Table 8. Nigeria indigenous chicken data set: posterior mean (regression coefficients) and median (variance parts), $95\mathrm{\%}$ probability intervals and the conditional and marginal criteria under the four fitted models, see Section 7.

	Model 9a			Model 9b			Model 9c			Model 9d
	Estimate	$2.50\mathrm{\%}$	$97.50\mathrm{\%}$	Estimate	$2.50\mathrm{\%}$	$97.50\mathrm{\%}$	Estimate	$2.50\mathrm{\%}$	$97.50\mathrm{\%}$	Estimate	$2.50\mathrm{\%}$	$97.50\mathrm{\%}$
${\beta }_0$	0.335	0.321	0.349	0.369	0.284	0.848	0.359	0.353	0.374	0.315	0.299	0.329
${\beta }_1$	−0.008	−0.014	−0.001	−0.009	−0.018	0.000	−0.028	−0.030	−0.021	−0.029	−0.035	−0.023
${\beta }_2$	0.239	0.229	0.249	0.308	0.227	0.853	0.235	0.231	0.245	0.232	0.221	0.242
${\beta }_3$	0.031	0.027	0.034	0.046	0.028	0.223	0.031	0.030	0.032	0.030	0.028	0.031
${\delta }_{b1}$	–	–	–	–	–	–	0.003	0.001	0.009	0.003	0.000	0.009
${\delta }_{b2}$	–	–	–	–	–	–	0.002	0.001	0.007	0.002	0.000	0.007
${\delta }_{b3}$	–	–	–	–	–	–	0.002	0.001	0.007	0.002	0.000	0.007
${\delta }_{ϵ}$	–	–	–	0.051	0.048	0.054				0.060	0.055	0.064
$d11$	0.013	0.011	0.015	0.013	0.011	0.319	0.015	0.014	0.017	0.014	0.012	0.016
$d12$	0.010	0.009	0.012	0.010	0.008	0.318	0.007	0.001	0.040	0.008	−0.012	0.031
$d13$	0.001	0.000	0.001	0.000	0.000	0.098	0.005	−0.002	0.023	0.004	−0.019	0.024
$d22$	0.010	0.008	0.011	0.010	0.008	0.383	0.008	0.003	0.122	0.009	0.001	0.085
$d23$	0.002	0.001	0.002	0.002	0.001	0.123	−0.003	−0.011	0.002	−0.003	−0.069	0.002
$d33$	0.001	0.001	0.001	0.001	0.001	0.039	0.008	0.004	0.081	0.006	0.001	0.068
${\sigma }_{ϵ}$	0.001	0.001	0.001	0.000	0.000	0.001	0.002	0.002	0.002	0.001	0.001	0.001
cDIC		−19117.4			−19809.10			−19710.85			−18574.70
cWAIC		−19782.2			−20361.42			−19117.48			−20128.30
cplppd		−15242.3			−15945.86			−15414.23			−16113.33
mDIC		−16821.6			−15673.10			−17269.46			−17362.04
mWAIC		−16808.5			−15472.20			−17488.41			−17511.63
mlppd		−16665.4			−16965.43			−16765.43			−17165.43