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Table 2 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 = 0.0, 0.4 (400 replications)

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

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)
0.0 0.00 M 0 0.000 1.63    1.73 1.73 0.953 0.047
   BYM 0.000 1.76    1.74 1.73 0.958 0.042
  0.12 M 0 0.119 1.61 -0.44 0.69 1.67 1.67 0.930 1.000
   BYM 0.120 1.72 -0.31 0.70 1.68 1.68 0.955 1.000
  0.21 M 0 0.210 1.60 0.49 0.39 1.64 1.64 0.948 1.000
   BYM 0.210 1.72 0.58 0.39 1.66 1.66 0.960 1.000
  0.33 M 0 0.329 1.57 -0.28 0.23 1.58 1.58 0.953 1.000
   BYM 0.329 1.70 -0.24 0.24 1.58 1.58 0.968 1.000
0.4 0.00 M 0 -0.001 1.72    1.76 1.76 0.955 0.045*
   BYM -0.001 1.90    1.78 1.78 0.975 0.025
  0.12 M 0 0.121 1.73 0.79 0.73 1.75 1.75 0.945 1.000
   BYM 0.121 1.91 0.78 0.74 1.78 1.78 0.968 1.000
  0.21 M 0 0.211 1.72 0.41 0.39 1.66 1.66 0.958 1.000
   BYM 0.211 1.90 0.50 0.39 1.67 1.67 0.973 1.000
  0.33 M 0 0.332 1.70 0.71 0.25 1.68 1.69 0.945 1.000
   BYM 0.332 1.89 0.70 0.25 1.70 1.71 0.973 1.000
  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.