Table 7.

The MLEs and their standard errors and model fit indices obtained by each model under consideration for the Epilepsy data using AGQ approach with 11 quadrature points.

	MP				MPL				MPA
Fixed effects	β	SE	γ	SE	β	SE	γ	SE	β	SE	γ	SE
(Intercept)	1.83***	0.11	–	–	1.86***	0.11	–	–	1.85***	0.11	–	–
T(drug)	$-$0.34*	0.15	–	–	$-$0.31*	0.15	–	–	$-$0.32*	0.15	–	–
logCS8	1.00***	0.11	–	–	1.00***	0.11	–	–	1.00***	0.11	–	–
P4	$-$0.16**	0.05	–	–	–	–	–	–	–	–	–	–
Random effects
(Intercept)	${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$			${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$			${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$
	0.25	0.50			0.10	0.31			0.12	0.35
logCS8	${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$			${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$			${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$
	0.05	0.23			0.05	0.22			0.05	0.22
Model fit indices
$-\ell$	667.23				654.48				646.42
Complexity	6				5				5
AIC	1346.46				1318.96				1302.84
BIC	1358.93				1329.35				1313.23

	MPH				MPLH				MPAH
Fixed effects	β	SE	γ	SE	β	SE	γ	SE	β	SE	γ	SE
(Intercept)	1.89***	0.10	$-$2.39***	0.25	1.65***	0.08	$-$2.39***	0.25	1.69***	0.08	$-$2.39***	0.25
T(drug)	$-$0.28*	0.14	–	–	–	–	–	–	–	–	–	–
logCS8	0.96***	0.10	$-$0.88*	0.34	1.06***	0.12	$-$0.88*	0.34	1.02***	0.11	$-$0.88*	0.34
P4	$-$0.15**	0.06	–	–	–	–	–	–	–	–	–	–
Random effects
(Intercept)	${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$			${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$			${\sigma }_{{\tau }_{0j}}^2$	${\sigma }_{{\tau }_{0j}}$
	0.18	0.42			0.07	0.27			0.08	0.29
logCS8	${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$			${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$			${\sigma }_{{\tau }_{1j}}^2$	${\sigma }_{{\tau }_{1j}}$
	0.07	0.26			0.08	0.29			0.09	0.30
Model fit indices
$-\ell$	658.02				655.12				649.74
Complexity	8				6				6
AIC	1332.04				1322.24				1311.48
BIC	1348.66				1334.71				1323.95

Notes: *p<0.05; **p<0.01; ***p<0.001.

AIC = -2 $\times \ell$ + 2 × Complexity. BIC = -2 $\times \ell$ + Complexity $\times \log$(J).

Complexity: The number of model parameters. J: The number of clusters in the data. AIC and BIC values are calculated in line with the summary output of mixed_model function in the R package GLMMadaptive.