Table 7.

Integrating the specific dimensions out of the summed score likelihoods

Multiply Cluster 1’s Summed Score Likelihoods by W1(ξ1)
	Quadrature Grid for (η, ξ1)
η	−2	−2	−2	···	0	···	2	2	2
ξ1	−2	−1	0	···	0	···	0	1	2
$L^1(0\mid \eta ,{\xi }_1)W_1({\xi }_1)=L_2^1(0\mid \eta ,{\xi }_1)W_1({\xi }_1)$	.054	.237	.371	···	.190	···	.011	.001	.000
$L^1(1\mid \eta ,{\xi }_1)W_1({\xi }_1)=L_2^1(1\mid \eta ,{\xi }_1)W_1({\xi }_1)$	.001	.007	.031	···	.174	···	.114	.032	.003
$L^1(2\mid \eta ,{\xi }_1)W_1({\xi }_1)=L_2^1(2\mid \eta ,{\xi }_1)W_1({\xi }_1)$	.000	.000	.001	···	.038	···	.277	.211	.052

Summing over ξ1, Leaving Cluster 1’s Summed Score Likelihoods as Functions of η Only
	η
	−2	−1	0	1	2
L1(0|η) = Σξ1L1(0|η, ξ1)W1(ξ1)	.891	.728	.469	.212	.062
L1(1|η) = Σξ1L1(1|η, ξ1)W1(ξ1)	.103	.235	.382	.411	.288
L1(2|η) = Σξ1L1(2|η, ξ1)W1(ξ1)	.006	.037	.148	.377	.649

Multiply Cluster 2’s Summed Score Likelihoods by W2(ξ2)
	Quadrature Grid for (η, ξ2)
η	−2	−2	−2	···	0	···	2	2	2
ξ2	−2	−1	0	···	0	···	0	1	2
$L^2(0\mid \eta ,{\xi }_2)W_2({\xi }_2)=L_2^2(0\mid \eta ,{\xi }_2)W_2({\xi }_2)$	.052	.217	.311	···	.100	···	.006	.001	.000
$L^2(1\mid \eta ,{\xi }_2)W_2({\xi }_2)=L_2^2(1\mid \eta ,{\xi }_2)W_2({\xi }_2)$	.003	.027	.086	···	.203	···	.086	.027	.003
$L^2(2\mid \eta ,{\xi }_2)W_2({\xi }_2)=L_2^2(2\mid \eta ,{\xi }_2)W_2({\xi }_2)$	.000	.001	.006	···	.100	···	.311	.217	.052

Summing over ξ2, Leaving Cluster 2’s Summed Score Likelihoods as Functions of η Only
	η
	−2	−1	0	1	2
L2(0|η) = Σξ2L2(0|η, ξ2)W2(ξ2)	.742	.519	.277	.106	.028
L2(1|η) = Σξ2L2(1|η, ξ2)W2(ξ2)	.230	.375	.446	.375	.230
L2(2|η) = Σξ2L2(2|η, ξ2)W2(ξ2)	.028	.106	.277	.519	.742

Multiply Cluster 3’s Summed Score Likelihoods by W3(ξ3)
	Quadrature Grid for (η, ξ3)
η	−2	−2	−2	···	0	···	2	2	2
ξ3	−2	−1	0	···	0	···	0	1	2
$L^3(0\mid \eta ,{\xi }_3)W_3({\xi }_3)=L_2^3(0\mid \eta ,{\xi }_3)W_3({\xi }_3)$	.050	.189	.190	···	.038	···	.003	.000	.000
$L^3(1\mid \eta ,{\xi }_3)W_3({\xi }_3)=L_2^3(1\mid \eta ,{\xi }_3)W_3({\xi }_3)$	.004	.052	.174	···	.174	···	.062	.013	.001
$L^3(2\mid \eta ,{\xi }_3)W_3({\xi }_3)=L_2^3(2\mid \eta ,{\xi }_3)W_3({\xi }_3)$	.000	.003	.038	···	.190	···	.337	.231	.054

Summing over ξ3, Leaving Cluster 1’s Summed Score Likelihoods as Functions of η Only
	η
	−2	−1	0	1	2
L3(0|η) = Σξ3L3(0|η, ξ3)W3(ξ3)	.469	.302	.166	.077	.029
L3(1|η) = Σξ3L3(1|η, ξ3)W3(ξ3)	.364	.396	.364	.285	.192
L3(2|η) = Σξ3L3(2|η, ξ3)W3(ξ3)	.166	.302	.469	.638	.779