Table 3.

Average mean square error (MSE) of the ability estimates for MAT and RAN under the MTIRT and the MIRT model for different testlet sizes and different testlet effect variances (${\sigma }_{\gamma }^2$).

		MAT				RAN
		MTIRT		MIRT		MTIRT		MIRT
Testlet Size	${\sigma }_{\gamma }^2$	MSE	SE	MSE	SE	MSE	SE	MSE	SE
3	0.0	0.150	0.002	0.150	0.002	0.233	0.002	0.234	0.002
	0.5	0.194	0.001	0.196	0.002	0.267	0.005	0.271	0.005
	1.0	0.230	0.002	0.241	0.002	0.296	0.004	0.309	0.003
	1.5	0.261	0.002	0.281	0.003	0.321	0.004	0.345	0.005
6	0.0	0.155	0.002	0.155	0.002	0.238	0.004	0.237	0.004
	0.5	0.229	0.003	0.243	0.003	0.297	0.005	0.317	0.006
	1.0	0.286	0.005	0.329	0.006	0.343	0.004	0.400	0.008
	1.5	0.336	0.005	0.405	0.005	0.386	0.007	0.482	0.007
9	0.0	0.161	0.002	0.161	0.002	0.242	0.003	0.242	0.003
	0.5	0.257	0.003	0.300	0.004	0.326	0.005	0.374	0.007
	1.0	0.329	0.004	0.446	0.005	0.395	0.011	0.516	0.009
	1.5	0.393	0.008	0.581	0.009	0.461	0.016	0.658	0.010

MAT, multidimensional adaptive testing; RAN, random testlet selection; MTIRT, multidimensional item response theory random effect testlet model; MIRT, multidimensional item response theory model.