Table 3:

Comparisons of models to assess measurement invariance of the unidimensional DQ, SUD, and EXT models.

	# Parameters	BIC	Difference	CFI	Difference
Delinquency Model
Unconstrained (ref)	144	1,660,689	-----	0.954	-----
Constrain a, b	34	1,660,051	−638	0.965	0.011
Constrain a, b, σ2	23	1,659,969	−720	0.973	0.019
Constrain a, b, x̅	23	1,660,397	−292	0.952	−0.002
Constrain a, b, x̅, σ2	12	1,661,023	+334	0.961	0.007
SUD Model
Unconstrained (ref)	144	1,268,727	-----	0.985	-----
Constrain a, b	34	1,268,001	−726	0.984	−0.001
Constrain a, b, σ2	23	1,267,905	−822	0.987	0.002
Constrain a, b, x̅	23	1,268,126	−601	0.970	−0.015
Constrain a, b, x̅, σ2	12	1,268,529	−198	0.974	−0.011
Externalizing Model
Unconstrained (ref)	288	1,874,060	-------	0.916	-------
Constrain a, b	46	1,872,550	−1,510	0.938	0.022
Constrain a, b, σ2	35	1,872,456	−1,604	0.946	0.030
Constrain a, b, x̅	35	1,873,226	−834	0.929	0.013
Constrain a, b, x̅, σ2	24	1,873,745	−315	0.939	0.023

Notes: a=Item discrimination coefficient, b=threshold, x̅=latent factor mean, σ²⁼latent factor variance.