. Author manuscript; available in PMC: 2023 Jan 23.

Published in final edited form as: Chin Engl J Educ Meas Eval. 2021 Mar;2(1):49–73.

Table 2.

Fit Statistics

Model	Loglikelihood	AIC	BIC	BIC (sample-size adjusted)	Entropy	Average latent class probabilities
Model	Loglikelihood	AIC	BIC	BIC (sample-size adjusted)	Entropy	EL_I	EL_NI
		ELA
0a	−1016055	2032261	2032941	2032702
0b	−1015516	2031322	2032637	2032176
1	−1000882	2002058	2003391	2002924	.973	.763	.764
2	−1000064	2000429	2001798	2001318	.990	.920	.922
		MATH
0a	−996717	1993576	1994220	1993994
0b	−995953	1992180	1993422	1992987
1	−981227	1962732	1963992	1963551	.977	.799	.795
2	−980623	1961533	1962829	1962375	.987	.888	.897

Note. Model 0a and 0b include only known groups of non-EL and EL students. Model 0a includes two known groups with invariant measurement, whereas 0b includes two known groups without constraints for measurement invariance. Models 1 and 2 include a known non-EL class and two latent EL classes. For one EL class, item parameters are invariant (EL_I) relative to non-EL parameters, and for the other EL class, item parameters are non-invariant (EL_NI) with the exception of an anchor item. EL status alone (Model 1) or EL status and subscale scores (Model 2) predict EL class membership. Bolded values show the best fitting model (within subject) per the relevant fit statistic.