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Table 3 Estimation of the ecological link β when E ¯ h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGfbqrgaqeamaaBaaaleaacqWGObaAaeqaaaaa@2F5C@ = 23.35 and ρ xx = 0.90, 0.95, 0.98

From: Robustness of the BYM model in absence of spatial variation in the residuals

(1)(2)(3)(4)(5)(6)(7)(8)(*)
ρ xx (1) β Model β ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqeaaaa@2E6C@ sim (2) σ ¯ β s i m MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFdpWCgaqeamaaBaaaleaacqWFYoGydaWgaaadbaGaem4CamNaemyAaKMaemyBa0gabeaaaSqabaaaaa@34BB@ MB(4) sd(MB) sd(β sim )(5) RMSE(6) π(β)(7) 1 - π(0)(8)
0.90 0.00 M 0 0.003 2.96    2.98 2.99 0.945 0.055*
   BYM 0.003 3.39    3.03 3.04 0.970 0.030
  0.12 M 0 0.122 2.98 2.07 1.24 2.99 3.00 0.958 0.973*
   BYM 0.123 3.44 2.51 1.27 3.07 3.08 0.973 0.938
  0.21 M 0 0.213 2.96 1.38 0.79 3.32 3.34 0.930 0.998
   BYM 0.213 3.41 1.31 0.81 3.41 3.42 0.955 0.998
  0.33 M 0 0.331 2.98 0.37 0.47 3.11 3.11 0.943 1.000
   BYM 0.331 3.43 0.39 0.47 3.13 3.13 0.965 1.000
0.95 0.00 M 0 0.002 4.07    4.04 4.04 0.950 0.050*
   BYM 0.002 4.72    4.14 4.14 0.975 0.025
  0.12 M 0 0.121 4.05 1.03 1.82 4.38 4.37 0.945 0.843*
   BYM 0.121 4.70 1.18 1.89 4.54 4.54 0.960 0.775
  0.21 M 0 0.208 3.99 -1.07 0.99 4.18 4.18 0.960 0.988
   BYM 0.208 4.62 -0.80 1.03 4.31 4.31 0.978 0.983
  0.33 M 0 0.333 4.16 0.78 0.66 4.33 4.33 0.963 1.000
   BYM 0.333 4.80 0.98 0.66 4.34 4.35 0.980 1.000
0.98 0.00 M 0 0.002 6.29    6.48 6.48 0.950 0.050*
   BYM 0.002 7.29    6.53 6.53 0.970 0.030
  0.12 M 0 0.121 6.23 1.22 2.49 5.98 5.98 0.953 0.545*
   BYM 0.122 7.20 1.26 2.47 5.99 5.98 0.975 0.420
  0.21 M 0 0.207 6.35 -1.36 1.57 6.61 6.60 0.960 0.845*
   BYM 0.207 7.35 -1.39 1.59 6.67 6.67 0.985 0.782
  0.33 M 0 0.330 6.27 0.09 1.00 6.64 6.63 0.935 0.985
   BYM 0.331 7.28 0.24 1.01 6.69 6.68 0.975 0.978
  1. (1) ρ xx : autocorrelation at 100 km
  2. (2) β ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqeaaaa@2E6C@ sim : 100 * mean of posterior means
  3. (3) σ ¯ β s i m MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFdpWCgaqeamaaBaaaleaacqWFYoGydaWgaaadbaGaem4CamNaemyAaKMaemyBa0gabeaaaSqabaaaaa@34BB@ : 100 * mean of posterior standard deviations
  4. (4)MB : 100 * Mean Bias
  5. (5) sd(β sim ) : 100 * standard deviation of posterior means
  6. (6)RMSE : 100 * Root Mean Square Error
  7. (7) π(β) : Coverage proportion β CI(β)
  8. (8) 1 - π(0) : Non-Coverage proportion 0 CI(β)
  9. (*) : Indicator of p-value < 5% from McNemar's test (1)(2)(3) for comparing proportions 1 - π(0) under M0 and BYM models.