Table 3.

Item Parameters of the Multidimensional Graded Response Model for the Simulation Design.

Item	Design
	Standard		Polytomous					Unequal $\alpha$		Two dimensions
	${\alpha }_j$	${\delta }_j$	${\alpha }_j$	${\delta }_{j1}$	${\delta }_{j2}$	${\delta }_{j3}$	${\delta }_{j4}$	${\alpha }_j$	${\delta }_j$	${\alpha }_{j1}$	${\alpha }_{j2}$	${\delta }_j$
1	1	−1.5	1	−3	−2	−1	0	0.5	−1.5	1	0	−1.5
2	1	−0.9	1	−2.4	−1.4	−0.4	0.6	2	−0.9	0	1	−0.9
3	1	−0.3	1	−1.8	−0.8	0.2	1.2	0.5	−0.3	1	0	−0.3
4	1	0.3	1	−1.2	−0.2	0.8	1.8	2	0.3	0	1	0.3
5	1	0.9	1	−0.6	0.4	1.4	2.4	0.5	0.9	1	0	0.9
6	1	1.5	1	0	1	2	3	2	1.5	0	1	1.5

Note.$\alpha$ = item discrimination, $\delta$ = item location.