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Table 3 Relative root mean squared error and relative bias (in parenthesis) of parameter and impact estimators for scenarios I, J, K, L 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 I
NCM 4.78 10.43 2.06 3.75 4.53 2.20 9.50 5.10
(\(-\) 0.16) (\(-\) 0.58) (0.16) (\(-\) 0.04) (\(-\) 1.03) (0.18) (0.29) (0.23)
DME 7.28 13.66 2.54 4.47 8.26 2.60 13.68 7.03
(\(-\) 3.83) (\(-\) 3.11) (0.04) (0.01) (5.93) (\(-\) 0.67) (\(-\) 9.36) (\(-\) 4.65)
PDM 86.67 26.44 3.04 4.27 33.63 2.80 38.25 18.46
(\(-\) 86.65) (\(-\) 21.59) (2.04) (\(-\) 1.04) (32.90) (\(-\) 0.81) (0.02) (\(-\) 0.43)
SPDM 8.79 14.00 2.34 4.03 7.46 2.37 15.96 7.80
(\(-\) 6.44) (\(-\) 5.42) (0.41) (0.29) (5.13) (\(-\) 0.01) (\(-\) 12.24) (\(-\) 5.62)
CIP 11.97 13.99 2.39 4.05 18.79 2.63 20.11 10.07
(\(-\) 10.03) (\(-\) 6.56) (0.31) (0.20) (17.30) (\(-\) 1.03) (\(-\) 17.12) (\(-\) 8.40)
Scenario J
NCM 5.06 9.60 2.06 3.40 4.47 2.20 9.92 5.28
(\(-\) 0.50) (0.04) (\(-\) 0.02) (0.16) (\(-\) 0.53) (\(-\) 0.07) (\(-\) 0.52) (\(-\) 0.27)
DME 11.91 14.89 2.76 4.79 14.31 3.09 21.37 10.84
(\(-\) 9.78) (\(-\) 6.59) (0.24) (0.35) (12.56) (\(-\) 1.32) (\(-\) 18.71) (\(-\) 9.29)
PDM 85.89 28.55 3.36 4.17 36.13 3.06 31.53 15.58
(\(-\) 85.88) (\(-\) 24.18) (2.12) (\(-\) 0.57) (35.25) (\(-\) 1.08) (\(-\) 17.68) (\(-\) 8.68)
SPDM 14.99 16.94 2.66 4.27 13.40 2.73 26.63 12.72
(\(-\) 13.51) (\(-\) 10.34) (0.62) (0.67) (11.74) (\(-\) 0.33) (\(-\) 24.77) (\(-\) 11.53)
CIP 18.84 16.15 2.59 3.98 28.81 3.00 30.17 14.91
(\(-\) 17.59) (\(-\) 10.87) (0.65) (0.96) (27.80) (\(-\) 1.69) (\(-\) 28.63) (\(-\) 14.03)
Scenario K
NCM 4.89 9.31 2.02 3.55 4.42 2.09 9.43 4.97
(\(-\) 0.48) (0.20) (\(-\) 0.02) (0.13) (\(-\) 1.20) (\(-\) 0.06) (\(-\) 0.52) (\(-\) 0.27)
DME 38.47 38.15 5.21 8.66 36.57 5.80 53.69 26.64
(\(-\) 36.89) (\(-\) 30.17) (1.58) (1.74) (35.05) (\(-\) 3.31) (\(-\) 52.39) (\(-\) 25.80)
PDM 81.42 50.07 5.18 8.30 45.17 5.04 65.30 31.27
(\(-\) 81.29) (\(-\) 43.86) (2.43) (1.42) (43.80) (\(-\) 1.86) (\(-\) 63.47) (\(-\) 30.09)
SPDM 45.94 45.60 4.95 8.20 38.18 4.97 67.31 32.06
(\(-\) 44.76) (\(-\) 39.29) (1.69) (1.98) (36.70) (\(-\) 1.84) (\(-\) 66.77) (\(-\) 31.60)
CIP 44.04 34.64 3.41 4.47 52.76 3.57 59.21 28.69
(\(-\) 43.14) (\(-\) 31.81) (2.49) (2.29) (52.13) (\(-\) 2.76) (\(-\) 58.55) (\(-\) 28.33)
Scenario L
NCM 4.84 9.44 2.01 3.40 4.93 2.16 9.57 5.13
(\(-\) 0.27) (\(-\) 0.47) (0.01) (\(-\) 0.23) (\(-\) 0.60) (0.00) (\(-\) 0.07) (\(-\) 0.03)
DME 20.28 22.43 3.52 6.00 24.59 4.16 33.16 16.73
(\(-\) 18.59) (\(-\) 15.55) (0.47) (0.14) (22.91) (\(-\) 2.41) (\(-\) 31.33) (\(-\) 15.66)
PDM 84.05 38.60 4.28 5.87 40.73 4.02 50.74 24.49
(\(-\) 84.00) (\(-\) 34.50) (2.54) (\(-\) 0.43) (39.48) (\(-\) 1.16) (\(-\) 42.00) (\(-\) 19.87)
SPDM 29.18 29.64 3.50 5.48 25.88 3.48 47.55 22.48
(\(-\) 28.07) (\(-\) 24.61) (1.18) (0.57) (24.12) (\(-\) 0.88) (\(-\) 46.65) (\(-\) 21.85)
CIP 27.94 22.79 3.12 4.21 40.35 3.27 41.89 20.44
(\(-\) 26.98) (\(-\) 19.15) (1.76) (1.55) (39.58) (\(-\) 2.05) (\(-\) 40.91) (\(-\) 19.86)
  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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