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Table 1 Prior distributions used for parameters in Sensitivity analysis

From: Missing in space: an evaluation of imputation methods for missing data in spatial analysis of risk factors for type II diabetes

Parameter Model 1 Parameter Model 2 Parameter Model 3 Parameter Model 4 Parameter Model 5
α N(0,0.01) α N(0,0.01) α N(0,0.01) α N(0,0.01) α N(0,0.01)
βj;j = 1,…,7 CAR(1/Ƭβj,R) βj;j = 1,…,7 N(0,1/ Ƭβj) βj;j = 1,…,7 N(0,σ2βj) βj;j = 1,…,7 N(0,1/ Ƭβj) βj;j = 1,…,7 N(0,1/ Ƭβj)
Ui;i = 1,…,N N(α,1/ƬU) Ui;i = 1,…,N N(α,1/ ƬU) Ui;i = 1,…,N N(α,σ2U) Ui;i = 1,…,N N(α,1/ ƬU) Ui;i = 1,…,N N(α,1/ ƬU)
Si;i = 1,…,N CAR(1/ƬS,R) Si;i = 1,…,N CAR(1/ƬS,R) Si;i = 1,…,N CAR((σ2S,R) Si;i = 1,…,N CAR(1/ƬS,R) Si;i = 1,…,N CAR(1/ƬS,R)
Ƭβj Ga(1,0.01) Ƭβj Ga(1,0.01) σβj U(0.01,5) Ƭβj Ga(1,0.01) Ƭβj Ga(1,0.01)
ƬU Ga(1,0.01) ƬU Ga(1,0.01) σU U(0.01,5) σU N(0,0.0625)I(0,) log(σU) N(0,4)
ƬS Ga(1,0.01) ƬS Ga(1,0.01) σS U(0.01,5) ƬS Ga(1,0.01) ƬS Ga(1,0.01)
  1. α = intercept, j = covariates 1 to 7, βj = vector of coefficients for covariates 1 to 7, i = Local Government Areas (LGAs) 1 to 71, Ui = uncorrelated residual error for LGAs 1 to 71, Si = correlated residual error for LGAs 1 to 71, Ƭβj = vector of precisions for covariate coefficients, ƬU = vector of precisions for uncorrelated residual error, ƬS = vector of precisions for correlated residual error, σβj = vector of standard deviations for covariate coefficients, σU = vector of standard deviations for uncorrelated residual error, σS = vector of standard deviations for correlated residual error, Ga = Gamma distribution, U = Uniform distribution, CAR = CAR normal prior centred around zero, denoted CAR(variance, adjacency neighbourhood weight matrix), R = adjacency neighbourhood weight matrix with diagonal entries equal to number of neighbours; ie. R ii  = m i .