TABLE 3.

Population-level parameter estimates based on the Bayesian hierarchical model for the motivating data set

Parameter	Posterior Median	Posterior Mean	MC SE	95% CI
Part I model parameters
β 0	−2.12	−2.10	0.42	(−2.89, −1.20)
${\sigma }_{{\beta }_0}$	0.82	0.94	0.46	(0.43, 2.15)
β 10	2.86	2.86	0.21	(2.45, 3.26)
${\sigma }_{{\beta }_{10}}$	0.20	0.26	0.27	(0.01, 0.92)
β 11	−2.05	−2.03	0.36	(−2.69, −1.26)
${\sigma }_{{\beta }_{11}}$	0.62	0.71	0.41	(0.23, 1.74)
β 2	0.01	0.01	0.09	(−0.16, 0.19)
β 3	0.09	0.09	0.07	(−0.05, 0.23)
β 4	−0.30	−0.30	0.08	(−0.45, −0.12)
Part II model parameters
α 0	0.50	0.50	0.07	(0.37, 0.65)
${\sigma }_{{\alpha }_0}$	0.12	0.14	0.07	(0.06, 0.32)
logQ0	2.99	2.99	0.10	(2.79, 3.19)
${\sigma }_{\log Q_0}$	0.19	0.22	0.11	(0.10, 0.50)
δ	3.20	3.20	0.03	(3.11, 3.24)
α 1	0.07	0.07	0.03	(0.02, 0.12)
α 2	−0.03	−0.03	0.02	(−0.08, 0.01)
α 3	−0.03	−0.03	0.02	(−0.06, 0.04)
γ 1	−0.17	−0.18	0.03	(−0.24, −0.12)
γ 2	0.06	0.05	0.02	(0.02, 0.08)
γ 3	−0.25	−0.25	0.02	(−0.29, −0.20)
σ	0.25	0.25	0.00	(0.25, 0.25)
Covariance matrix for (aki, dki, cki)
Σ[1,1]	1.25	1.32	0.26	(0.90, 1.91)
Σ[1,2]	−0.04	−0.04	0.02	(−0.07, −0.01)
Σ[1,3]	0.20	0.21	0.01	(0.18, 0.24)
Σ[2,1]	−0.04	−0.04	0.02	(−0.07, −0.01)
Σ[2,2]	0.33	0.33	0.01	(0.32, 0.35)
Σ[2,3]	0.07	0.07	0.00	(0.06, 0.08)
Σ[3,1]	0.20	0.21	0.01	(0.18, 0.24)
Σ[3,2]	0.07	0.07	0.00	(0.06, 0.08)
Σ[3,3]	0.15	0.15	0.01	(0.14, 0.16)

Note. MC SE: Monte Carlo standard error; CI: credible interval.