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

Table 1 Prior distributions used for parameters in Sensitivity analysis

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)
β_j;j = 1,…,7	CAR(1/Ƭ_βj,R)	β_j;j = 1,…,7	N(0,1/ Ƭ_βj)	β_j;j = 1,…,7	N(0,σ²_βj)	β_j;j = 1,…,7	N(0,1/ Ƭ_βj)	β_j;j = 1,…,7	N(0,1/ Ƭ_βj)
U_i;i = 1,…,N	N(α,1/Ƭ_U)	U_i;i = 1,…,N	N(α,1/ Ƭ_U)	U_i;i = 1,…,N	N(α,σ²_U)	U_i;i = 1,…,N	N(α,1/ Ƭ_U)	U_i;i = 1,…,N	N(α,1/ Ƭ_U)
S_i;i = 1,…,N	CAR(1/Ƭ_S,R)	S_i;i = 1,…,N	CAR(1/Ƭ_S,R)	S_i;i = 1,…,N	CAR((σ²_S,R)	S_i;i = 1,…,N	CAR(1/Ƭ_S,R)	S_i;i = 1,…,N	CAR(1/Ƭ_S,R)
Ƭ_βj	Ga(1,0.01)	Ƭ_βj	Ga(1,0.01)	σ_βj	U(0.01,5)	Ƭ_βj	Ga(1,0.01)	Ƭ_βj	Ga(1,0.01)
Ƭ_U	Ga(1,0.01)	Ƭ_U	Ga(1,0.01)	σ_U	U(0.01,5)	σ_U	N(0,0.0625)I(0,)	log(σ_U)	N(0,4)
Ƭ_S	Ga(1,0.01)	Ƭ_S	Ga(1,0.01)	σ_S	U(0.01,5)	Ƭ_S	Ga(1,0.01)	Ƭ_S	Ga(1,0.01)

α = intercept, j = covariates 1 to 7, β_j = vector of coefficients for covariates 1 to 7, i = Local Government Areas (LGAs) 1 to 71, U_i = uncorrelated residual error for LGAs 1 to 71, S_i = correlated residual error for LGAs 1 to 71, Ƭ_βj = vector of precisions for covariate coefficients, Ƭ_U = vector of precisions for uncorrelated residual error, Ƭ_S = vector of precisions for correlated residual error, σ_βj = vector of standard deviations for covariate coefficients, σ_U = vector of standard deviations for uncorrelated residual error, σ_S = 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.

ISSN: 1476-072X