Table 6.

Simulation Results: Bifactor model, Power at .05 Alpha Level

K	N	df	null model			TKL10			TKL30
			M	RMSEA (90% CI)	rej	M	RMSEA (90% CI)	rej	M	RMSEA (90% CI)	rej
test statistic based on full one- and two-way marginal tables (M2)
2	750	75	74.4	.006 (.000,.019)	.049	77.6	.007 (.000,.020)	.070	104.6	.022 (.010,.032)	.694
	1500	75	74.7	.004 (.000,.013)	.044	77.7	.005 (.000,.015)	.087	105.1	.016 (.007,.023)	.695
3	750	390	390.1	.004 (.000,.012)	.047	397.5	.005 (.000,.014)	.082	458.1	.015 (.007,.021)	.734
	1500	390	389.8	.003 (.000,.009)	.039	406.5	.005 (.000,.011)	.133	529.0	.015 (.012,.019)	.996
4	750	915	888.7	.002 (.000,.008)	.009	901.1	.002 (.000,.009)	.020	974.0	.009 (.000,.014)	.383
	1500	915	891.2	.001 (.000,.006)	.010	908.6	.002 (.000,.007)	.046	1061.2	.010 (.007,.013)	.938
5	750	1650	1601.5	.001 (.000,.006)	.008	1614.3	.001 (.000,.007)	.008	1698.1	.006 (.000,.011)	.203
	1500	1650	1604.8	.001 (.000,.004)	.007	1625.1	.001 (.000,.006)	.018	1796.8	.007 (.004,.010)	.783
test statistic based on reduced one- and two-way marginal tables ( $M_2^{\ast }$)
3	750	60	59.4	.006 (.000,.021)	.052	64.3	.009 (.000,.024)	.111	106.8	.032 (.020,.042)	.941
	1500	60	59.4	.004 (.000,.014)	.042	70.3	.009 (.000,.019)	.220	153.8	.032 (.025,.038)	.999
4	750	45	45.2	.007 (.000,.023)	.059	50.2	.011 (.000,.026)	.129	84.3	.033 (.020,.045)	.925
	1500	45	45.1	.005 (.000,.015)	.042	56.2	.011 (.000,.022)	.303	121.6	.033 (.025,.041)	.996
5	750	30	29.8	.006 (.000,.024)	.055	33.3	.011 (.000,.030)	.125	60.4	.035 (.018,.050)	.872
	1500	30	30.1	.004 (.000,.017)	.047	37.1	.011 (.000,.024)	.237	93.0	.037 (.027,.047)	.997

Notes. K is the number of categories. N is the sample size. The reference distribution of M₂ and $M_2^{\ast }$ statistics is central chi-square with df degrees of freedom. Note that M₂ is equivalent to $M_2^{\ast }$ when K is 2. Means are reported under M and the empirical rejection rates at alpha level of .05 are shown under column heading “rej.”