Table 7.

Examples of Response Patterns That Favor Neither The Bifactor or Unidimensional Models

df				65	65			9	7
Patterna	LogLU	LogLB	INDCHI	$d_{\mathit{\text{sB}}}^2$	$d_{\mathit{\text{sB}}}^2$	ωU	ωB	$d_{\mathit{\text{rU}}}^2$	$d_{\mathit{\text{rB}}}^2$	PU	PB	PN
43332 34233	−9.91	−9.91	0	69.86	70.1	1	1	10.26	9.32	0.33	0.23	0
23231 12322	−13.88	−13.88	0	185.04	185.73	0.7	0.7	18.19	18.82	0.03	0.01	1
43321 21322	−12.81	−12.81	0	146.81	146.42	0.78	0.78	17.79	11.61	0.04	0.11	3
33224 21412	−18.6	−18.6	0	483.43	484.51	0.43	0.43	31.82	28.73	0	0	4
33232 22314	−16.14	−16.14	0	260.7	260.82	0.59	0.59	24.19	24.48	0	0	1
33221 21111	−9.51	−9.51	0	51.98	52.13	1	1	7.34	5.33	0.6	0.62	5
32233 32222	−9.99	−9.99	0	57.68	57.21	1	1	12.36	5.4	0.19	0.61	2
44333 33331	−12.29	−12.29	0	146.49	146.97	0.78	0.78	15.41	13.57	0.08	0.06	4
33322 33132	−9.21	−9.21	0	40.5	40.55	1	1	9.1	7.79	0.43	0.35	1
44433 33443	−10.3	−10.3	0	69.99	69.67	1	1	10.37	7.14	0.32	0.41	1
43333 33312	−9.61	−9.61	0	60.8	60.94	1	1	9.56	7.43	0.39	0.39	4
44334 34224	−12.08	−12.08	0	117.66	117.92	0.87	0.87	13.56	13.17	0.14	0.07	3
22321 23222	−9.41	−9.41	0	62.48	62.4	1	1	9.4	6.68	0.4	0.46	−1
33332 22332	−9.25	−9.25	0	44.18	44.44	1	1	8.47	8.72	0.49	0.27	2
23322 13121	−11.69	−11.69	0	117.78	117.57	0.87	0.87	14	13.12	0.12	0.07	4
32321 21311	−11.85	−11.85	0	112.26	112.64	0.89	0.89	13.29	13.2	0.15	0.07	3
23221 21112	−10.06	−10.06	0	68.31	68.58	1	1	8.06	8.35	0.53	0.3	3
13321 21111	−13.06	−13.06	0	147.07	147.97	0.78	0.78	14.65	14.81	0.1	0.04	4
34434 43233	−10.51	−10.51	0	85.3	85.75	1	1	10.18	10.15	0.34	0.18	3
33432 22422	−11.57	−11.57	0	117.19	117.48	0.88	0.87	14.31	14.06	0.11	0.05	3
43332 32224	−12.24	−12.24	0	118.63	118.91	0.87	0.87	15.21	15.28	0.09	0.03	2
43343 32433	−11.72	−11.72	0	101.73	101.8	0.94	0.94	14.42	13.42	0.11	0.06	2
14322 22312	−17.67	−17.67	0	391.62	392.11	0.48	0.48	27.42	27.82	0	0	2
33211 43133	−15.96	−15.96	0	288.96	288.7	0.56	0.56	31.24	14.33	0	0.05	−4
22211 21311	−9.84	−9.84	0	56.59	56.51	1	1	7.89	6.28	0.55	0.51	0
34334 34432	−12.86	−12.86	0	171.37	172	0.72	0.72	15.62	15.8	0.08	0.03	1
34433 44441	−20.6	−20.6	0	628.82	629.1	0.38	0.38	33.68	33.34	0	0	0
44444 41443	−17.76	−17.76	0	381.89	382.12	0.48	0.48	28.33	27.17	0	0	4
43344 43333	−9.57	−9.57	0	55.2	54.87	1	1	8.72	4.45	0.46	0.73	2
34333 33232	−8.71	−8.71	0	38.19	38.35	1	1	7.09	6.81	0.63	0.45	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.