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. Author manuscript; available in PMC: 2010 Jun 1.

Published in final edited form as: J Am Stat Assoc. 2009 Jun 1;104(486):429–438. doi: 10.1198/016214508000000904

Table 1.

Models under consideration

	Settings
Models	B_i	Prior for B_i	R_i11	$Σ_{i, 22}^{*}$
M₁	B_i = 0	-	Unconstrained	Unconstrained
M₂	B_i = 0	-	R_i,11 = R₁₁	$Σ_{i, 22}^{} = Σ_{22}^{}$
M₃	B_i = 0	-	R_i,11 = I_T×T	$Σ_{i, 22}^{} = diag (σ_{i 1}^{}, \dots, σ_{i T}^{2})$
M₄	B_i ≠ 0	Hierarchical prior	Unconstrained	Unconstrained
M₅	B_i ≠ 0	Hierarchical prior	R_i,11 = R₁₁	$Σ_{i, 22}^{} = Σ_{22}^{}$
M₆	B_i ≠ 0	Hierarchical prior	R_i,11 = I_T×T	$Σ_{i, 22}^{} = diag (σ_{i 1}^{}, \dots, σ_{i T}^{2})$
M₇	B_i ≠ 0	Normal prior^*	Unconstrained	Unconstrained
M₈	B_i ≠ 0	Normal prior^*	R_i,11 = R₁₁	$Σ_{i, 22}^{} = Σ_{22}^{}$
M₉	B_i ≠ 0	Normal prior^*	R_i,11 = I_T×T	$Σ_{i, 22}^{} = diag (σ_{i 1}^{}, \dots, σ_{i T}^{2})$

^*

The normal prior is the fractional prior based on (8) with δ_i = 1.