 4.58 2.19 9.70 5.14
(\(-\) 0.48) (\(-\) 1.40) (0.05) (\(-\) 0.19) (\(-\) 1.01) (0.01) (\(-\) 0.42) (\(-\) 0.19)
DME 24.43 27.55 3.63 6.04 24.82 4.26 38.00 19.01
(\(-\) 22.95) (\(-\) 21.33) (0.90) (0.13) (23.33) (\(-\) 2.63) (\(-\) 36.53) (\(-\) 18.17)
PDM 89.09 50.58 4.86 5.73 43.11 4.09 54.25 26.19
(\(-\) 89.06) (\(-\) 46.77) (3.27) (\(-\) 1.09) (42.11) (\(-\) 1.71) (\(-\) 48.39) (\(-\) 23.10)
SPDM 31.01 33.33 3.50 5.69 25.33 3.56 49.13 23.46
(\(-\) 29.85) (\(-\) 28.52) (1.26) (0.54) (23.89) (\(-\) 1.41) (\(-\) 48.23) (\(-\) 22.86)
CIP 32.87 27.86 3.04 4.67 44.74 3.34 47.38 23.09
(\(-\) 31.94) (\(-\) 24.23) (1.86) (1.34) (44.01) (\(-\) 2.34) (\(-\) 46.54) (\(-\) 22.59)
  1. Direct (D), indirect (M) and total (T) impact estimates refer to the second regressor (whose coefficient is \(\beta _1\)). All values are multiplied by 100
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