Do differences in the administrative structure of populations confound comparisons of geographic health inequalities?

Table 2 Summary of the Gini coefficient and mean region size models and results

			Parameter Estimates
Model #	Description	Equation for within country variation	β ₀	β ₁	β ₂ (95% CrI)	β ₃ (95% CrI)	DIC
Baseline random model
1	Random	σ _u(j)~ U(0,1)	-0.17	-	-	-	5605
Gini coefficient models
2	Log	$\log (σ_{u (j)}) ~ N (β_{1} + β_{2} G_{j}, σ_{r}^{2})$	-0.18*	-2.71*	1.14 (-0.2 2.37)	-	5601
3	Log (deterministic)	log (σ _u(j)) ~ N(β ₁ + β ₂ G _j, 0.0001)	-0.19*	-2.74*	1.28* (0.44 2.11)	-	5600
4	Linear	$σ_{u (j)} ~ N (β_{1} + β_{2} G_{j}, σ_{r}^{2})$ , σ _u(j)> 0.0001	-0.18*	0.06*	0.11 (-0.02 0.22)	-	5601
5	Linear (deterministic)	σ _u(j)~ N(β ₁ + β ₂ G _j, 0.0001), σ _u(j)> 0.0001	-0.19*	0.06*	0.12* (0.02 0.22)	-	5600
Mean region size models						(Million inhabitants)
6	Log	$\log (σ_{u (j)}) ~ N (β_{1} + β_{3} R_{j}, σ_{r}^{2})$	-0.18*	-2.43*	-	0.19 (-0.04 0.42)	5601
7	Log (deterministic)	log (σ _u(j)) ~ N(β ₁ + β ₃ R _j, 0.0001)	-0.18	-2.40*	-	0.18* (0.05 0.32)	5601
8	Linear	$σ_{u (j)} ~ N (β_{1} + β_{3} R_{j}, σ_{r}^{2})$ , σ _u(j)> 0.0001	-0.14	0.09*	-	0.02 (-0.00 0.05)	5602
9	Linear (deterministic)	σ _u(j)~ N(β ₁ + β ₃ R _j, 0.0001), σ _u(j)> 0.0001	-0.22*	0.09*	-	0.02* (0.00 0.04)	5600
Combined Gini coefficient and mean region size models						(Million inhabitants)
10	Log	$\log (σ_{u (j)}) ~ N (β_{1} + β_{2} G_{j} + β_{3} R_{j}, σ_{r}^{2})$	-0.19	-2.70*	0.85 (-0.57 2.17)	0.14 (-0.10 0.38)	5601
11	Linear	$σ_{u (j)} ~ N (β_{1} + β_{2} G_{j} + β_{3} R_{j}, σ_{r}^{2})$ , σ _u(j)> 0.0001	-0.16*	0.06*	0.09 (-0.06 0.21)	0.01 (-0.01 0.04)	5601

Parameters marked * have 95% posterior credible intervals which do not include zero. Values quoted are the medians of the posterior distributions. The parameter β ₁ is the constant in the equations listed in the third column. The parameter β ₃ has been rescaled to millions of inhabitants for clarity.

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