Table 3.

Simulation Results: Unidimensional Model, Null Condition

K	N	reps	M2			RMSEA		rejection rates
			df	Mean	Var	Mean	(90% CI)	.150	.100	.050	.010
test statistic based on full one- and two-way marginal tables (M2)
2	750	1000	90	90.9	183.4	.006	(.000,.019)	.164	.104	.053	.016
	1500	1000	90	89.9	162.0	.004	(.000,.013)	.133	.075	.044	.008
3	750	1000	405	399.8	781.8	.003	(.000,.011)	.099	.062	.032	.009
	1500	1000	405	396.2	794.8	.002	(.000,.008)	.082	.063	.031	.005
4	750	1000	930	904.8	1857.9	.002	(.000,.008)	.055	.033	.010	.002
	1500	1000	930	903.5	1716.1	.001	(.000,.006)	.054	.034	.015	.001
5	750	1000	1665	1622.1	3380.4	.001	(.000,.007)	.042	.020	.010	.001
	1500	1000	1665	1619.6	3320.3	.001	(.000,.004)	.033	.022	.008	.000
test statistic based on reduced one- and two-way marginal tables( $M_2^{\ast }$)
3	750	1000	75	75.7	158.5	.006	(.000,.020)	.160	.106	.061	.020
	1500	1000	75	75.5	149.8	.004	(.000,.014)	.155	.103	.053	.012
4	750	1000	60	60.2	120.2	.006	(.000,.021)	.159	.106	.056	.010
	1500	1000	60	60.4	129.4	.005	(.000,.015)	.165	.117	.056	.012
5	750	1000	45	45.0	95.5	.007	(.000,.023)	.150	.105	.057	.019
	1500	1000	45	45.1	91.7	.005	(.000,.016)	.158	.106	.052	.012

Notes. K is the number of categories. N is the sample size. The number of valid (converged and stable) solutions are reported under the column heading “reps.” 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.