Table 4:

SIM1 Fit Statistic Quantiles and Median Ranks with No True Model (N = 500)

Models:		Extra Parameters			Dropped Loadings			Dropped and Extra				Dropped β Only
		M6	M8	M9	M2	M3	M4	M5	M7	M11	M12	M10
BIC
	Median	5.79	5.78	11.14	6.39	9.27	30.01	10.69	129.51	247.79	6.77	195.97
	IQR	1.18	1.23	2.20	9.58	12.20	19.36	12.32	33.77	49.74	3.37	41.10
	Median Rank	3	3	6	4	5	8	6	9	11	4	10
HBIC
	Median	3.95	3.94	7.46	8.23	12.95	35.52	12.52	129.51	255.15	4.94	199.65
	IQR	1.18	1.23	2.20	9.58	12.20	19.36	12.32	33.77	49.74	3.37	41.10
	Median Rank	2	2	5	5	6	8	6	9	11	3	10
IBIC
	Median	11.36	8.84	19.82	3.37	3.20	20.62	10.74	126.82	229.88	11.08	187.64
	IQR	1.14	1.12	2.15	9.31	12.02	18.76	11.61	33.33	48.66	3.20	41.04
	Median Rank	5	3	7	2	2	8	5	9	11	5	10
SPBIC
	Median	3.51	3.62	6.64	8.75	13.40	35.74	12.00	132.26	257.60	16.00	195.53
	IQR	1.18	1.16	2.19	9.33	12.26	19.56	11.92	33.66	48.43	4.69	40.75
	Median Rank	2	2	3	4	6	8	5	9	11	6	10

Note: Cells report median and interquartile range (IQR) values of the fit statistics across the simulations, with median model ranks below. Lower numbers indicate better fit.