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Table 4 Estimation of the ecological link β when ρ xx = 0.95 while E ¯ h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGfbqrgaqeamaaBaaaleaacqWGObaAaeqaaaaa@2F5C@ varying

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

(1)(2)(3)(4)(5)(6)(7)(8)(*)
E ¯ h MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWGfbqrgaqeamaaBaaaleaacqWGObaAaeqaaaaa@2F5C@ β Model β ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqeaaaa@2E6C@ sim (1) σ ¯ β s i m MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFdpWCgaqeamaaBaaaleaacqWFYoGydaWgaaadbaGaem4CamNaemyAaKMaemyBa0gabeaaaSqabaaaaa@34BB@ MB(3) sd(MB) sd(β sim )(4) RMSE(5) π(β)(6) 1 - π(0)(7)
46.6 0.00 M 0 -0.001 2.84    2.76 2.76 0.958 0.042*
   BYM -0.001 3.40    2.85 2.85 0.975 0.025
  0.12 M 0 0.118 2.81 -1.34 1.21 2.91 2.91 0.945 0.960*
   BYM 0.119 3.38 -1.18 1.21 2.91 2.91 0.980 0.930
  0.21 M 0 0.212 2.87 0.94 0.69 2.89 2.89 0.955 1.000
   BYM 0.212 3.47 0.75 0.70 2.95 2.96 0.983 1.000
  0.33 M 0 0.329 2.88 -0.21 0.47 3.10 3.10 0.953 1.000
   BYM 0.330 3.45 -0.08 0.48 3.19 3.19 0.980 1.000
23.3 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 4.34 0.963 1.000
   BYM 0.333 4.79 0.98 0.66 4.34 4.35 0.980 1.000
2.33 0.00 M 0 0.007 12.4    13.5 13.4 0.935 0.065
   BYM 0.008 13.3    13.4 13.4 0.948 0.052
  0.12 M 0 0.112 12.5 -6.94 5.38 12.9 12.9 0.953 0.162*
   BYM 0.113 13.4 -5.65 5.43 13.0 13.0 0.965 0.130
  0.21 M 0 0.206 12.8 -1.92 3.45 14.5 14.5 0.927 0.410*
   BYM 0.206 13.8 -1.98 3.46 14.6 14.5 0.940 0.368
  0.33 M 0 0.341 13.0 3.38 2.12 14.00 14.0 0.938 0.738*
   BYM 0.343 13.9 4.05 2.14 14.1 14.2 0.960 0.715
  1. (1) β ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFYoGygaqeaaaa@2E6C@ sim : 100 * mean of posterior means
  2. (2) σ ¯ β s i m MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaaiiGacuWFdpWCgaqeamaaBaaaleaacqWFYoGydaWgaaadbaGaem4CamNaemyAaKMaemyBa0gabeaaaSqabaaaaa@34BB@ : 100 * mean of posterior standard deviations
  3. (3) MB : 100 * Mean Bias
  4. (4) sd(β sim ) : 100 * standard deviation of posterior means
  5. (5) RMSE : 100 * Root Mean Square Error
  6. (6)π(β) : Coverage proportion β CI(β)
  7. (7) 1 - π(0) : Non-Coverage proportion 0 CI(β)
  8. (*) : Indicator of p-value < 5% from McNemar's test for comparing proportions 1 - π(0) under M0 and BYM models.