Table 1:

Statistical simulation results across scenarios. Entries show MSE, coverage (%), and CI length for treatment $\left(\delta \right)$ and correlation parameters ($\alpha$’s) under ngee+FG, by second-order cluster size $K$.

Second-order cluster size K
	20	40	60	80
Simple exchangeable
MSE
$\delta$	4.3 × 10−2	2.2 × 10−2	1.5 × 10−2	1.1 × 10−2
${\alpha }_1$	4.7 × 10−4	2.5 × 10−4	1.7 × 10−4	1.3 × 10−4
Coverage (%)
$\delta$	93.5	94.3	94.8	95.0
${\alpha }_1$	84.6	89.9	91.8	92.3
CI length
$\delta$	8.1 × 10−1	5.7 × 10−1	4.7 × 10−1	4.1 × 10−1
${\alpha }_1$	7.8 × 10−2	6.0 × 10−2	4.9 × 10−2	4.3 × 10−2
Nested exchangeable
MSE
$\delta$	1.04 × 10−2	0.56 × 10−2	0.38 × 10−2	0.28 × 10−2
${\alpha }_1$	1.72 × 10−4	0.81 × 10−4	0.62 × 10−4	0.43 × 10−4
${\alpha }_2$	1.39 × 10−4	0.64 × 10−4	0.48 × 10−4	0.34 × 10−4
Coverage (%)
$\delta$	94.1	94.4	94.7	94.6
${\alpha }_1$	90.4	93.3	93.0	94.4
${\alpha }_2$	83.9	91.6	91.5	91.5
CI length
$\delta$	0.40	0.29	0.24	0.21
${\alpha }_1$	4.8 × 10−2	3.6 × 10−2	2.9 × 10−2	2.6 × 10−2
${\alpha }_2$	4.1 × 10−2	3.1 × 10−2	2.6 × 10−2	2.3 × 10−2
Block exchangeable
MSE
$\delta$	7.1 × 10−2	3.0 × 10−2	2.0 × 10−2	1.5 × 10−2
${\alpha }_1$	9.1 × 10−4	4.4 × 10−4	3.0 × 10−4	2.2 × 10−4
${\alpha }_2$	6.5 × 10−4	3.2 × 10−4	2.2 × 10−4	1.7 × 10−4
${\alpha }_3$	1.16 × 10−3	0.52 × 10−3	0.37 × 10−3	0.30 × 10−3
Coverage (%)
$\delta$	90.9	94.0	95.1	94.7
${\alpha }_1$	83.9	88.6	89.8	90.4
${\alpha }_2$	86.0	88.1	91.1	91.7
${\alpha }_3$	91.5	91.7	93.6	94.5
CI length
$\delta$	9.5 × 10−1	6.8 × 10−1	5.5 × 10−1	4.7 × 10−1
${\alpha }_1$	9.9 × 10−2	7.3 × 10−2	6.1 × 10−2	5.3 × 10−2
${\alpha }_2$	8.8 × 10−2	6.6 × 10−2	5.5 × 10−2	4.8 × 10−2
${\alpha }_3$	1.2 × 10−1	9.0 × 10−2	7.3 × 10−2	6.4 × 10−2