Table 3:

SIM1 Fit Statistic Quantiles and Median Ranks with No True Model (N = 100)

Models:		Extra Parameters			Dropped Loadings			Dropped and Extra				Dropped β Only
		M6	M8	M9	M2	M3	M4	M5	M7	M11	M12	M10
BIC
	Median	4.16	4.12	7.76	−1.90	−3.92	−2.74	−1.38	25.04	36.58	4.11	33.61
	IQR	1.06	1.43	2.29	4.36	6.10	9.13	5.25	13.81	21.37	1.73	17.55
	Median Rank	6	5	8	3	2	2	3	9	10	6	10
HBIC
	Median	2.32	2.28	4.09	−0.06	−0.24	2.77	0.45	25.04	43.93	2.27	37.28
	IQR	1.06	1.43	2.29	4.36	6.10	9.13	5.25	13.81	21.37	1.73	17.55
	Median Rank	5	4	7	3	3	6	4	9	11	5	10
IBIC
	Median	8.05	5.48	13.19	−3.20	−6.65	−7.27	0.45	22.08	25.78	6.60	28.58
	IQR	0.95	1.42	2.17	3.93	5.04	8.07	3.69	12.87	18.56	2.47	17.26
	Median Rank	7	5	8	3	2	1	4	10	10	6	10
SPBIC
	Median	1.88	2.00	3.35	0.57	0.05	2.95	−0.15	27.46	46.20	13.59	32.71
	IQR	1.03	1.35	2.37	4.44	5.94	8.75	4.76	15.70	19.28	6.75	16.44
	Median Rank	4	4	6	4	3	5	3	9	11	8	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.