Table 5.

Examples of Response Patterns That Favor the Unidimensional over the Bifactor

df				65	65			9	7
Patterna	LogLU	LogLB	INDCHI	$d_{\mathit{\text{sU}}}^2$	$d_{\mathit{\text{sB}}}^2$	ωU	ωB	$d_{\mathit{\text{rU}}}^2$	$d_{\mathit{\text{rB}}}^2$	PU	PB	PN
11444 11211	−26.66	−32.73	−12.15	1774.96	1778.37	0.22	0.22	68.91	24.43	0	0	8
11444 11414	−36.91	−42.85	−11.88	3644.06	3658.99	0.16	0.16	88.16	59.23	0	0	3
11444 14423	−29.72	−35.17	−10.89	2648.96	2662.52	0.18	0.18	69.72	39.52	0	0	0
11344 11444	−32.35	−37.52	−10.34	2308.3	2305.34	0.2	0.2	78.57	50.98	0	0	−1
11444 34144	−26.33	−30.55	−8.45	1997.8	2009.76	0.21	0.21	58.71	27.68	0	0	−2
11433 14222	−22.08	−26.23	−8.3	1359.78	1371.94	0.26	0.26	46.9	31.42	0	0	1
11433 13344	−24.92	−29.04	−8.24	1631.59	1646	0.23	0.23	53.21	38.81	0	0	−3
11434 14444	−31.31	−35.33	−8.03	2640.6	2651.01	0.18	0.18	69.37	47.38	0	0	−4
11144 11111	−26.17	−30.08	−7.82	1287.47	1301.9	0.26	0.26	72.58	10.22	0	0.18	6
11344 14244	−29.33	−33.04	−7.4	2474.72	2475.69	0.19	0.19	68.9	35.34	0	0	−2
11343 31122	−20.64	−24.19	−7.1	944.23	946.37	0.31	0.31	46.2	16.56	0	0.02	3
12344 31111	−21.75	−25.28	−7.06	975.06	975.36	0.3	0.3	52.43	13.64	0	0.06	7
11444 34443	−25.64	−29.05	−6.81	1622.58	1626.69	0.24	0.23	55.7	22.95	0	0	−4
12244 11211	−21.97	−25.36	−6.78	829.58	835.17	0.33	0.33	57.48	14.07	0	0.05	7
11441 14411	−34.33	−37.71	−6.76	3573.61	3614.62	0.16	0.16	71.88	61.89	0	0	0
11422 12234	−20.85	−24.16	−6.63	1014.53	1030.97	0.3	0.3	40.04	34.05	0	0	−2
11344 42222	−22.25	−25.54	−6.56	1078.21	1078.63	0.29	0.29	51.57	10.92	0	0.14	1
44111 34132	−21.65	−24.86	−6.42	954.78	961.89	0.31	0.31	45.25	31.33	0	0	−2
11441 12112	−26.76	−29.96	−6.42	1850.86	1883.85	0.22	0.22	52.49	42.05	0	0	4
11422 21241	−24.88	−28.08	−6.42	1371.69	1378.43	0.26	0.26	47.14	44.47	0	0	0
44111 21221	−16.77	−19.95	−6.35	604.39	615.46	0.39	0.38	29.26	19.14	0	0.01	3
44121 41111	−21.82	−25	−6.35	1061.32	1071.79	0.29	0.29	41.81	38.84	0	0	4
11421 11141	−26.53	−29.7	−6.33	1631.72	1644.38	0.23	0.23	49.2	50.06	0	0	1
11243 12111	−20.26	−23.42	−6.32	819.29	818.55	0.33	0.33	48.91	6.74	0	0.46	5
11411 11244	−25.43	−28.5	−6.14	1386.98	1395.96	0.25	0.25	51.26	38.95	0	0	−4
11422 11211	−15.68	−18.73	−6.1	395.55	403.69	0.48	0.47	25.46	21.17	0	0	4
11342 21111	−20.18	−23.2	−6.03	824.14	828.3	0.33	0.33	41.83	16.53	0	0.02	5
11423 42122	−20.98	−23.96	−5.97	929.52	938.03	0.31	0.31	40.46	30.4	0	0	0
12244 22111	−19.73	−22.67	−5.89	685.77	688.89	0.36	0.36	48.96	5.67	0	0.58	6
11414 14111	−32.47	−35.4	−5.86	2557.28	2570.72	0.19	0.19	65.88	56.58	0	0	3

Note: df is degrees of freedom for distance measures; LogL_U is the log-likelihood under the unidimensional model; LogL_B is the log-likelihood under the bifactor model; INDCHI is individual contribution to chi-square; d_sU is “implausibility” distance in unidimensional model; d_sB is “implausibility” distance in bifactor model; ω_U is case weight based on d_sU in unidimensional model; ω_B is case weight based on d_sB in bifactor model; d_rU is “unmodelability” distance in unidimensional model; d_rB is “unmodelability” distance in bifactor model; P_U and P_B are significance levels of d_rU and d_rB respectively; PN is the difference between scores based on positively-worded items and negatively-worded items.

^aThe first five items (1, 2, 4, 6, 7) are positively worded, and the second five items (3, 5, 8, 9, 10) are the negatively worded.