Table 5. Configurations of hyperparameter values for informative priors in the Bayesian model [Eqs (11 and 12)].

Here b₀ and B₀ denote respectively the prior mean vector and precision matrix for the regression coefficients, and c₀/2 and d₀/2 denote respectively the shape parameter and scale parameter for the inverse Gamma prior on σ² (the variance of the disturbances). These latter two parameters can be respectively interpreted as indicating the amount of information, and the sum of squared errors, from c₀ pseudo-observations, for the inverse Gamma prior on σ² (the variance of the residuals) [16]. Note that (a) depicts the baseline uninformative priors used in the primary analyses, whereas (b) to (h) illustrate seven alternate priors.

Setting	(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)
b0	(0,0,0,0)	(0,0,0,2.6)	(0,0,0,2.6)	(0,0,0,2.6)	(0,0,0,0)	(0,0,0,0)	(0,0,0,0)	(0,0,0,2.6)
diag(B0)	(0,0,0,0)	(0,0,.2,.2)	(5,5,5,5)	(0,0,5,5)	(0,0,0,0)	(0,0,0,0)	(0,0,5,5)	(0,0,0,0)
c0	0.0001	0.0001	0.0001	0.0001	20	20	20	20
d0	0.0001	0.0001	0.0001	0.0001	100	5	100	100
Int.	0.00047	0.0044	-0.0027	-0.0028	0.011	0.0060	-0.64	0.0060
	(0.026)	(0.026)	(0.026)	(0.026)	(1.4)	(0.30)	(0.28)	(0.30)
X	0.00020	0.00020	0.00026	0.00026	0.00018	0.00019	0.0062	0.00019
	(0.00029)	(0.00029)	(0.00029)	(0.00029)	(0.015)	(0.0034)	(0.0033)	(0.0034)
IHE	-0.0075	-0.0073	-0.0021	-0.0021	-0.017	-0.0096	0.41	-0.0096
	(0.023)	(0.023)	(0.023)	(0.023)	(1.2)	(0.27)	(0.23)	(0.27)
LHTL	0.026	0.027	0.035	0.035	0.024	0.026	0.79	0.26
	(0.025)	(0.025)	(0.025)	(0.025)	(1.3)	(0.29)	(0.27)	(0.29)
σ2	0.0011	0.0011	0.0011	0.0011	2.9	0.14	0.17	0.14
	(0.00042)	(0.00042)	(0.00043)	(0.00043)	(0.71)	(0.035)	(0.047)	(0.045)