Table 6.

Examples of Response Patterns That Favor the Bifactor over the Unidimensional

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
11111 44444	−34.63	−24.48	20.29	991.31	985.98	0.3	0.3	80.61	3.87	0	0.79	−15
11111 44344	−32.5	−22.98	19.04	883.97	877.6	0.32	0.32	74.68	4.38	0	0.73	−14
11111 44434	−33.07	−23.94	18.26	993.87	984.27	0.3	0.3	75.54	9.08	0	0.25	−14
11111 44244	−31.91	−23.05	17.72	958.7	949.88	0.31	0.31	72.47	8.35	0	0.3	−13
11111 34444	−31.71	−23.07	17.29	888.39	879.67	0.32	0.32	71.47	3.61	0	0.82	−14
11121 43444	−30.59	−22.05	17.08	861.13	849.99	0.32	0.33	67.05	4.47	0	0.72	−13
12111 44444	−31.77	−23.29	16.97	903.9	896.5	0.32	0.32	72.88	6.58	0	0.47	−14
11111 44144	−32.86	−24.7	16.32	1220.07	1207.85	0.27	0.27	73.98	15.78	0	0.03	−12
12111 44443	−30.94	−23.11	15.64	955.39	945.87	0.31	0.31	69.34	11.23	0	0.13	−13
11111 43343	−28.53	−20.85	15.37	746.36	740.02	0.35	0.35	62.45	5.88	0	0.55	−12
12112 44443	−29.94	−22.3	15.29	911.1	903.32	0.31	0.32	64.01	13.6	0	0.06	−12
11112 44333	−27.9	−20.3	15.21	679.5	675.22	0.36	0.36	58.97	10.45	0	0.16	−11
11212 44444	−30.02	−22.7	14.63	870.98	867.97	0.32	0.32	67.29	6.11	0	0.53	−13
21111 44244	−30.2	−22.95	14.5	976.3	968.74	0.3	0.3	68.02	13.31	0	0.06	−12
11122 44333	−25.23	−18.24	14	538.45	530.29	0.41	0.41	51.88	5.84	0	0.56	−10
11111 34234	−26.75	−20.02	13.44	721.64	709.17	0.35	0.36	56.65	9.05	0	0.25	−11
11111 34333	−24.98	−18.33	13.29	514.4	505.7	0.42	0.42	52.08	5.99	0	0.54	−11
12212 44444	−26.88	−20.59	12.58	689.12	685.18	0.36	0.36	58.51	7.27	0	0.4	−12
11111 44141	−36.13	−29.86	12.54	1940.75	1930.74	0.22	0.22	76.76	38.83	0	0	−9
11113 34333	−27.23	−21.09	12.3	820.4	814.27	0.33	0.33	53.98	14.72	0	0.04	−9
11112 34423	−26.61	−20.61	11.99	757.51	749.06	0.34	0.35	53.93	14.69	0	0.04	−10
11111 24244	−27.72	−21.73	11.99	926.32	906.78	0.31	0.31	58.67	10.56	0	0.16	−11
11144 44444	−32.07	−26.1	11.93	1249.39	1254.27	0.27	0.27	72.11	3.11	0	0.87	−9
11211 44144	−29.77	−23.95	11.64	1092.2	1084.47	0.29	0.29	67.59	16.43	0	0.02	−11
12113 33444	−28.01	−22.27	11.48	936.02	927.56	0.31	0.31	55.9	16.72	0	0.02	−10
11133 44333	−25.26	−19.61	11.3	661.09	655.29	0.37	0.37	52.62	3.76	0	0.81	−8
11111 44222	−25.9	−20.26	11.29	661.69	656.81	0.37	0.37	53.58	18.83	0	0.01	−9
12111 43144	−27.5	−21.86	11.28	901.57	890.64	0.32	0.32	59.13	15.79	0	0.03	−10
22111 44244	−26.01	−20.4	11.21	671.54	667.25	0.37	0.37	57.73	11.04	0	0.14	−11
12111 34234	−24.39	−19.01	10.75	614.85	607.27	0.38	0.38	50.22	11.78	0	0.11	−10

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.