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Table 2 Posterior summary statistics of the different models

From: A practical illustration of spatial smoothing methods for disconnected regions with INLA: spatial survey on overweight and obesity in Malaysia

 

Model I

Model II

Model III

Model IVa

Model IVb

Model Va

Model Vb

Mean (95% Credible interval)

Mean (95% Credible interval)

Mean (95% Credible interval)

Mean (95% Credible interval)

Mean (95% Credible interval)

Mean (95% Credible interval)

Mean (95% Credible interval)

Intercept

       

 Malaysia

− 1.192 (− 1.297, − 1.085)

− 1.174 (− 1.261, − 1.087)

 

− 1.173 (− 1.262, − 1.084)

   

 Borneo

  

− 1.208 (− 1.421, − 0.996)

 

− 1.205 (− 1.421, − 0.986)

− 1.205 (− 1.427, − 0.983)

 

 Peninsular

  

− 1.167 (− 1.263, − 1.070)

 

− 1.166 (− 1.265, − 1.067)

 

− 1.167 (− 1.261, − 1.072)

Variance

       

 Malaysia

       

  Structured REa

0.109 (0.001, 0.780)

0.020 (0.002, 0.079)

0.019 (0.002, 0.074)

    

  Unstructured REa

0.082 (0.033, 0.160)

0.066 (0.021, 0.147)

0.069 (0.024, 0.148)

    

 Borneo

       

  Structured REa

   

0.033 (0.020, 0.040)

0.023 (0.018, 0.025)

0.071 (0.006, 0.363)

 

  Unstructured REa

   

0.051 (0.038, 0.099)

0.051 (0.036, 0.077)

0.060 (0.003, 0.228)

 

 Peninsular

       

  Structured REa

   

0.010 (0.002, 0.029)

0.006 (0.002, 0.009)

 

0.018 (0.002, 0.081)

  Unstructured REa

   

0.056 (0.017, 0.119)

0.064 (0.022, 0.138)

 

0.059 (0.017, 0.135)

DICb

206.4

203.8

205.3

203.2

204.5

85.7

121.2

WAICc

208.1

206.3

207.9

205.4

207.1

87.2

123.4

  1. Model I: A single sum-to-zero constraint (adjust.for.con.comp = FALSE) and a common intercept
  2. Model II: Sum-to-zero constraints for each region (adjust.for.con.comp = TRUE) and a common intercept
  3. Model III: Sum-to-zero constraint (adjust.for.con.comp = TRUE) and intercept for each region
  4. Model IVa: Split random effects and a common intercept
  5. Model IVb: Split random effects and intercept for each region
  6. Model Va: Separate analysis for Borneo region only
  7. Model Vb: Separate analysis for Peninsular region only
  8. a RE: random effects
  9. b DIC: Deviance information criterion [24]
  10. c WAIC: Watanabe information criterion [25]