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Table 1 Relative root mean squared error and relative bias (in parenthesis) of parameter and impact estimators for scenarios A, B, C, D 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 A
NCM 4.78 10.40 2.29 3.85 4.20 2.43 9.57 5.22
(\(-\) 0.40) (\(-\) 0.70) (-0.11) (-0.15) (-0.59) (-0.14) (-0.46) (-0.28)
DME 23.74 24.58 3.99 6.16 25.41 4.59 37.50 18.81
(\(-\) 22.25) (\(-\) 17.98) (0.68) (0.28) (24.09) (\(-\) 2.57) (\(-\) 36.00) (\(-\) 17.89)
PDM 83.95 39.36 4.13 5.88 40.72 4.11 49.03 23.78
(\(-\) 83.89) (\(-\) 34.71) (2.00) (\(-\) 0.02) (39.54) (\(-\) 1.67) (\(-\) 43.44) (\(-\) 20.82)
SPDM 29.67 30.19 3.80 5.80 25.70 3.97 48.34 23.10
(\(-\) 28.50) (\(-\) 24.85) (0.74) (0.82) (24.23) (\(-\) 1.33) (\(-\) 47.44) \(-\) 22.46
CIP 33.01 27.50 3.14 4.57 44.09 3.77 47.87 23.46
(\(-\) 32.11) (\(-\) 23.75) (1.48) (1.36) (43.36) (\(-\) 2.61) (\(-\) 47.06) (\(-\) 22.98)
Scenario B
NCM 9.84 9.93 2.17 3.50 4.51 2.20 13.81 4.63
(\(-\) 0.19) (\(-\) 0.63) (\(-\) 0.05) (\(-\) 0.23) (\(-\) 0.85) (\(-\) 0.03) (0.22) (0.04)
DME 29.15 17.39 3.18 5.01 9.79 3.42 36.19 11.44
(\(-\) 25.81) (\(-\) 9.36) (\(-\) 0.22) (0.06) (7.32) (\(-\) 1.27) (\(-\) 32.69) (\(-\) 10.08)
PDM 84.15 20.88 3.06 4.87 12.89 3.35 49.32 15.05
(\(-\) 84.05) (\(-\) 14.62) (0.00) (\(-\) 0.23) (10.99) (\(-\) 1.16) (\(-\) 45.28) (\(-\) 13.53)
SPDM 36.51 19.10 3.00 4.84 9.71 3.19 47.20 14.26
(\(-\) 34.22) (\(-\) 12.70) (\(-\) 0.18) (0.38) (7.33) (\(-\) 0.96) (\(-\) 45.38) (\(-\) 13.42)
CIP 38.88 17.78 2.26 3.62 14.22 2.71 46.52 14.27
(\(-\) 36.64) (\(-\) 13.23) (\(-\) 0.19) (\(-\) 0.18) (13.07) (\(-\) 1.50) (\(-\) 44.43) (\(-\) 13.54)
Scenario C
NCM 2.42 10.99 2.21 3.76 4.92 2.36 7.79 5.54
(\(-\) 0.34) (\(-\) 0.93) (\(-\) 0.20) (\(-\) 0.13) (\(-\) 0.86) (\(-\) 0.33) (\(-\) 0.91) (\(-\) 0.70)
DME 17.58 42.81 4.86 8.64 58.44 7.08 43.65 30.03
(\(-\) 16.66) (\(-\) 33.12) (2.04) (1.03) (56.86) (\(-\) 5.79) (\(-\) 42.98) (\(-\) 29.48)
PDM 84.69 86.62 8.58 8.46 109.38 5.54 48.59 32.33
(\(-\) 84.66) (\(-\) 81.77) (7.35) (2.63) (108.13) (\(-\) 2.27) (\(-\) 40.87) (\(-\) 26.86)
SPDM 22.30 51.97 5.29 7.21 59.68 4.53 51.00 33.02
(\(-\) 21.60) (\(-\) 44.62) (3.24) (2.08) (57.89) (\(-\) 0.96) (\(-\) 50.39) (\(-\) 32.45)
CIP 28.41 49.80 6.70 7.43 110.29 5.39 53.90 36.01
(\(-\) 27.92) (\(-\) 45.83) (5.81) (5.18) (109.49) (\(-\) 4.42) (\(-\) 53.50) (\(-\) 35.69)
Scenario D
NCM 6.35 14.79 3.30 4.97 4.87 3.30 12.12 6.51
(\(-\) 0.76) (0.69) (0.37) (0.54) (\(-\) 0.80) (0.30) (\(-\) 0.42) (\(-\) 0.03)
DME 24.23 27.68 5.00 7.58 15.30 5.13 37.42 18.65
(\(-\) 21.96) (\(-\) 16.14) (1.15) (1.23) (13.30) (\(-\) 2.06) (\(-\) 35.01) (\(-\) 17.16)
PDM 84.20 39.79 5.34 7.35 25.13 4.86 48.32 23.31
(\(-\) 84.14) (\(-\) 31.45) (2.56) (0.82) (23.89) (\(-\) 1.18) (\(-\) 42.58) (\(-\) 20.15)
SPDM 30.77 31.76 4.79 7.48 16.03 4.60 48.73 23.08
(\(-\) 29.17) (\(-\) 22.53) (1.40) (1.84) (14.30) (\(-\) 0.77) (\(-\) 47.46) (\(-\) 22.17)
CIP 34.08 29.41 4.20 6.01 27.21 4.12 48.42 23.50
(\(-\) 32.67) (\(-\) 22.32) (2.03) (2.09) (26.27) (\(-\) 2.09) (\(-\) 47.14) (\(-\) 22.74)
  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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