Table 5.

Observed and model reproduced response proportions for graded response and log-logistic models

	Response proportions
Item	0	1	2	3	4
Original data
1	.47	.21	.18	.09	.05
2	.42	.20	.21	.11	.06
3	.40	.21	.22	.12	.05
4	.28	.25	.28	.14	.06
5	.43	.20	.21	.10	.06
6	.35	.22	.24	.14	.06
7	.28	.25	.28	.13	.06
8	.44	.19	.20	.12	.05

		1	2	3	4	${\chi }^2$
Reproduced from GRM
1	.47	.21	.18	.09	.05	2.62
2	.42	.20	.21	.11	.06	1.69
3	.40	.21	.22	.12	.05	2.63
4	.29	.24	.28	.14	.05	20.70*
5	.43	.20	.21	.10	.05	3.17
6	.36	.21	.24	.13	.06	10.84
7	.30	.24	.28	.14	.05	18.71*
8	.45	.19	.20	.12	.04	6.29

		1	2	3	4	${\chi }^2$
Reproduced from LL
1	.47	.21	.18	.09	.04	5.92
2	.42	.20	.21	.10	.06	6.81
3	.41	.21	.22	.12	.05	5.67
4	.29	.24	.28	.14	.05	19.86*
5	.44	.20	.21	.11	.05	6.78
6	.36	.21	.24	.14	.05	8.01
7	.30	.24	.28	.13	.05	20.01*
8	.44	.19	.20	.11	.05	2.23

${}^{\ast }$ Chi-square significant alpha $=.99$.